Full text of "Addey 1977 Harmonics In Astrology An Introductory Textbook To The New Understanding Of An Old Science"

Harmonics in Astrology is one of the cornerstones upon which
the future of astrology is being built.

Astrology 76

Finally, a practical textbook is available which represents the
definitive work in this field ... I was struck by the enormous
scope of this book.

Horoscope

This book is a magnificent introduction to an astrological
viewpoint that uniquely combines the precisions of science
with the richest traditions of our discipline. As a textbook on
the harmonic technique, it starts from scratch and carefully
explains what harmonics are, how they relate to more
familiar concepts and how they can be put to work. Mr. Ad-
dey goes to great lengths to show the interpretive power of
harmonics in horoscope analysis.

A FA Bulletin

THE AUTHOR

One of the world’s leading research astrologers, JOHN AD-
DEY holds an advanced degree from the University of Cam¬
bridge, England. He is co-founder, former President and
Patron of the Astrological Association of Great Britain. Mr.
Addey is the author of two other books on astrology and
many journal articles, which, at last, have now been made
more accessible in two anthologies published in 1976.

HARMONICS IN ASTROLOGY

An Introductory Textbook
to the New Understanding of
an Old Science
By John M. Addey, M.A.

DEDICATION
HARMONICS IN ASTROLOGY
©John M. Addey, 1976
Second Printing, 1977

This book was completed in June 1975, exactly 20 years
after 1 started the work which led to its writing. During the
intervening years I have received help—all sorts of help and
often on a lavish scale—from fellow students at home and
abroad who shared, in some degree, my vision of a restored
astrology. To them, and to the ideal which inspired us, this
book is gratefully dedicated.

Published by Cambridge Circle, Limited
463 Vande Hex Road , Green Bay , Wisconsin, U.S.A.

CONTENTS

My indebtedness to others in the writing of this book, and
more particularly in the years of research of which it is the f

fruit, is so extensive that it would be quite impossible to ac- ;

knowledge all the help I have received. Some have contributed *

ideas and suggestions, some have helped me to understand
matters which were unfamiliar to me, many have devoted
countless hours to the extraction and tabulation of astrological
data. Some have been my friends and associates throughout
this work, others have been more or less birds of passage who
alighted for a time to make their contribution before flying on.

To all these, although I cannot thank them individually, I f

have made what amends I can in the Dedication.

In the production of the book itself I am indebted to
E. R. Dewey of The Foundation for the Study of Cycles for
permission to print the diagram and accompanying table in
Chapter 21, to Colin Bishop and other members of the Astro¬
logical Association’s Research Section for advice in the writing
of Appendix II, to James Buchanan and Michael Southgate
for drawing the diagrams, to Peggy Lance and Gladys Back-
mann for typing, to Marcy Emmer Graham for the cover ^

design, to Charles M. Graham for proofreading and indexing,
to Dr. Jim and Betty Williamsen for getting it onto the book- j

stands and, above all, to my wife for standing by for all
emergencies and coping so well tor so long.

For the Cambridge Circle edition of Harmonics in Astrology,
considerable editorial work has been done on the original
manuscript with a view to improving its readability and use¬
fulness as a textbook. I am indebted to Dr. Williamsen and
Mr. Graham for this work. >

J.M.A. !
March, 1976 *'
Publisher’s Note: In this second prinling minor corrections have been
made. The Navamsa example on p. 97 has been ,
changed from the original otic involving Lenin and the ,
Russian Revolution. The replacement concerns Enrico
Fermi and the atomic bomb.

PART ONE: THE GENERAL THEORY

1 What This Book Is Ahout. 3

2 IrUroducing Waves .. 11

3 More about. Waves . 18

4 Down to Work. 22

5 A Conceptual Framework for the Symbolism of Harmonics 34

6 Harmonics in the Diurnal Circle. 41

7 Harmonics in the Ecliptic Circle (1). D 1

8 Harmonics in the Ecliptic Circle (II). 60

9 Harmonics in the Aspect Circle . 67

10 Recapitulation. 83

PART TWO: PRACTICAL APPLICATIONS

11 The Navatnsa Chart . 91

12 The Fifth Harmonic Chart ..100

13 Other Harmonic Charts.114

14 New Light on Aspects . 124

15 Harmonics and Degree Areas.144
16 Harmonics in Progressions, Transits and Other Direction
Procedures... .151

PART THREE: PROBLEMS
17 Some Wave Complexes . ...
18 What Determines Phase?.. . . . .
19 Tropical or Sidereal..
20 Astrology, Harmonics and Genetics.
21 The Relevance of Other Cycle Studies . . .
22 Summing Up.-.

Appendix J

A Simple Working Plan for the Individual
Small Group of Researchers
or
243
Appendix II
Some Points Bearing on Harmonic Analysis
259

General Index
265
Index of Astrological Studies

PART ONE

THE GENERAL THEORY

WHAT THIS BOOK IS ABOUT

Throughout the twentieth century a steady revival has
been taking place in the study of astrology. At the same time
there has naturally, and quite properly, been a movement
towards the reassessment and reformulation of the old teachings.
But the traditional knowledge of this subject and the concepts
handed down to us for the expression of astrological ideas and
relationships are elaborate and do not lend themselves to any¬
thing like ‘patching up’ or piecemeal adjustment; that would
be a case of new' wine in old bottles. What was needed was
some new insight which would allow us to see better just how
astrology worked and what sort of laws and principles we were
dealing with. If such an insight could be found and if it were
to be securely based on the realities of our science, then one
could expect it to illuminate the whole field of astrology,
straightening out misconceptions, making good deficiencies and
shedding new light on problems which have long perplexed us.

It is only in the past fifteen or twenty years that this new
picture has begun to emerge and even now the new concepts,
which will certainly revolutionise the study and pave the way
for a period of new growth, are still in their infancy and are
not understood by the great majority of students.

The reason for this lack of understanding may be partly
due to the ineptitude of those presenting the new concepts but
there is a much more valid reason.

There is nothing harder than to see old and thoroughly
familiar ideas in a new and strange light or to accept that
the truths we have acquired by diligent study and tested in
practice with care may yet, whilst they contain much truth
and have a sound underlying-basis, have become distorted
or oversimplified in the course of long centuries of transmission
in good times and bad, by competent and incompetent leach-
el’s, and through epochs when man had neither the means
nor the inclination for radical research and reassessment.

No doubt some will feel that astrology is perfectly all
right as it is and needs no radical re-examination. Yet the
truth is that no science or body of knowledge can be effec¬
tively applied unless and until its constituent elements can be

clearly distinguished and defined, and this state of affairs does
not yet apply in the field of astrology. In this sense we are
all, or should be, as astrologers, engaged in the building of a
science, a science which, of course, has a practical application
as an art. But what are the “stones” with which this science
is to be built? This is an important question, for before any
science can be truly unfolded, so as to realise its full poten¬
tialities, it must first be reduced to its fundamental concepts,
to the simple units of which it is really composed. This is ab¬
solutely vital. A man who tries to build up a science without
first finding the real units with which it is to be built is like
a man who must try to build a house out of the rubble from
other buildings. Every time he picks up a brick he Finds part
of another brick sticking to it, and probably part of the origi¬
nal brick missing as well. The pieces are the wrong shape and
mixed up with other, non-essential elements. They are not
flexible enough; they help him but they hinder him at the
same time.

One can find plenty of examples of this in the history of
science. Until the true basis of a science is found nothing
quite “fits” and each new discovery only raises fresh problems.
Once it is found everything falls into place and each new dis¬
covery confirms what is already known. 1

Because I hope that this book will be read by those whose
knowledge of astrology is not extensive, I am reluctant at this
stage to enter upon the discussion of details. Yet those who
know astrology well will acknowledge, if they are perceptive
and honest, that our present “building materials” are uncer¬
tain and ill-defined. There are disputes (and they cut deep)
about the “right” Zodiac to be used; there are pronounced
differences between the Eastern and Western traditions which
are tactfully ignored. The houses are a notorious battleground
of disagreement; quite apart from the rival systems there
are divergent views about cusps as boundaries or centres of
houses, even about the correct number of houses!

On the face of it, aspects would at least seem to be defi¬
nite enough but they are not really so. Even putting aside the
important question of “minor” aspects and glossing over the
problem of “orbs” (for which we can do no better than pro¬
pound quite arbitrary rules which seem “about right”), we
are still left with the whole difficulty of interpreting aspects.

Our rough and ready division into “good or bad” (or “hard
or soft” or “harmonious or inharmonious”) is really only ser¬
viceable for as long as one does not look too closely at it. In
reality, just as each sign is not simply “good” or “bad” but
embodies a definite principle, so too does each aspect embody
a definite principle which can operate to our advantage (even
the square) or disadvantage (even the trine). These principles
are in need of clear delineation. One could go on and take
each and every factor in use in present-day astrology and
show it to be surrounded by a host of uncertainties.

Of course, those who practice astrology must make up
their minds how they are going to deal with these uncertain¬
ties. They must, and do, adopt whatever plan of practical
procedure seems best and most sensible to them. One admires
them for this and must be grateful that there are those who,
despite the difficulties, usually manage to produce something
useful out of this rather patchwont science.

Still, there is a time for taking stock of our deficiencies.
The very fact that the same problems have been debated in
the same inconclusive terms for three-quarters of a century can
only mean that the issues are not clearly seen, and that the
real criteria have not been laid bare so that the answers, or
the keys to the answers, are self-evident to all.

What is needed is a vision of the underlying realities of
our science in the light of which astrological concepts can be
co-ordinated, simplified and unified. Now at last we appear to be
in sight of such a vision. And it is not one that has been de¬
vised by speculation or armchair theorising. Rather, it has
emerged from long and painstaking study of astrological data so that
the truth has emerged to force itself, unexpected and even at
first and in some ways scarcely recognisable, upon our under¬
standing.

The picture that has so emerged is one of the harmonics ,
that is, the rhythms and sub-rhythms of cosmic periods, which
can be demonstrated to provide the basis of all astrological
doctrine both ancient and modern. It is a picture, furthermore,
which can be seen to be in harmony not only with the purest
traditions of Western (and, indeed, Oriental) philosophy, but
also with the most illuminating discoveries of modern science.

and especially with present-day studies of biological and other
rhythms in man and nature.

This book attempts to explain as simply as possible the
new picture which has emerged, or is emerging, to give illus¬
trative examples of the scientific results on which it is based,
to point to some of the ways in which a revision of traditional
ideas is implied, and to suggest some of the applications (im¬
mediate and potential) in terms of practical horoscopy which
the new knowledge affords.

Above all, perhaps, since we are dealing with a develop¬
ing field of research, I have tried to convey the sort of infor¬
mation and feeling for the subject which will allow students
who are so inclined to pursue researches of their own, and en¬
able them to think about astrological problems for themselves
in the light of the emerging concepts. I have also drawn at¬
tention to some of the long-standing problems in astrology to
which the new ideas seem to yield, or to promise, solutions.

Two warnings: First, I am always conscious of the fact
that there is a type of student — often possessed of a percep¬
tive mind in other respects — who is frightened to death by
the sight of what he conceives to be scientific graphs and dia¬
grams, and who is convinced that if the whole thing depends
on mathematics then he might as well give up straight away.

Now it so happens that not one person in twenty who
reads this book will fit more firmly into this category than
does the author. This is literally true and, indeed, I ought
perhaps to begin the book with an apology to experienced
mathematicians and statisticians for my very naive and elemen¬
tary approach to this aspect of the work, and my indifferent
grasp of matters which will seem to them important. From the
outset I have had to struggle to understand my own work in
mathematical terms and if I had not had the help and guid¬
ance of able mathematicians and scientists, I should not have
been able to unravel the problems involved. Fortunately, the
issues dealt with do not really depend upon any but the very
simplest arithmetical processes, and by dint of asking myself
questions, finding out the answers and then drawing diagrams
of what my own results and those of others told me, I have
been able to arrive at a reasonably coherent picture.

I mention this partly to reassure those who are like my¬
self, that it can be done and that they may in fact benefit
from having a teacher who fully shares their own difficulties,
and partly to emphasise that the plurality of diagrams which
follow are designed to help and should be regarded as friends
and not enemies. Similarly, my primary purpose in the book
is not the detailed scientific justification of harmonics in astrol¬
ogy (this is something which I am not scientifically qualified
to attempt and in any case they are now making their own
way in life and providing their own justification in practice),
but simply to explain the subject as well as I can to those
who now wish to understand it better. The relative lack of
anything like mathematical or astronomical finesse is not of great
consequence from this point of view. The broad idea of har¬
monics is very simple and, as I have already had the oppor¬
tunity to observe, it is more important to develop a feeling for
the broad perspective than to be an expert in the mathematics
of the subject. These, indeed, are essential to future develop¬
ment but their lack is not an impediment to an understanding
of the general theory and practice.

My second warning is addressed to all: make no mistake, you
will not be able to read through this book and feel that you
understand its implications straight away. Again and again you
will be able to understand the explanations (I hope) at their
face value but you will need time to digest their significance.
This will probably apply even more — not less — to those who
are accustomed to assimilating scientific data (and this is where
the student who is better at looking below the surface of
things comes into his own). The problem is not one of mathe¬
matics or physics or the like though some may see it in those
terms at first. Basically, it is one of the dynamics of number
symbolism. Be content to go slowly if necessary; be willing to
put the book down, even put it away, for a time and think
about what it is telling you. Let the new ideas sink in and
then return to tackle the next chapter.

It is important to emphasise that this is an introductory
textbook. There are aspects of the subject which I have not
attempted to deal with and there are others where, in groping
for answers to some of the problems raised, I realise that I

have not always been very lucid or consistent. I have even
made suggestions in some parts of the book which are incom¬
patible—or may at first seem so—with suggestions put forward
in other parts. 1 make no apology for these anomalies; they
are part of the process of exploring the new concepts.

Those students who are already familiar with astrology
will constantly feel that they want to translate the new way of
looking at things into the old familiar terms. They will find
that this is not always easy or possible, though where it can
be done I have given some help. It is better to learn to think
harmonically.

Finally, what kind of student will benefit most from this
book?

It is true that those who persevere will find that they
acquire techniques and insights which are eminently applic¬
able in practical work and greatly extend their grasp of horo-
scopic symbolism, but it is also true, I believe, that the stu¬
dents who will benefit most are those who love astrology for
its own sake, who are not content with rules of thumb which
they can immediately rush to apply to the horoscope but who
desire to penetrate into the mysteries and beauties of the sub¬
ject, who want to see more clearly the real principles which
underlie astrology (including those who are interested in astro¬
logical research) and, especially, those who can suspend fof a
time their desire to crystallise their thought prematurely and
can allow the fuller picture to take shape in their minds by
degrees. Those who can adopt this approach will find that
they gradually unfold an altogether wider and deeper compre¬
hension of the subject as a whole.

I have come to the conclusion, somewhat at the last mo¬
ment, that a further passage needs to be added to this intro¬
ductory chapter.

Up to the time of the Renaissance the prevailing world¬
view was firmly based upon spiritual realities and upon a vis¬
ion of the universe as a manifest expression of an inner and
higher order of truth. But because that world view tended, in
practice, to look too exclusively at noumenal aspects of truth
and to pay too little attention to the phenomenal vrorld, there

was a reaction which rejected the spiritual (and truly rational)
basis of scientific thought in favour of a strictly empirical and
generally materialistic approach. 2

The evil consequences of this reaction no longer need re¬
statement; the results are all around us. Essentially, the effect
was to deprive all knowledge of real meaning and content, to
render it mechanistic and soulless in the sense that the quali¬
tative significance of phenomena depend upon the inner spirit¬
ual realities of which they are an expression. The good which
this movement did was to stimulate men to observe the cosmos—
the “written” Word of God — much more carefully and to
develop and cultivate, to a far higher degree than formerly,
observational methods for extracting truth from the phenome¬
nal world.

There is some tendency, now', to react again and to
equate these very valuable observational methods (including
statistical procedures) with the world view which stimulated
their development, and to think that the scientific method of
making observations is the same thing as the misinterpretation
and misapplication of the results of those observations by ma¬
terialistic minds. This is a mistake; the two things are not
inseparable and should be distinguished. To reject the most
important benefit to come out of the scientific revolution can
only lead to obscurantism and superstition, and would be as
disastrous in the long run as the earlier rejection of the spirit¬
ual basis of knowledge. The methods of making observations,
as such, are neutral; it has been the viewpoint of those who
have misinterpreted the results of observation which has caused
all the trouble. The same sort of observations can, and should,
be the starting point for spiritually orientated thought. What is
now needed is a synthesis of what was best in both movements.

Nor is it true, as is sometimes said at present, that scien¬
tific methods as such tend to ignore the individual and deal
only with people in the mass. What is true is that it is Astrol-
ogy-as-an-art which is applied in the service of people, indi¬
vidually and collectively, but the art of astrology depends
upon Astrology-as-a-science, the office and function of which is

to arrive at a dear understanding of the laws and principles
of the subject. The art and the science are interdependent in
this field as in all others.

Therefore, the purpose in using statistical procedures in
astrological studies is simply to make careful observations in
order that we can improve the knowledge of how astrology
works so that practitioners can use it more effectively. In this
book, although the author is not a trained scientist (as will
no doubt be apparent), full use has been made of statistical
studies, avoiding, as far as possible, technicalities, rejecting the
materialistic standpoint with which such studies have com¬
monly been associated in the past 300 years, but trying to
clarify the laws of astrology so that they can be applied with
greater understanding, in conformity with a spiritually orien¬
tated world-view, for the benefit of mankind both individually
and collectively.

Thus, I have drawn upon statistical evidence where this
was appropriate, I have tried to indicate something of the
philosophical context in which I believe such evidence should
be assessed, and I have shown how the results of such studies
can be applied to the individual horoscope in practice. 1 hope
this explanation will remove misunderstandings and enable the
reader to see what is being aimed at.

NOTES

1. These comments are adapted from Addey, John and Peter Roberts,

The Basis of Astrology, parts 1 & 2, Astrological Journal (Astrological
Association, London) VI (1964), nos. 3 & 4. The article also appears
in John Addey: Selected Writings, Tcmpe, Az.: American Federation of
Astrologers, 1976; also in The Harmonic Anthology, Green Bay, Wi.:
Cambridge Circle, 1976.

2. For a fuller discussion of this see my monograph. Astrology Reborn,
Green Bay, Wi.: Cambridge Circle, 1975. (Previous editions in 1971
and 1972 by Astrological Association, London.)

INTRODUCING WAVES

Throughout this book we shall be dealing with waves. It
is therefore important from the outset that the reader should
know something about waves and wave forms. Thus, Chapters
2 and 3 provide a simple guide to this subject. There are one
or two references to astrological points but these two chapters
can be read without any special regard to the astrological con¬
text in which we shall later apply this knowledge.

As a matter of fact the kind of waves we shall be dealing
with are called sine waves. There is no need to go in for
elaborate definitions. Sine waves are just those which are pro¬
duced by simple harmonic motion such as is produced by a
swinging pendulum or a tuning fork or the motion of light

There are three things we shall need to know about waves
and they are all quite easy to understand; it is largely a ques¬
tion of learning the terms used.

1. The first thing is length.

‘Long’ and ‘short’ are relative terms but it is obvious
that if wc have two waves in a given period or distance,
each of them will be longer than six waves in the same
period (Fig. 1). So it is a question of how many waves there
are in the period. The more waves there are the shorter
they will be.

Now if two waves fit exactly into a given period — they
must go exactly then they may be said to repiesent the 2nd
harmonic of that period (Fig. la), If six waves are exactly
completed in the period (Fig. lb), they represent the 6th
harmonic. If there is one wave, it may be said to be the first
harmonic and sometimes called the fundamental of that period.

Fig. 1

Actually there are two places in this chapter, and this
is one of them, where 1 have departed from accepted or
traditional usage — in this case from accepted musical ter¬
minology. If the string of a musical instrument is plucked
and allowed to vibrate along its whole length (one wave, so to
speak), this gives the fundamental note. If it is touched
exactly halfway along its length, then the two halves of the
string will vibrate separately (two waves), and it is this
which in musical terms is called the first harmonic. It is an
octave higher than the fundamental. However, it seems
better to adopt the practice of equating the number of the
harmonic with the number into which the whole length is
divided.

Thus we see that the 2nd harmonic of a period divides
it exactly into two, the 3rd divides it into three, and so on.

Now in this book we shall always be dealing with the
harmonics of a circle. This makes it easy; the period we shall
be dealing with is always the same — one complete circle
of 360°.

We illustrate some of these in Fig. 2: 2a shows the 3rd
harmonic of a circle, 2b shows the 4th, 2c the 12th.

the number by which the circle is divided and this deter¬
mines the length of the wave. The more numerous the
waves (the higher the number of the harmonic) the shorter
the waves become. Thus the 3rd harmonic of a circle has
three waves of 120° each in length; the 4th has four waves
each of 90° in length; the 12th harmonic has 12 waves
of 30 c each, and so on. There is no limit to the number
of waves one might have; for example, the 120th harmonic
has 120 waves each 3° in length.

Of course, some harmonics will give a very ‘awkward’
wave length. We have just said that the 120th harmonic
gives a wave of 3°, but the 125th, for example (which, of

course divides the circle into 125 parts) gives a wave of
2° 52.8’.

So much for the length of the wave.

2. The second thing which interests us is amplitude.

This again is easily shown (Fig. 3). The amplitude is
the amount by which the wave rises and falls above or
below the mean. The two waves in Fig. 3 have the same
length but the amplitude of the first is large, that of the

If the string of a musical instrument is plucked gently,
the amplitude of its vibration is small and it gives out a
qmet sound. If it is plucked vigorously, the amplitude of the
vibration is large and it gives out a loud sound. In other
words the amplitude of the wave represents the strength or
vigour of the phenomenon measured. Again, by way of
example, if one is measuring the action of some force which
rhythmically increases and decreases, one can express the
increase and decrease as a percentage of its average or
mean strength.

In Fig. 4 the mean is represented by 100. The wave
rises to 120 at its highest point and falls to 80 at its lowest.
So its amplitude is 20%. In this book the amplitude of the
wave is always expressed in this way.

It is easy to see the percentage rise and fall when the
mean is 100. If the mean is some other number, say 65,
we may have to do a little arithmetic to find out the
percentage rise and fall of the wave.

In Fig. 5, the mean is 65, the wave rises to 78 and falls
to 52; a rise and fall of 13. Thus we have a simple propor¬
tion sum:

13 is to 65 as ? is to 100.

13 is one fifth of 65; one fifth of 100 is 20. So the amp¬
litude of the wave in Fig. 5 is still 20%.

3. The third thing we must know about a wave is its phase.

In Figure 6, four waves are shown. They all have the
same amplitude, but they are phased differently.

For the purposes of discussing this aspect of waves, let
us adopt the terms shown in Figure 7.

We can now say that, in Figure 6, wave a is phased so
that the ascending node comes at the beginning of the
period, as drawn, the descending node conies in the middle,
the peak comes one-quarter of the way along.

In wave 6b all this is exactly reversed; the peak comes
three-quarters of the way along.

In 6c the peak falls in the middle and the trough falls,
as it were, at the edges.

In 6d the peak falls between a quarter and half way
along the wave.

Fig. 6

This is a rather cumbersome way of expressing the
phase and we shall need a simpler and more precise way
of expressing this matter. This is done as follows:

Every wave is, in a sense, a cycle or circle, so we can
treat every wave as if it were passing through 360°. This
simply means, in effect, that we treat the length of each
wave whatever its actual length may he in other respects as being
360° in extent. Thus although the 3rd harmonic of the
circle is 120° in length, we treat it, for purposes of express¬
ing the phase, as being one complete cycle or circle of 360°.

We can now re-draw Fig. 6 with this scale marked along
the bottom (Fig. 8).

0 ’ « » IJ5 IB0 Ui m JI5 J«

To describe the phase of the wave now becomes easy
because we have a scale of reference. We give the phase
angle of the wave as being the distance in degrees at which
the peak of the wave falls along our scale. Thus wave a has
a phase angle of 90° and d (which we could only express
rather vaguely before) has a phase angle of 135*.

This is the way the phase of a wave is expressed
throughout this book, and this is the second place where I
have departed from accepted usage. In mathematical par¬
lance the phase angle is a measurement related to the ascend¬
ing node. For this reason some students prefer to use the
term “peak phase” or “peak direction” when referring to
the point where the peak comes.

Of course, waves are continuous, following one after
another, so if one has a series of waves, one must have
some definite starting point for one’s phase measurement.
There is no problem here. For waves along the ecliptic
(i.e. in the Zodiac) we shall make the tropical point 0°
Aries our starting point. For waves in the diurnal circle
(houses) we shall use the Ascendant , and when considering
the harmonic distribution of one planet in relation to an¬
other (aspects) the slower moving planet will he our starting
point.

The reader now knows nearly all he needs to know about
waves. It would be a good idea for anyone who, at this point,
is not sure about any of the three factors we have described,
to go over this chapter, or its relevant parts, again.

To recapitulate, there arc three things to be understood.
The first is the length of the wave and this is determined by
the number of the harmonic: the higher the number of the
harmonic, the shorter the wave (Fig. 2). We would normally
express the length of the wave in degrees — or degrees and
minutes if necessary. Thus the 3rd harmonic is 120° in length.
But we may note that in giving the number of the harmonic
we automatically imply the length of the wave. Thus wc know
when the 8th harmonic is referred to that the circle has been
divided by eight, giving a wave of 45°.

The second is the amplitude or the amount by which the
wave rises and falls above and below the mean. In any partic¬
ular case this is expressed as a percentage of the mean.

The third is the phase which tells where the peak of the
wave comes along its length. This is expressed as a phase an¬
gle from 0° to 361)°, treating all waves as being for this pur¬
pose 360° in length.

In addition to the foregoing we have also introduced a
number of other terms: harmonic and fundamental, ascending
and descending node, peak and trough.

NOTES

1. This does not prejudge the Tropical-Sidereal issue, it is just that some
definite and agreed starting point must be adopted. Later, after the
student has mastered the basic concepts and principles, he may wish
to explore the Tropical-Sidereal issue more fully. Aspects of this issue
are discussed in Chapter 19.

MORE ABOUT WAVES

Chapter 2 has provided us with the basic concepts which
we shall need in this book and the terms for dealing with
them. But in order that the reader may understand easily
some of the issues we shall be looking at in forthcoming chap¬
ters, it will be as well to take a little longer with our prelim¬
inaries and to explore one or two other matters which are
really developments of what has been set out in the last chap¬
ter.

In Fig. 9 we have seven series of waves, They all fall be¬
tween the uprights X and Y, that is to say they all occupy
the same space and differ only in the number of waves in
each series. Line ‘A’ represents the 1st or fundamental har¬
monic of the period XY; ‘B’ represents the 2nd harmonic,
‘C’ the 3rd, ‘D’ the 4th, ‘E’ the 12th, ‘F’ the 15th and ‘G’
the 17th. Notice that in every line there is a whole number of
completed waves. They all start at the ascending node and
finish at the ascending node.

This being so we can say that the wave length in lines
B, C, D, E, F and G are all sub-harmonics of the fundamental
A, because they all fit exactly with no part of a wave left
over, into the wavelength of A.

We can also see that the wave length in line D is a sub¬
harmonic of the wave in line B. This is because there are
four waves in line D and two in line B; thus, since two will
divide into four, exactly two waves are completed in line D
for every one in line B. But notice that the wave length in
line C is not a sub-harmonic of B because two will not divide
exactly into three. For the same reason D is not a sub-har¬
monic of C, because three will not divide into four.

In the case of line E however, the wave is a sub-harmon¬
ic of B, G and D, because two, three and four will all divide
into twelve. Thus, if we look carefully we shall see that exact¬
ly six waves of line E are completed whilst one wave of line
B is being completed, four waves of E in one of line G, and
three waves of E in one of line D. This of course reflects the
fact that two, three and four are all factors of twelve.

At this point it may be as well to acknowledge that
whereas most students will find a thing of this sort perfectly
simple, there are others who, whilst fully capable of seeing
that they get the correct change when they buy a box of
matches, are yet inclined to make heavy weather of matters
such as this, even though they are just as simple.

To them I say: Do not be put off; you are probably one
of those who can see a principle as soon as it is applied in a
practical context but have difficulty with theoretical explana¬
tions. Try once more to grasp the principle involved and then
pass on. Make full use of the diagram (Fig. 9).

Fig. 9

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Now a question: Of what harmonics, B, C or D, is the
wave in line F (which has 15 waves) a sub-harmonic? Yes, it
is a sub-harmonic of the wave in line C (because three will
divide into 15) but not of B or D, because two and four will
not divide into 15 exactly. In other words, while five of the
small waves in line F are completed exactly in the space of
one wave of line C, the wave-lengths of B and D do not
measure out an exact number of waves in line F. Another
question: Of which harmonics, A, B, C, D, E and F, is the

wave of line G a sub-harmonic? Yes, it is a sub-harmonic of
the fundamental of A only, because 17 is a prime number and
has no factors except one.

For the last stage of the preliminaries, there is one more
point which should be made clear. It is a question of how
waves combine. Again and again in this book we shall find
that we arc not dealing merely with a single wave form but
with a complex or combination of wave forms. That is to say
that we shall have to combine, or study the combination of, a
given harmonic with some of its sub-harmonics.

To start with a simple example, consider Fig. 10a which
show's two waves, a fundamental and its 2nd harmonic. These
two waves may be taken to represent the action of two sep¬
arate forces. How shall we represent the result if both forces
are operating together? Of course, a mathematician would or
could deal with the problem mathematically, but for our pur¬
poses there is no need for this. We are simply going to draw
the 2nd harmonic superimposed on the fundamental.

Having drawn our waves (Fig. 10a) we first note the am¬
plitude. of the 2nd harmonic, or the amount by which it rises
above or falls below the horizontal line. We can then mark
in this amount on the fundamental. We shall do well, too, to
mark in nodes as in Fig. 10b. We can now draw in the new,
combined, formation (Fig. 10c). It is as easy as that; and
however many sub-harmonics to the fundamental we may have
to draw in, the process is the same.

Thus if we wish to combine three harmonics, as shown in
Fig. 11, we can do so in the manner shown.

Fig. 11

It may be worth mentioning that the characteristic tim¬
bre of different musical instruments arises from the way in
which the sub-harmonics of their notes combine. The same
note played on different instruments makes a different sound
because each type of instrument has its own unique construc¬
tion and this allows certain of the sub-harmonics to sound and
others not. One instrument may produce a sound wave very
much like the one at the bottom of Fig. 11, another will pro¬
duce something quite different.

We mention this not only for its interest, and because it
may help to give an added insight into this problem, but also
because the analogies between astrology and music are many.
The concept of the ‘harmony of the spheres’ is no chance
metaphor.

DOWN TO WORK

In most textbooks of astrology one is presented with a
ready-made picture; a body of knowledge and a set of rules
derived from traditional sources. In these cases the author
does not expect to have to justify his statements; if he says
that two planets are 4 in aspect’ when they arc so many de¬
grees apart and that the list of aspects is thus and thus, the
reader must take him at his word. It is, for the most part, a
case of learning a received tradition.

In this book we shall not go right back to ‘square one’
because it will be assumed that the student has a minimum
familiarity with the elementary knowledge and terms of ortho¬
dox astrology. Nevertheless this textbook differs from most
others in that we shall, step by step, examine evidence de¬
signed to show the true nature of the underlying laws and
principles. Thus we shall actually be building up a picture of
demonstrable veracity as we go along. This is necessary because
many of the traditional concepts are demonstrably false, at
least to the extent that they are extreme over-simplifications.

Again, the body of evidence of which we shall make use
has been accumulated in the course of researches carried out
over the past twenty years. We shall not observe any chrono¬
logical order in the way we present that evidence. Our job in
this book is to unfold a coherent picture and in doing this we
shall make use of whatever items in this body of evidence are
appropriate to our purpose at each step. At an early stage
(Chapter 5) we shall offer the student a simple conceptual
framework for thinking about harmonics in relation to astrol¬
ogy, but it will help us if wc first examine some examples.

When I first began to realise the harmonic basis of astro¬
logical factors in the mid-l950’s, the examples I had found
were of harmonics which divided the circle by quite high
numbers; but to begin our study now wc need simple exam¬
ples of major harmonic patterns, that is to say, those based on
divisions of the circle by low numbers. For this the work of
Michel and Francoise Gauquelin will serve us well.

For the benefit of those not familiar with the work erf
Michel Gauquelin and his wife, it should be said in passing
that Gauquelin is a French statistician and psychologist who,
with some background knowledge of astrology, set out in about
1950 to see what justification he could find, as a statistician,
for some of the traditional teachings of astrology. His work
has grow'n steadily in scope over the past twenty years and is
now, in terms of sheer magnitude, the greatest single contribu¬
tion to the modern re-examination of astrological ideas.

Besides a number of general works on the subject for the
lay reader 1 he has published all his huge collection of data
and details of his main experiments in some sixteen volumes. 2
He has often criticised astrologers for an unscientific attitude
and an easy acceptance of fallacious beliefs. He has been criti¬
cised in turn for evidently adopting a somevdiat materialistic
standpoint alien to the true nature and philosophy of astrology.
There is no doubt some truth on both sides, but it is perhaps
best to remember that no one could have achieved what he
has done without a great desire to uncover the truth and a
heroic determination to persevere in the search despite bigoted
criticism from the ranks of orthodox science and a marked re¬
luctance among many astrologers to acknowledge the full value
of his work.

His approach has been strictly empirical. No doubt some
of his criticism has been directed at what was obviously spur¬
ious in present-day astrology and was designed to publicly
affirm his rejection of this. As time has gone by, he has appar¬
ently moved steadily towards a more sympathetic rapport with
other researchers in astrology and is finding more common
ground with them. But above all whatever one may think of
his astrological viewpoint, one must acknowledge with grati¬
tude the Herculean labours he has performed in freely pro¬
viding fellow researchers everywhere with a huge reservoir of
valuable data for furthering the common enterprise.

At an early stage in his work Gauquelin came across the
work of an astrologer called Leon Lassons who had made
studies of the distribution of the various planets in the diurnal
circle (i.e., their daily rising, culmination and setting) in the

(

horoscopes of different professional groups. Lasso ns’ thesis was
that the planets traditionally associated with different activities
such as Mars for athletes or soldiers, Jupiter for actors, etc.,
tended to occupy certain parts of the diurnal circle (the houses)
much more often than other parts.

Gauquelin made a collection of the nativities of members
of different professional groups from the standard works of
reference and discovered Lassons’ thesis to be substantiated. He
then proceeded greatly to enlarge his collections and to verify
the findings on a scale which left no room for doubt.

The problem of dividing the diurnal circle for purposes of
statistical study in such a w r ay that there would be no built-in
bias in the distribution pattern is quite a complicated one.
Those desiring to satisfy themselves on this score must be re¬
ferred to Gauquelin’s own work. 3 Suffice it to say that his
work has been thoroughly scrutinised by sceptical specialists
and no flaw has ever been found in his methods in this re¬
spect.

It must be remembered that in continental countries
whence Gauquelin’s birth data were drawn, birth times are
recorded and the time of each separate birth was ascertained
from the records of the registrars of births. Thus Gauquelin
was able to calculate the position in its diurnal circle of each
planet.

For the purposes of noting the positions of the planets and
analysing their distribution in the diurnal circle Gauquelin
divided this circle first into twelve sectors, later into eighteen,
and later still into thirty-six. The admitted element of approx¬
imation in most birth records does not warrant a division of
the diurnal circle into smaller sectors than this. 4 Fig. 12
shows each of Gauquelin’s three ways of dividing the circle,
how the sectors fall and how they are numbered in his work.

We can now look at a typical example of one of Gauque¬
lin’s distribution patterns. Fig. 13a shows the distribution of
Saturn in the nativities of 3647 physicians and scientists. In
other words the names, dates and localities of birth of 3647
scientists and physicians have been culled from works of refer¬
ence, their times of birth obtained from the birth registers and
the positions of the planets tabulated for these times. The total
number of times which Saturn fell in each of the eighteen
sectors of the circle (see Fig. 12) were then counted and the
frequency plotted around the circle of what astrologers would
usually call the ‘houses’ of the chart, except that, here,
eighteen sectors are used, not twelve.

If we look at Fig. 13a we can see that there are four
bulges in the distribution pattern, representing the parts of the
diurnal circle which Saturn tended to occupy in the maps of
these scientists and physicians. One is at, and just above, the
Ascendant, one is just after the Midheaven, one is after the
planet has set, and one just after its lower culmination. It is
true that the bulges are not equal in size and, of the peaks to
which they rise, two (those near the Ascendant and Mid¬
heaven) are higher than the other two (those near setting and
lower culmination). We shall consider the reason for this short¬
ly but let us concede at present that this distribution pattern
is largely, and quite clearly, dominated by a 4th harmonic
figure, as shown in the little figure 13b. Of course, the eighteen
totals of Gauqudin's distribution have been joined up by
straight lines (in Fig. 13a), but if we can picture them joined
up by a curving line we should see something like the fourfold
wave of 13b.

This tendency of the planet or planets appropriate to a
particular profession to show a 4th harmonic distribution is a
frequent feature of Gauquelin’s results. It is such a common

feature, in fact, that at an early stage in his work, Gauquelin
was able to put together most of the distribution patterns in
his collections and show that even when many different results
were lumped together, this 4th harmonic pattern held good.
Fig. 14a show r s this particular result: the top line includes
11,000 positions of Moon, Mars, Jupiter and Saturn as dis¬
tributed in professional groups collected in France and the
bottom line shows 19,000 positions of the same planets in the
precisely corresponding professional groups as collected in Ger¬
many, Belgium, Holland and Italy. 5

In Fig. 14a the result is given as a straight-forward hori¬
zontal graph instead of round the circle as in Fig. 13. The
message is the same in either case, but the student must get
used to looking at both kinds of diagrams. We can also see in
Fig. 14 that the four waves of the 4th harmonic, with their
peaks just after the points of rising and setting, upper and
lower culminations, are superimposed upon a long 1st har¬
monic (Fig. 14b). This raises the first two peaks above the
second two.

Fig. 14

In order to ‘keep our eye in’, so to speak, with the things
we learned in the introductory chapters, let us find orit a
little more about that diagram of the distribution of Saturn in
the nativities of scientists and physicians. (Fig. 13).

At this stage the student will have to take it on trust that
it is possible by mathematical means to break down any dis¬
tribution pattern into its component harmonic elements. This
is called harmonic analysis or, after the mathematician who
devised the method, Fourier analysis. It simply involves ex¬
tracting from a distribution pattern such as wc arc dealing
with in Fig. 13 each harmonic or wave form which is present
and calculating its amplitude (how strong it is ) and its phase
(where it falls).

The Astrological Association’s Research Section has carried
out harmonic analyses of all Gauquelin’s results 6 (we shall
have fuller examples of these later). We can therefore say
exactly where the 4th harmonic falls in Fig. 13 and how
strong it is. As a matter of fact the Astrological Association,
in carrying out these analyses, kept the scientists (1095 in
number) and the physicians (2552) separate; 7 however we
can arrive at a very close estimate of the amplitude and phase
of the two sets put together. The details are as follows:

SATURN 4th HARMONIC

Amplitude Phase Angle

Physicians 9.3% 49°

Scientists 15.9% 47°

It will be seen that the phase angles are very close: 49“
and 47°, so in combining the two sets we can safely say that
the combined phase angle will be 48°. In forming an estimate
of the combined amplitude we must remember that there are
more or less twice as many physicians as scientists, so the
amplitude when the two sets arc put together will be nearer
9.3% than 15.9%. Let us call it 12% for the sake of a round
Figure.

Let us then refresh our memory'. What do we mean
when we say that in Fig. 13 the amplitude of the 4th har¬
monic is 12% and the phase is 48"? We arc dealing with 3647

Saturn positions and these are distributed through eighteen
sectors of the circle. The average for each sector will be 3647
divided by 18 or 202.6; this is the number of Saturn positions
wc should expect to find in each of the eighteen sectors if
they were evenly spread around the diurnal circle. But we
know that the 4th harmonic has an amplitude of 12%. That
is to say that there is a fourfold rhythm in operation which
alternately lifts the distribution above the mean by 12% and
then depresses it by 12%. 12% of 202.6 is 24.3, (202.6 x 12)
-=r- 100. Thus this force, whatever it is, is such that it would,
by itself, lift the distribution at the top of the wave to 202.6
plus 24.3 (or about 227 cases) and at the bottom of the wave
would produce a distribution of 202.6 minus 24.3 (or about
178 cases). This is shown in Fig. 15.

What do we mean when we say the phase angle is 48° ?
Remember that wc are dealing with the 4th harmonic and
therefore the wave is 90° of the whole circle in length. Re¬
member, _too, that we measure the phase angle from the
Ascendant 8 and that we treat every wave/or the purposes of the
phase angle as if it were a cycle of 360“. Therefore we can mea¬
sure out a quarter of the circle (90°) from the Ascendant and
mark off our scale of 360°. We can now see exactly where the
peak of the wave comes—at 48° along the scale or about 12°
of the whole circle above the Ascendant (48° -s- 4). This is
shown in Fig. 16.

The student will have understood by now that we arc
always dealing with an absolutely regular wave form, the peaks in
this case exactly 90° apart, the troughs 9(P apart, and the rise
and fall of the wave absolutely regular: 12% peaks above the
mean in the astrologers’ twelfth house, 12% in the ninth,
sixth and third houses, and 12% troughs below the mean fall
midway between these points.

But, the student will ask, if the wave is absolutely regular
why does Fig. 13 show a much higher score for Saturn posi¬
tions just above the Ascendant in comparison with the third or
sixth house peaks (Gauquelin’s sectors 16 and 11)? The an¬
swer, quite simply, is that we are not dealing with a 4th har¬
monic only.

In the particular case we have chosen for our example,
Saturn in the nativities of scientists and physicians, the har¬
monic analysis has been taken from Lhe 1st to the 18th har¬
monic . We have already indicated that, of these, the 4th
is easily the strongest. The second strongest, and probably the
only other one which could qualify as significant in in the
scientists and physicians combined , is the 3rd harmonic. Here
are the details:

SA TURj\ 3rd HARMONIC

Amplitude Phase Angle

Physicians 7.7% 1°

Scientists 6.5% 354°

Thus we can say that in the two sets put together the com¬
bined amplitude will be very roughly 7% and the phase, since
there are more than twice as many physicians as scientists,
about 359°.

Remember that we are now dealing with the 3rd har¬
monic, so to show the phase angle we shall have to stretch our
360® scale along the first 120° starting from the Ascendant, and
along this scale our 3rd harmonic wave will peak almost at
the end of this as shown in Fig. 17. Similarly, with an ampli¬
tude of 7% and a mean distribution of about 200 (actually
202.6), this harmonic by itself will alternately raise and de¬
press the total by about 14, or 7% of 200.

Fig. 17

A5C

In order to see the combined effects of these two harmon¬
ics. the 4th and 3rd, when they are operating together, we
can draw in the 3rd harmonic and then superimpose the 4th —
just as we did at the end of the last chapter. This has been
done in Fig. 18. The drawing is only an approximate one but
a comparison of the heavy line in this diagram w'ith the Sa¬
turn distribution shown in Fig. 13a will show basically why
the peaks at the Ascendant and after the M.C. are more pro¬
nounced than the other two. At the Ascendant the two har¬
monics lie very close to each other and in effect ‘'build upon’

each other; at the M.C. they are a little less close and at the
other two points the harmonics are working against each
other.

Although wc are actually dealing with two regular forces
represented by wave forms, the way in which they combine is
such as to produce an irregular result. We shall see in this
book that all astrological forces are built up along these lines.
From this it follows that the simple division of the mundane
circle into twelve sectors or houses does not lend itself to a
clear representation of what happens.

NOTES

1. For example, see his The Cosmic Clocks, From Astrology to a Modem
Science, London: Peter Owen, 1969; Astrology and Science, London: Peter
Davies, 1970; and Cosmic Influences on Human Behavior, London: Gam-
stone Press, 1974. The American publishers of these three works are,
respectively, Chicago: Henry Regnery, 1967; New York: Mayflower
Paperbacks, 1972; New York: Stein and Day, 1973.

NOTES

2. Gauquclin’s data and results have been published in 16 volumes, vis.,
Gauquclin, Michel and Francoise; Birth and Planetary Data Gathered
Since 1949 . Paris: Laboratoirc D’Etude des Relations entre Rhythms
Gosmiques et Psychophysiologiques.

a. Series A. Vol 1 Sports Champions (1970)

b. Series A, Vol. 2 Men of Science (1970)

c. Scries A, Vol. 3 Military Men (1970)

d. Series A, Vol. 4 Painters & Musicians (1970)

e. Series A. Vol. 5 Actors & Politicians (1970)

f. Series A, Vol. (> Writers & Journalists (1971)

g. Series R, Vol. 1 Heredity Experiment (1970)

h. Scries R, Vol. 2 Heredity Experiment (1970)

i. Scries B, Vol. 3 Heredity Experiment (1970)

j. Scries R, Vol. 4 Heredity Experiment (1970)

k. Scries R, Vol. 5 Heredity Experiment (1971)

l. Scries R, Vol. 6 Heredity Experiment (1971)

m. Series G, Vol. 1 Profession — Heredity (results of Scries A & B)
(1970)

n. Scries C, Vol. 2 The Mars Temperament & Sports Champions
(1973)

o. Scries C, Vol. 3 The Saturn Temperament & Men of Science
(1974)

p. Series C, Vol. 4 The Jupiter Temperament & Actors (1974)

No self-respecting university library' should be without these works.
(I.aboratoire editions show French and English text on facing pages.)

3. Full details of his method of dividing the diurnal circle are well sum¬
marised by Gauquelin in Series C, Vol. 1, cited in Note 2 above.

4. Gauquelin, Francoise, in “Terrestrial Modulations of the Daily Cycle
of Rirth,” Journal of Interdisciplinary Cycle Research , II (1971), pp. 211-
217, examines the whole question of the accuracy of registered birth-
times in the countries from which Gauquelin draws his data.

5. Gauquelin, Michel, Les Hommes et les Astres, Paris: Dcnoel, 1960,
p. 193.

6. T hese harmonic analyses are held by the Astrological Association’s Re¬
search Section. They arc, however, as yet unpublished.

7. One should indeed separate these, for research scientists and physicians
are two different creatures however much they may have in common.
It should perhaps be mentioned that these analyses were based on a
further breakdown of the totals into 36 sectors.

8. Actually, the measurement is made from the planet’s own point of
rising.

9. This analysis was based on 36 totals, not 18.

10. The question of significance will be dealt with in due course (see
Appendix II).

5 a conceptual framework

FOR THE SYMBOLISM OF HARMONICS

Having examined an actual example of harmonics in astrol¬
ogy, what we now need is some guidance as to how we are to
relate astrological symbolism to harmonics. We arc used, in
astrology, to taking as the fundamental symbolic elements, the
signs of the Zodiac, the houses of the horoscope and aspects be¬
tween planetary and other points in the chart. These all rest
upon the symbolism of relationship . 1 That is to say they are
concerned with symbolic relationships within a circle of pos¬
sible relationships. In the first case the circle is the ecliptic
(more or less), in the second it is the circle of diurnal motion
and in the third it is basically the circle of the synodic peri¬
ods of the planets (i.e., their motion from conjunction to con¬
junction).

Now we have already seen in our first example that a
division of the diurnal circle into twelve sectors of 30° — the
houses — is a totally inadequate tool for describing the signifi¬
cant positions of a planet (in this case Saturn) when its position
in the diurnal circle is dominated by a 4th harmonic (which
must have four positive and four negative phases each 45 s in
length) and still less so when this is mixed with other harmon¬
ics. A twelve fold division is simply not adapted to the clear
identification of such significant positions in the circle; the
limits of the conventional houses do not correspond to the
realities of the situation. And this will be true of all harmonics
save only the possible exception of the 6th harmonic, which
would have six positive and six negative phases of 30°. Even
these phases would not coincide with the conventional houses
unless the node of the wave fell exactly at the Ascendant.
Furthermore, the operative force is one which fluctuates gradu¬
ally round the circle rather than one which has distinct bound¬
aries or cusps.

The same situation applies, as we shall show, to forces in
the zodiacal circle and in the aspect circle. The conventional
divisions of the ecliptic and the conventional aspects are only
a partial formulation of a much wider and more flexible idea.

What then is the new picture that we are looking at? So
far as the relationship of the different facLors of astrology is

concerned we are always dealing with a circle of potential re¬
lationships; the symbolic significance of the relationship is
based on the number by which the circle must be divided to
yield that relationship. Thus when we speak of Sun trine Mars,
for example, we ascribe a certain significance to the idea of a
trine and this is based on the division of the circle by the
number three. We consider this to be qualitatively different
from the division of the circle by the number four or any
other number.

These differences between numbers are inherent in the
ideas of the numbers themselves because each number suggests
or implies a different structure of relationships.

When we depart from the idea of unity (one) which must
include within itself all the potentialities of number, and move
to the idea of two, we may view this number as representing
the idea of polarity, or of opposition, or of complementariness,
or of positive and negative, or of subject and object, or of that
which acts and that which is acted upon, or in countless other
ways, but all these different ways imply the idea of duality
and are derived from it.

But when we proceed again to the idea of threeness we
must leave this set of ideas behind because wc arc now in¬
volved with a triangular relationship in which we can now no
longer think simply of subject and object, positive and nega¬
tive, etc. A third factor has been introduced and this implies
a new order of relationships which has a different set of appli¬
cations and a different symbolism.

Now in astrology, when the symbolism of, say, the num¬
ber three is involved, IT IS ^45 IF three positive points were
established at equal distances round the circle (Fig. 19a) and
these positive points imply the presence of three negative
points midway between them (19b). This again implies gradual
fluctuation between positive and negative poles as we move

Fig. 19

Where the symbolism of the number four is involved it is
as if four positive and four negative points were established at
equal distances round the circle with a fourfold fluctuation be¬
tween them, and so with every other number.

It is upon this principle that all astrological relationships
in the circle of the horoscope are based. We can demonstrate
that this is so and study examples of different numerical po¬
tencies at work in astrology quite easily and as follows:

Man must have known something of magnetism from re¬
mote times and he must have speculated about its nature and
tried to frame some idea of magnetic forces. But one day
someone of an experimental turn of mind must have had the
idea of spreading, say, a sheet of paper over a magnet and
sprinkling iron filings over it. Then tapping the paper he
would find that the iron filings formed a distinctive pattern
and he would realise that this was an image of the magnetic
field. This would be a revelation; for the first time he would
be able to think more clearly about lines of magnetic force.
One iron filing would have told him nothing and twenty
might have misled him, but a large number would reveal the
true picture.

Similarly experiments have been formed by scattering sand
on discs which were allowed to vibrate in response to different
sounds. Here the sand was found to form patterns. Again it
was because of the many grains of sand, free to respond to
the forces at work, that the pattern became visible.

In astrology the same thing occurs when large numbers of
a particular type or class of horoscope are collected and the
positions studied en masse. The individual positions act as do
iron filings in relation to the field of the magnet and their distri¬
bution reveals an ascertainable picture of the astrological forces
at work.

The salient difference between the true picture, thus re¬
vealed, and the conventional one is twofold: First the tradi¬
tional emphasis on the number twelve (twelve signs of the
Zodiac, twelve houses of the horoscope, twelve main aspect
points') is shown to be one of extreme poverty. Once the

v -- 1

harmonic principle is grasped it can be seen that all numbers
play their part in the symbolism of astrological relationships,
including not only such numbers as five, seven and nine and
their multiples (which do sometimes appear in astrological tra¬
dition, as in the case of the ninefold or Navamsa division in
Indian astrology, the 27 lunar mansions or aster isms, etc.)
but also all the numbers beyond twelve. The prime numbers
of course have a special place in the scheme of things.

It is not too much to say that traditional astrology is
based upon restricted analogies, rather like a botanical science
in which the leaves and petals of plants could be only threefold,
fourfold or twelvefold, but never fivefold, sevenfold, ninefold,
elevenfold, or multiplex in their formation. In this sense alone
the doctrine of harmonics in astrology opens a window onto a
new and richer world of symbolism and one which is adapted
to an integral study of man in all his complexity.

The second major difference between conventional teachings
and the new understanding is that the significant ‘units' in
traditional astrology, so far as the circles of the signs and
houses are concerned, are considered to be sectors of the circle,
whereas the truly relevant factors are seen to be points (not
sectors) of maximum and minimum intensity of significance (as
in Fig. 19c). Thus the first 30 degrees of the ecliptic from the
spring equinoctial point are considered to be a uniform whole—
Aries — and in the diurnal circle the first sector above the
Ascendant is considered to be a uniform whole — the twelfth
house. The reality is that the significance of these sectors is
not uniform but one that ebbs and flows in Intensity.

The half-realization that this is so is reflected in the un¬
certainty which astrologers feel about whether a planet just
above the Ascendant (or similarly placed near another house
cusp) is to be treated as a first or a twelfth house factor. It is
also reflected in theories which are sometimes entertained a-
bout house cusps as centres of houses. But these issues can
now be more fully clarified.

The important message of this chapter, however, is that
the truly significant factors in the relationships of the horo¬
scope are the numbers upon which the harmonic divisions are

based. We have seen that Gauquelin’s studies of the distribu¬
tion of planets in the diurnal circle in the nativities of leading
members of different professions very often tend to reveal a
dominant 4th harmonic.

Gauquelin is a statistician and is understandably more in¬
terested in demonstrating the strict scientific validity of his case
for some sort of connection between planetary positions and
human life than in trying to clarify astrological principles. Be¬
cause of this he has been content to demonstrate the high sta¬
tistical significance of certain sectors of the circle, notably the
abnormal strength of the sectors which occur after a planet’s
rising and upper culmination, rather than try to get at the
deeper principles underlying his results. For this reason he hits
not tended to think in terms of harmonics and has not real¬
ised, though we may be sure that he will, that the significant
elements in his results are really the individual harmonics.

But as astrologers wc must penetrate below the surface
and try to see the significance of his results. Thus we must ask
why it is that the 4th harmonic is so much a feature of the
nativities of those who have achieved the higher reaches of
their professions.

The symbolism of the different numbers will become clear¬
er as fuller studies of harmonics in astrology are made. Never¬
theless it seems safe and adequate at this stage to say that the
number four is evidently connected with the idea of difflculty-
effort-achievement and that it is because this element is a com¬
mon feature of Gauquclin’s nativities of successful men lhaL
this harmonic so often appears in his results. It is doubtful
if the phrase ‘difficulty-effort-achicvcment’ can be taken to
represent the root idea of the number four. A more philosophi¬
cal treatment of the subject might take us to something behind
this phrase, but it seems sufficiently close to the root idea for
our present purpose. Thus, to make the matter clear, it is
suggested that the 4th harmonic distribution pattern, as in
Fig. 13, represents the striving-to-manifest which characterises
these nativities, especially in relation to the particular planet
which might be said to go with the particular profession in
question.

But it is noteworthy that it is not by any means always
the 4th harmonic which is strongest and we might consider
another example. Why, for example, in the nativities of 2088
sports champions is the distribution of Mars (which is the
strongest planet in this group) dominated by the 3rd harmonic
(albeit with the 4th a close second)? Fig. 20a show's the actual
distribution pattern in this case and we can see quite clearly
that the 3rd harmonic, as indicated in Fig. 20b, is the strong¬
est factor.

UK
:50
140

Fig. 20

What perhaps distinguishes the sports champions from
Gauquelin's other groups is that w'hcrcas all the other cate¬
gories are strictly professional groups, that is to say they relate
to some kind of work, this group alone — as the word ‘sport’
implies — introduces the idea of play. In other words we may
suppose the sports champion to be motivated by sheer enjoy¬
ment. zest and enthusiasm to a much greater extent than say,
the soldier or physician. That is not to say that other profess¬
ions do not enjoy their work or that sportsmen are not capa¬
ble of determination and hard work, but the element of sheer
pleasure in the exercise of his strength and power (Mars) must
be very strong in the sports champion. This would lead us to
suppose that the number three is more distinctively connected

with, among other things, the idea of enjoyment. In contrast,
the motives of effort and duty arc uppermost in the symbol¬
ism of the number four.

We shall find in this book that the study of harmonics in
astrology requires us to clarify our insights into number sym¬
bolism to a much greater extent than heretofore, because the
number of each harmonic represents a particular quality or
range of qualities and their related effects. At the same time
we shall also find that our study of number symbolism is ren¬
dered both easier and surer by virtue of the fact that we can
constantly relate our hypothesizing to actual examples of differ¬
ent numerical potencies at work in the harmonics we examine.

NOTES

1. Of course, there is the symbolism of the heavenly bodies themselves
but this is of a different order.

2. Although in the case of conventional aspects the semi-squares and
sesqui-quadrates must be added.

^ HARMONICS IN THE DIURNAL CIRCLE

One of the criticisms which has been leveled at the stud¬
ies of large collections of astrological data such as we have
been drawing upon is that they do not produce results which
are applicable to individual nativities and that they therefore
have no practical utility. We shall see in due course that this
is very Jar from the truth and that even at this early stage
some very striking additions to our directly interpretative un¬
derstanding of the horoscope are emerging. Nevertheless before
we can appreciate and explore some of the practical applica¬
tions and implications it will be necessary for us to spend sev¬
eral more chapters simply looking at different examples of har¬
monics in astrology so as to become thoroughly used to the
idea and to see their operation in different contexts.

First, then, let us have a closer look at harmonics in the
diurnal circle, that is in the apparent daily revolutions of the
planets about the earth. And, in order to get to grips with
the subject, let us try our hand at a simple but effective kind
of harmonic analysis. There is nothing which teaches one
better and more quickly about a subject than practical work
on its problems.

Among his collections of different professional groups
Gauquelin has given us the positions of the planets at birth
for 3,046 successful military men.' Not surprisingly the dis¬
tribution of Mars in these nativities provides us with an in¬
teresting study, so let us take this as our example. We want
to be able to carry our investigation as far as we reasonably
can, so the more sector-totals we use for our diurnal distribu-

! tion the better. The largest number of divisions into which

Gauquelin. divides his circle is 36 (see Fig. 12) so let us have
the total number of Mars positions in each of these 36 sectors
for our 3,046 soldiers. In order to have it clearly in mind
what these totals represent we will give them in circular form
on a diagram of their daily rising, culminating and setting.

Fig. 21 then gives the number of times which Mars
appeared in each of the sectors and Fig. 22 shows the distri¬
bution drawn out as a circular graph. Ignore for the time
being the little crosses which have been marked around the
outside of the distribution — we shall come to these presently —
and look, instead, at the little 4th harmonic wave placed in
the centre of Fig. 22. We can see that there is a fairly clear
4th harmonic in this distribution pattern phased as indicated
by the little figure in the middle.

We can see that the peaks after Mars has risen and af¬
ter its upper culmination are stronger than those after its set¬
ting and lower culmination, just as with Saturn in the scien¬
tists (see Fig. 13a). We know this must be because the 4th
harmonic is combined in some way with other harmonics.
How can we take out the 4th harmonic from the pattern,
disentangling it, so to speak, from the other harmonics present,
so that we can have a look at it in isolation and see just how

strong it is (its amplitude) and just where it falls (its phase)?
There is a very simple technique for doing this which we shall
use from time to time in this book. It requires the use of
only simple arithmetic and graph paper.

We know that every harmonic is perfectly regular and
that if there is a 4th harmonic present, it will repeat exactly
at 90® intervals around that circle with a regular rise and fall.
From this it follows that we can take our totals in regular se¬
quence for each of the four 90° sectors and set them down
under each other so that the peaks and troughs of the 4th
harmonic will exactly coincide in each 90° run of totals. If
there are other harmonics which do not repeat regularly with¬
in the quarter-circle, these will be cancelled out (we shall see
why this is so presently.)

Starting from the Ascendant and going around in a clock¬
wise direction, the nine totals from each of the four sectors
arc as follows:

Table 1

Sectors 1 - 9

105

109

•102

Sectors 10-18

116

Sectors 19*27

101

Sectors 28-36

_92

105

103

377

360

377

347

291

323

297

317

357

Before we draw our graph from these final totals let us
pause and ask ourselves what it will show us, what it can
show us and what it cannot. We know that every harmonic is
absolutely regular; if there is a 4th harmonic with a peak just
after the Ascendant in sector one, there will also be peaks in
sectors 10, 19 and 28. There will also be troughs halfway be¬
tween these points because the pattern will repeat at regular
intervals. But if there were to be any of the sub-harmonics of
the 4th, namely the 8th, (two waves exactly repeating in each
quarter circle), the 12th (three waves exactly repeating), or
the 16th (four waves), then they also will be seen if they are
strong enough to be of any account.

First of all let us simply mark our nine points on the
graph without attempting to join them up (Fig. 23), We can
mark our degrees from 0 to 90 along the bottom and we will
draw in the line representing mean distribution which will be
3046 - 5 - 9 = 338. It will help the student to use squared

graph paper.

DLMEtS IN OWDMHT

336

Fig. 23

A little experience is needed before one can deal confi¬
dently with such graphs as this but we can see straight away
that there is a high-scoring area near the beginning of the
series and a low-scoring area just over halfway through it. We
can assume therefore that there is a 4th harmonic and that
the peak probably comes somewhere between the two highest
scores (i.e. between 10° and 20 a along the horizontal scale)
and similarly that the trough (which must be 45° away from
the peak) comes somewhere between the two lowest points. We
also know that if there are other harmonics present they will
fluctuate about this line.

Let us then draw in our 4th harmonic, trying to adjust
it so that it moves smoothly and evenly through the other
points, with peak and trough spaced equal distances apart
(see Fig. 24). It may help us to extend our graph a little to
the right using a dotted line so as to see just what is happen¬
ing as the wave begins to repeat. Remember to get the peaks
and troughs of the wave neither too rounded (they are not
semi-circles) nor too pointed. (As if to drive home the lesson,
our artist has, for once, got the wave too pointed. Nobody is
perfect).

}

Having drawn our 4th harmonic we can now see that
there is a fluctuation about our main line and we can see
almost at a glance what it is. There are three quite regular
waves superimposed upon our fundamental 4th. These there¬
fore reveal the presence of the 12 th harmonic (three waves in
each quarter circle).

If we mark our phase-angle scale along the bottom of the
graph from 0° to 360° we can now sec that the phase of the
4th harmonic is somewhere about 50°. If we wish to estimate
the amplitude of this wave we can see how much the wave
rises above and falls below the mean and do a little sum. It
rises to roughly 378 and falls to about 298, that is to say a

rise and fall of 40 above and below the mean of 338. So, if

the amplitude is 40 on a mean of 338, what will it be on a
hundred, so as to give us our amplitude in terms of percent¬
age? It will be (40 -h- 338) x 100. This is a simple long di¬

vision sum and gives an answer of 11.8. The student will soon
find that he can usually estimate such things fairly accurately,
remembering always that the rise and fall must be the same.

Actually, the amplitude and phase given in the mathema¬
tically exact harmonic analysis by computer 2 is:

AiARS 4th HARMONIC Amplitude Phase Angle

Military Men 11.5 52°

We can see from this that our estimate of the amplitude and
phase is very close. My experience is that these graphs of har¬
monics will usually give a very close approximation of the true
figures.

Turning our attention to the fluctuations about the 4th
harmonic in Fig. 24 we arc not left with much doubt that it
is simply a 12th harmonic which is shown. The rise and fall
above and below our dominant 4th are fairly, though not per¬
fectly, regular and they are quite equally spaced.

Wc must not fall into the trap of thinking that the phase
angle scale for the 4th harmonic will do for the 12th. If wc
wish to get a better idea of the phase and amplitude of this
wave, we can do it quite easily from the nine totals given in
Table 1. We know that the 12lh harmonic is 30° in length
and that it will repeat regularly three times each 90*. There¬
fore we can set out our nine totals from Table 1 in runs of
three, thus:

Table 2

377 360 377 ,347 291 323, ,297 317 337, (from Tabic 1)

347 291 323 < 1

297 317 357 <--

1021 968 1057

We can now attempt a graph of these three totals. After a
little experimenting with a pencil to get our wave in the right
place with an equal rise and fall, wc shall be able to draw
out our 12th harmonic. Wc can make our phase angle scale
along the bottom and as we have now divided our 3,046 sol¬
diers into three totals, the mean will be 3,046 -r- 3 = 1,015
(See Fig. 25).

Fig. 25

Examining our graph we can see that our phase angle
must be about 330° to 340°. Since the rise and fall of the
wave is about 50, or just over, on a mean distribution of
about 1,000 (actually 1,0151, we know that the amplitude will
be about 5% — (50 4-1000) x 1(X). Referring to the exact

harmonic analysis by computer we find:

MARS MILITARY MEN

Amplitude

Phase

8th Harmonic

0.2

202

12th Harmonic

5.1

336

16th Harmonic

2.8

142

We can see from this that our estimate of the amplitude (5%)
and the phase (330 to 340) are almost exactly correct for the
12th harmonic and that wc were also correct in deducing that
the 12th was the only other harmonic of any note, the 8th
and 16th having very small amplitudes.

Actually there is another harmonic which is worth noting
in our Mars distribution pattern, Our reconnaissance of the
4th harmonic and its sub-harmonics has revealed the presence
of the 12th, and shown us that the 8th and 16th are not
strong. In just the same way, if we made a systematic recon¬
naissance of the 3rd and its sub-harmonics we should be able
to see whether the 3rd (120°), 6th (60°), 9th (40°), and 15th
(24°) — all multiples of three — played any significant part in
our original Mars distribution. Wc should also come across our
friend the 12th again, because the 30° wave will also fit into
the 3rd exactly. Of these it is the 9th which is, as it happens,
the second strongest of all the Mars harmonics in the soldiers’
nativities. Just to give ourselves another chance to become fa-
mihar with this simple kind of harmonic analysis which we
have been learning, let us look at this 9th harmonic.

The 9th part of a circle is 40°, so our 9th harmonic will
be a wave of 40° in length. As it happens our circle has been
divided into 36 sectors of 10° each, so that by taking our to¬
tals in runs of four we shall be able to isolate the 9th har¬
monic. This wc will proceed to do.

V PiWx WC.E

Going back to our original totals given in Fig. 21 and
proceeding as before from the Ascendant clockwise we have;

Table 3

Sectors 1- 4

105

109

Sectors 5- 8

102

Sectors 9-12

116

Sectors 13-16

Sectors L7-20

Sectors 21-24

Sectors 25-28

101

Sectors 29-32

105

Sectors 33-36

103

731

821

782

712

Using these four totals we can draw our graph, Fig. 26, and
from this we can see that our phase angle will be about 150°
to 160°. To estimate the amplitude, we see that the mean dis¬
tribution is 761 (3,046 -i- 4). The top of the wave rises to
just above 820 and falls to about 700, a rise and fall above
and below the mean of about 60 cases. Thus our amplitude
will be (60 761) x 100 = 7.9%.

Fig. 26

The analysis by computer for this harmonic gives;

MARS MILITARY MEN
9th harmonic

Amplitude

7.9

Phase

155

Our estimates were again very close. We can also see that
our 9th is evidently not distorted significantly by an 18th
which is the only other harmonic which could show in our
graph. For the sake of interest the places where the peaks of
the 9th harmonic fall have been marked with little crosses in
Fig. 22 and we can see that it forms a significant element in
distribution.

A little practice in drawing out these harmonic graphs
will soon show the student that once the knack of drawing a
smooth, even sine wave has been gained, he can obtain quite
good results from this simple method of harmonic analysis. A
fuller example is given in Appendix I.

Where a distribution of totals gives a baffling wave shape
he can assume that he is dealing with a complex of waves
which may take a little time and care to sort out. These may
indeed prove too difficult for the beginner. Again we must
recognise that there are some harmonics which arc difficult to
get at by this graphic method. The 13th or 17th, for example,
could not be detected, unless the student was very experi¬
enced in looking at the basic distribution, except by more
elaborate mathematical means. We are also restricted by the
number of original totals and the intervals at which they are
given.

Before ending this chapter we have one very important
lesson to learn. Why was it that when we put our totals down
in runs of nine totals in order to see our 4th harmonic and
its sub-harmonics more clearly, it had the effect of cutting out
all other harmonics except the 4th and its family of sub-har¬
monics? Why, for example, did the 9th (which, as we have
seen, was quite a strong one) not appear in this result to con¬
fuse the issue? Look at Fig. 27a. Here we can see the nine
waves of the 9th .harmonic. If we divide the circle into four
quarters there will be 2V4 waves in each quarter. If we put
these four divisions on top of each other (Fig. 27b) the waves
will not coincide and will have the effect of exactly cancelling each
other out, every high score in one sector being exactly cancelled
out by a low score in another sector.

HARMONICS IN THE
ECLIPTIC CIRCLE (I)

Therefore we can remember that if we divide any circle
into a number of sectors of equal length (say four sectors of
90 s or nine of 40°) and set down our totals for each sector in
order (as we did in Tables 1, 2 and 3 above) then this will
have the effect of revealing more clearly the harmonics which
will fit into that sector-length, because it also has the effect of
eliminating, in the result, all harmonics of the whole circle
which will not fit into that sector-length. This provides us with
a useful tool which we can use when necessary to show more
clearly the presence of a particular harmonic.

NOTES |

1. See Chapter 4, Note 2, where full reference to Series G, Vol. 1 is
given. This volume gives full details.

2. It would be nice if one could report that the computer really did 1

give a strictly truthful ‘result’, but as a matter of fact the computer j

also has certain limitations. These are explained in Appendix TI.

In Chapter 5 we suggested that the traditional division of
the ecliptic into twelve zodiacal signs, although based on the
idea of harmonic intervals expressing a twelvefold order of re¬
lationships, was nevertheless a very limited application of the
harmonic concept. In point of fact the division of the ecliptic
by every number has its astrological significance. The number
twelve derives some pre-eminence from the fact that it is the
lowesl common multiple of two, three, four and six and so
embraces the symbolism of these important numbers.

The usual conception of the Zodiac is of twelve "boxes,’
placed end to end round the circle of the ecliptic. When a
planet is passing through one of the boxes its "influence’ is
considered to be uniformly coloured by that sign throughout
its transit. When it moves out of the sign, it is immediately
in the next one and takes on a new colouring which it keeps
until it again moves into another sign. This view has a certain
practical value but it is not really in conformity with the as¬
trological truth. If it were, we should be able to examine the
distribution pattern of large numbers of solar, lunar or plane¬
tary positions and see the sudden change of emphasis when
the boundary between two signs was reached, But very many
suck studies have been made and there is never any evidence of such a
sudden change in emphasis 1 at the sign boundary.

Consider for example the study of the dates of birth of
7302 doctors of medicine by the late Rupen Gleadow and
Brig. R. Firebracc. 2 From this huge collection of birth dates
we can consider the distribution of the Sun round the circle
of the Zodiac. This gives us a solar distribution total for each
one of the 360 degrees of the circle, representing, approxi¬
mately, 3 the number of doctors born on each day of the year.
Fig. 28 shows this distribution. For the purpose of this graph
a six-degree moving total has been used in order to smooth
the line slightly without, however, removing local zodical fluc¬
tuations.

The term "moving total’ is one which may not be famil¬
iar to every student and an explanation is called for. The idea
is quite simple: if wc gave the ‘raw 7 ’ total of Sun positions for
each degree, the line showing the distribution would have
many minor oscillations from degree to degree. Because of this
it would be rather difficult to see Lhe general trend of the dis¬
tribution. We therefore move along the totals for each degree
adding them up in runs of six degrees.

Fig. 28

For example here are the total Sun positions for the last
three degrees of Pisces and the first thirteen degrees of Aries
from the sample of 7302 doctors. From these we can give a
moving total for each set of six degrees from 0' to 10° Aries,
moving along the line of totals, dropping successively those
to the left and taking in totals to the right. In other words,
each of the moving totals is the sum of three preceding and
three following degree totals. The moving totals arc given un¬
derneath the degree totals.

Pistes T Aries Aijs.

Dcjri'rx 2H :j

H> 1 2

4 f*

‘J Hi II

12 U

l)ce. Totals 21 If) 2

2 2f> 14

2i, 21

Ifi 17

2'.

12 2 r i 21

h m

Moving Totals 11") 114 ll!> US HU 110 111 Ilf. 11>> 111 11:'.

new scale down the right-hand side of the graph in which the
left-hand scale has been divided by six.

We have now scattered our iron filings, so to speak, over
the zodiacal influences at work (for the Sun) in the nativity of
the typical doctor. As we look at our graph, we can indeed
see a clear tendency to high-scoring and low-scoring areas in
different parts of the zodiacal circle, even after a 6° moving
total has smoothed the line. These do not, however, show any
obvious tendency to conform with the boundaries of the signs.
In fact high-scoring and low-scoring areas non across the sign
boundaries just as if the boundaries were not therel

In order to see more clearly that what we are really deal¬
ing with are harmonic fluctuations, let us simplify our graph.
Fig. 29 shows the same distribution pattern by plotting one
total for every) five degrees round the circle (we are no longer
using a moving total). Thus the first point in the graph repre¬
sents the number of doctors bom with the Sun between 0°
and 4°59’ of Aries, the second the total of those born between
5° and 9°59’, and so on. It is basically the same diagram as
Fig. 2S but simplified in order that we can make a compari¬
son with the twelvefold zig-zag placed above the distribution
line. If we compare the distribution carefully with the zig-zag
we can see that the two have a general correspondence. The
distribution tends to be lower near the beginning of the signs
than it is later in the signs showing that the 12th harmonic is
one of the important elements in the distribution of the Sun in
the nativities of our doctors.

The lower line of figures provides us with the first ten
totals shown on our distribution graph (Fig. 28); this is a six-
dcgrcc moving total. If we want to change it to a six-degree
moving average we should divide each of the derived totals by
six, but wc can achieve the same effect exactly by marking n

If we make use again of the technique demonstrated in
the last chapter we. can isolate (more or less) this 12th har¬
monic. Remember that we are dealing with an absolutely reg¬
ular wave form; therefore if we have a twelvefold wave as in
Fig. 29 we can divide the distribution into any number of

sectors, provided that each contains the same whole number of
waves. By collecting the sectors together, we shall tend to ob¬
tain a clearer picture of the harmonics which fit into the
length of the sector. Thus in Fig. 30, if we cut the twelve
waves into three sectors, each of four waves and collect the
three sectors together by adding up the totals for the corres¬
ponding points in each series, the waves will exactly coincide
and we shall expect to see a clear fourfold wave in our result.

Fig. 30

In Fig. 29 we have a total for each block of 5° around
the Zodiac. If we divide the Zodiac into three sectors, Aries to
Cancer inclusive, Leo to Scorpio, Sagittarius to Pisces, and
set down the totals for each 5“ block underneath each other,
just as we did in the last chapter, we shall obtain twenty-four
totals, six for each of the quadruplicities, fire, earth, air and
water. From these totals we can draw another graph (Fig. 31).
We can now clearly see the four waves in each third part of
the Zodiac showing beyond doubt the regular rhythm of the
12th harmonic in the complete circle.

'TJLje I I

Fig- 31

This shows again the value of this technique for exposing
particular harmonics in a complex of harmonics. As it is so
important let us state the general principle of the method

again: By dividing any circle of distribution totals into sectors of
equal length and collecting those sectors together, the effect is to remove
all trace of those harmonics of the full circle which are not harmonics
of that sector length. One is left only with those harmonics which do
fit exactly into that sector length.

Let us have another example from the Sun positions of
the doctors and in doing so confirm, at the same time, anoth¬
er point wc have been making. For our 7302 doctors we have
a separate total for the number of times the Sun occupies each
degree of the Zodiac. If we divide our zodiacal circle into six
sectors of 6tT each we shall have six runs of 60 totals. Each
sector will include one positive and one negative sign exact¬
ly, Let us collect these six sectors together by adding up
the totals for the first degree of all the sectors (i.e., the first
degree of Aries, Gemini, Leo, Libra, Sagittarus, Aquarius),
then the totals for the second degree in each of these signs,
then the third and so on right to the last degrees of Taurus,
Cancer, Virgo, Scorpio, Capricorn, Pisces. We shall finish with
60 totals, one for each degree of the positive signs put together
and one for each degree of the negative signs put together.

This gives us in effect the typical distribution pattern for
the sixth pan of the circle. Now we know that the harmonics
which will precipitate into this distribution will be those, and
those only, which will fit exactly into a sixth of a circle. If in
the doctors 1 solar distribution there is a 6th harmonic (60° in
length) it will fit exactly once into our pattern and appear as
one long wave. If there is a 12th harmonic (and we already

know that there is) it will appear as two waves of 30° each.
If there is an 18lh harmonic (20°) that, too, will fit exactly
into our 60° sector and will show as three waves. The 24th
harmonic will show as four waves of 15° and so on. Fig. 32
show's the result of this exercise giving the 60° distribution pat¬
tern.

There arc only two points at present to which wc need to
draw attention in this graph. The first is that we can clearly
see the 6th harmonic of (60°) and the 12th (of 30°). These
have been drawn out underneath in Fig. 32. The 12th is eas¬
ily the strongest of all the solar harmonics in the nativities of
our doctors and the 6th is also a strong one. These two to¬
gether form the "framework’, so to speak, of the whole pattern
and carry all the shorter sub-harmonics "on their back’ as it
were. (The presence of the 6th is shown in Fig. 31 because the
second and fourth waves are higher than the first and third).

The second thing to which attention is especially drawn is
that there really is. as we have said, no sudden jump to high¬
er or lower totals at the boundary between the positive and
negative signs. One can now' actually see that there is only the
steady and gradual sweep of the wave from a high point to a
low point between the points of maximum and minimum in¬
tensity in each harmonic. Of course, the shorter sub-harmonics
are super-imposed upon them." 1

One should perhaps point out, at this stage, the mistaken
nature of so much of the kind of astrological research which is
based on the counting of positions in the signs of the Zodiac.
Countless conclusions have been drawn, including much of the
evidence for the value of the Sidereal Zodiac, on the quite
erroneous basis of the "box-type’ Zodiac, that is, sectors of
the ecliptic with distinct boundaries.

The problem of the truth about the rival Zodiacs remains,
scientifically, an open question. However, it cannot be solved
without an appreciation of the harmonic character of the for¬
ces at work in the circle of the ecliptic. This is a subject to
which we shall return in a later chapter.

Michel Gauquelin himself, who has done so much to
elucidate the characteristics of the diurnal or mundane circle,
says he can make no sense of planetary distributions in the
circle of the Zodiac or in the aspect circle. This is quite sim¬
ply because so far he has not fully grasped the harmonic na¬
ture of all such astrological factors. He has so far persisted, in
consequence, in continuing to count distributions in the con¬
ventional signs of the Zodiac instead of breaking the ecliptic
into smaller units and examining the results in terms of har¬
monics.

In the case of 7302 doctors referred to above, by far the
strongest single element in the solar distribution is the 12th
harmonic. This is a wave of 30° in length with a high point
and a low point in each 30° sector of the circle. It docs not
matter where these twelve waves are divided into twelve com¬
partments, there will always be a high and a low in each
‘box.’ If, then, one counts the total number of Sun-positions
in each 30° sector, one will always be adding the positive and
negative halves of the -wave together and these will always
cancel each other out. Thus the single most significant element
will have been completely thrown away. This is the reason, in
principle, why good astrological statistics have in the past
proved so difficult to produce.

It is true that even after this important 12th harmonic
has been removed in this case (or in others) there will still be
high and low-scoring parts of the ecliptic circle, but they will
be the result of other harmonics, say, the 3rd or 4th or 5th.
These have nothing to do with a Zodiac of twelve signs as
such. The problem of the Zodiac must be seen in the context
of the basic fact that we are always dealing with points, and
not sectors, spaced round the circle. The nearest one can get,
in terms of harmonics, to the traditional idea of twelve equal
and significant sectors of the ecliptic, is the case of the 6th
harmonic (Fig. 33).

Fig. 33

The 6th harmonic produces 12 equal sectors alternating
between positive and negative. I have always held that the
most likely situation (in terms of psychological factors at least)
in which one would be likely to find a collection of nativities
showing a pure 6th harmonic distribution would be in the
case of a study of psychological types. One would focus upon
the distinction between positive and outgoing, and negative
and inward-turning types.

Jeff Mayo, formerly principal of the Faculty of Astrologi¬
cal Studies, has recently undertaken a most thorough and
searching experiment along these lines. It is designed to corre¬
late the classical introvert and extrovert types of modern phys-
chology with horoscopic factors. At the time of writing no re¬
sults of this work have actually been published. However,
when Mayo gave a talk on the results of his two large-scale
experiments to date, he said that both had shown a perfectly
consistent correlation between the six positive signs and the
extrovert type and the six negative signs and the introverts.
The extroverts showed a solar distribution as in Fig. 33 and
the introverts showed the inverse pattern. His results evidently
greatly impressed London University’s Department of Psychol¬
ogy-

Individual scientists have recently begun to interest them¬
selves in zodiacal distribution patterns. These sometimes pro¬
duce results which seem to the scientific world mildly aston¬
ishing, even when examined on this rather rudimentary basis
of the twelve conventional signs. The leading British scientific
journal, Nature, recently published (April 26. 1974, pp. 788) a
study of the dates of birth of molecular biologists and taxono¬
mists, made by Donald A. Windsor of Norwich, New York. It
showed the relative frequency of the Sun’s placement in the
twelve signs for these scientists. Such highly specialised groups
always show very specific harmonic combinations. These are
not really revealed by reducing the distribution to twelve to¬
tals, which can only show harmonics up to the 6th. Needless
to say, there was no Indication in this instance of the basis
upon which the results could be explained. This could have
been done using harmonics.

notes

1. On theoretical grounds one can see that there would be certain rare
cases when a combination of harmonics would produce such a change

at the end of a sign. . ,, > _ .

2. See Firebrace, Brig. R. C., "Astrological Statistics, Astrological Journal
(Astrological Association, London), XI (1969), no. 4.

3. Approximately, that is, because the difference between 360 degrees
and 365 days in a year.

4. For a fuller study of this subject, see Addey. John 1 Seven-thousand
doctors,” Astrological Journal (Astrological Association, London), XI
(1969), no. 4.

8 HARMONICS IN THE
ECLIPTIC CIRCLE (II)

So far, in discussing harmonics in both the diurnal and
ecliptic circles, we have confined ourselves very largely to what
might be called the major harmonics, that is to those with
harmonic numbers up to twelve. But exactly the same princi¬
ples apply to the higher numbers as well as to those lower
numbers, such as seven and nine, which are less used in con¬
ventional astrology.

Ifwc look at Fig. 32a wc can see that superimposed upon
the combined 6th and L2th harmonics (as shown in 32b) there
are many quite vigorous oscillations from degree to degree.
These might be thought to be merely random fluctuations
about the mean, but although this random factor imist enter
into it, yet it can be shown that those oscillations are partly
at least the result of identifiable and significant high-numbered
harmonics. 1

As it happens this solar distribution for doctors docs not
provide us with a simple, clear and easily-manageable example
of the high-numbered harmonics. To examine such an example
it will be best to take another instance, this time from the
nativities of children who suffered from paralytic poliomyelitis.
The Sun position of 1023 such children were tabulated through
the 360 degrees of the Zodiac. The sector-length we need to
take from this example, for our present purpose, is the twenty-
fourth part of the circle — the sector of 15°. So in this case
we have divided our 360 degree-totals for the Sun's position
into 24 runs of 15 totals.

By dividing these 24 sets of 15° into two groups of twelve
sets and collecting these together we can compare two typical
15° distribution patterns. Fig. 34 shows the way in which the
circle has been divided and the two sets of sectors. The twelve
sectors marked a have been collected together and the distri¬
bution in these compared with the twelve sectors marked b.
Fig. 35 shows the two distributions.

Here we can see a good example of the shorter harmonics
at work. No doubt is left in our minds from a comparison of
the two distributions shown in Fig. 35 that they are telling
the same story and that both are reflecting the same combi¬
nation of harmonics.

iwi r-.sz rr?«rsrr

Fig. 34 Fig. 35

There are three harmonics which outstandingly determine
this distribution. They are the 24th harmonic of the complete
circle (a wave of 15° in length, the first or fundamental in Fig.
35), the second sub-harmonic of this series (the 48th of the
circle), twx> waves of 7V2®; and the 5th sub-harmonic of this
series (five waves of 3° each) representing the 120th of the
whole circle. We have drawn these out in full (Fig. 36) so
that the student can see exactly how the distribution pattern
of Fig. 35 is produced. A comparison of the combined wave
form at the bottom of Fig. 36 with the actual distribution
shown in Fig. 35 will show the student what is meant. A de¬
tailed study of this aspect of the polio-prone nativities has been
published separately. 2 The student is referred to this for
fuller details.

Thus far we have considered harmonics in the circle of
the ecliptic which have some sort of relationship to the usual
twelvefold division of the circle; the 6th harmonic, the 12th,
the 24th, the 48th, and so on. But as we said earlier, one of

the lessons of the harmonic approach to astrology is that this
range of numbers can be seen to be only a part of the pic¬
ture. Consider, for example, the Sun positions on the dates of
birth of 1974 British clergymen. * When this solar distribution
was analysed from the 1st to the 180th harmonic, the three
most outstandingly strong harmonics were the 7th, the 49th
(7 2 ) and 98th (7 2 x 2); these were the only harmonics with an
amplitude of more than 10%.

The association of the number seven with sacred and
religious matters is proverbial; even so it is impressive to find
its appearance with such strength in the nativities of those
who exercise the priestly function in society. We shall have

more lo say about the significance of the 7th harmonic later
but in the meantime it is instructive on several counts to see
this solar distribution in the nativities of clergymen in graphic
form. For one thing, a control set of birthdates was made
having an equal number of samples and the same general
parameters as in the case of the clergy. For another, the ex¬
ercise illustrates a number of technical points.

Fig. 37

Fig. 87b shows the actual degree by degree distribution of
the Sun in nativities of 1974 clergymen in each 7th part of the
ecliptic or zodiacal circle, the seven sectors having been col¬
lected up in the way with which we are now familiar. Fig.
87a shows the combination of the fundamental 7th (dotted
line), the 49th (seven waves superimposed upon the one basic
7th) and the 98th (two waves to each one of the 49th series).
Fig. 87c shows the distribution in the control group.

Looking at Fig. 37 we can see, first, that the actual solar
distribution for the clergy (Fig. 87b) has a clear, regular and
vigorous rhythm with w'ide divergences from the mean, where¬
as in the control the divergences arc weak and irregular. Sec¬
ondly, we can sec that the 49th and 98th coincide on the
downbeat to give seven low' scores marked with crosses. Thirdly,
we can see that the crests of the 49th -tend to be cleft because
of the two peaks of the 98th superimposed upon them.

There are several technical points of interest. First, the
7th part of a circle is approximately 51°26’. Iiow then, since
there are not a whole number of degrees in each sector, did
we manage to obtain our distribution graph when we have
totals for whole degrees only? In a situation of this kind, if we

want to draw the result in graph form, we must do the best
we can. In fact, the degree totals were set down in seven runs
of 51°, 52 s , 51°, 52°, 51°, 52°, and 51°, the final score in the
lines with 52 totals being dropped. If one thinks about this
ploy one can see that the result will be quite adequate to the
purpose. No line of totals will be more than V 2 0 out of phase
with the first line of totals. Since even the shortest wave (the
98th) will be about 3-3/4° in length this element of approxi¬
mation still allows the effect of the shortest wave to show in
the result.

Secondly, it will be noticed that whereas there is usually
an interval of seven degrees between the strong downbeats
marked with crosses, there are two places where there is an
interval of eight degrees. This, of course, is because seven does
not divide exactly seven times into 51, but has a remainder
of 2.

Finally, it will be noticed that the strong downbeat and
double-crest effect is well shown at some points in the graph
but much less so at others. This again is partly because the
regular, ideal seven-fold pattern shown in Fig. 37a is not
regularly picked up by the 51 totals in Fig. 37b. This sort
of situation is not uncommon and arises where the ‘readings’
taken at regular intervals fall irregularly in relation to the
waves of the ideal pattern.

For example, in Fig. 38 the five waves are perfectly reg¬
ular and the nine points at which readings are taken are
equally spaced, yet, because they fall irregularly in relation to
the waves, the nine points taken do not accurately reflect the
regular wave pattern. This is a snare which the research stu¬
dent should look out for in drawing conclusions from drawn
graphs of distribution patterns.

Fig. 38

The collection of birthdates of British clergy was an
attempt to repeal an investigation into the birthdates of 2492
American clergy by the late Don Bradley of the United
States. 4 The Sun positions of these American clergy did not
show so great an emphasis on the 7th and its sub-harmonics 5
although there were striking similarities. The strongest single
harmonic here was the 125th (5 3 ). As this was also one of the
very strong harmonics in the British clergy, with a phase angle
very close to that of the American clergy, the 125th was the
strongest in the combined total of 4466 clergymen of both
countries.

In the nativities of 7302 physicians already referred to the
25th (5 2 ) was one of the strongest of the solar distributions,
although not as strong as the 12th. In the birthdates of 2875
artists (culled by Charles Harvey from Who's Who in Art and
held by the Astrological Association) it was the 5th which was
the third strongest of the first hundred harmonics.

The number five certainly has much to do with Man
himself and with human divisions and categories. It is there¬
fore not suprising that the 5th harmonic and its sub-harmon¬
ics should appear in collections of nativities of those who fol¬
low the different branches of human occupations which must,
in the nature of things, correspond to different aspects of
man’s nature and constitution.

One of the important things noticed in this chapter is that
certain kinds of collections of birth data tend to exhibit the
presence of what we might call “families” of harmonics. In
the polio nativities the solar harmonics were dominated by the
12th series, that is the 24th, 36th, 48th and others; in the
clergy it was the 7th and its sub-harmonics; in others the 5th
and its sub-harmonics. This is a widespread phenomenon in
the field of cycle research and it is one which is abundantly
confirmed by the very extensive evidence accumulated by the
Foundation for the Study of Cycles, Pittsburgh, Pennsylvania,
which wc shall refer to later.®

To sum up, we have tried to show in this and the pre¬
ceding chapter that the traditional concept of the Zodiac as
twelve equal sectors of the ecliptic is one limited application
of the idea of harmonic intervals in this circle. The true pic¬
ture is one in which the symbolism of all numbers can and
should be brought into play, not in terms of sectors but in
terms of an ebb and flow between equally spaced points
around the circle, as shown in Fig. 19.

NOTES 1 |

1* See Chapter 15 on degree area influences. |

2. Addey, John, The Discrimination of Birth types in Relation to Disease, Green ^

Bay, WI.: Cambridge Circle, 1974. ^

3. The degree by degree distribution is held by the Astrological Associa-
tion Research Section. The original study was made by Firebrace,

Brig. R. C. and A. J. Kelly, in “Statistical Research Project,” Astro¬
logical Journal (Astrological Association, London), II (1960), no. 3,
though this is now difficult to obtain.

4. Bradley, Donald A., Profession and Birtkdate, Los Angeles, C A.: Llewellyn
Publications, 1960.

5. This is possibly because clergy in the U.S. do not show so great a

homogeneity of religious allegiance as British clergy who are mostly \

Church of England.

6. See Chapter 21.

HARMONICS IN THE ASPECT CIRCLE

No part of this work is likely to present greater difficul¬
ties, either for the reader or the author, than this chapter
which deals with the question of harmonics in the aspect cir¬
cle. There are a number of reasons for this, and the reasons
which must make it difficult for the student of traditional
astrological teachings are not the same ones which will make
it difficult for the writer who is up against a different set of
problems — problems, incidentally, which are made worse by
a lack of information.

From the standpoint of the reader who has been educated
in terms of the prevailing concepts, the great difficulty is likely to
be that of replacing his current ideas about what aspects are
like, as described in the textbooks, with what they are like, in
reality. According to the textbooks, aspects are things which
pop tip here and there in the aspect circle; traditionally there
are twelve main points at 30° intervals in the circle which are
said to be ‘In aspect’. An additional four at 90° intervals start
from the semi-square of 45°. These 16 aspects, together with
any others the astrologer may fancy, are envisaged as being
angular relationships in the circle at which two planets are
brought into a significant relationship. A certain highly vari¬
able. not to say, indeterminate, 'orb is allowed on cither side
of the exact aspect-point. When two planets move out of orbs
of an aspect, the relationship between them is deemed to pass
into some sort of limbo.

The picture in the astrologer's mind is something like
Fig. 39 which shows ‘bleeps’ in the circle corresponding to the
standard aspect points. The sort of strength and orb associated
with each is roughly indicated. This picture is a mass of
anomalies and uncertainties. It is not merely that a wholly
unreasonable choice has been made in favour of certain num¬
bers for dividing the circle (twelve and eight), or that what
constitutes an ‘orb’ has never been intelligibly defined and
cannot, as things stand, be so defined, except on an arbitrary
basis. Rather, it is the notion that two planets can somehow
cease to have a significant relationship which puts the finishing
touch of absurdity to the whole scheme.

In actuality the same principles apply to the aspect circle
as apply to the diurnal and zodiacal circles. In the diurnal
circle the symbolism of a certain number, say four or 120,
when called into play expresses itself through four points or
120 points at regular intervals round the circle. The astrologi¬
cal force at work is represented by a regular series of waves
measured from the Ascendant or. according to the factor in¬
volved, from the M.C, or some other point in the diurnal cir¬
cle at which great circles of the mundane sphere intersect. In
the case of planetary positions in the ecliptic the symbolism of
different numbers is similarly expressed through harmonics
which are evidently measured from the equinoctial or solstitial
points (and/or from some other point or points not yet estab¬
lished 1 ). In both of these cases the harmonics express the
alternating positive and negative phases of a relationship be¬
tween a moving body and another significant point such as the
intersection of the horizon and ecliptic (Ascendant-Descendant)
or the ecliptic and celestial equator (0° Aries-Libra).

In this sense the distinction we have made in several
places in this book between zodiacal placings, mundane plac-
ings and aspect relationships is a false distinction. In the larger
sense, zodiacal placings are no more than aspects to a point in
the ecliptic circle (such as 0° Aries) and mundane placings are

no more than aspects to points (such as the Ascendant) in the
diurnal circle. If this fact had always been recognised, then
the famous Tropical-Sidereal controversy would have been
seen in a different light. It would have been seen to resolve
itself into a question of what valid points, potentially capable
of generating harmonic effects, exist in the ecliptic circle. This
is dealt with in Chapter 19.

In the case of the aspect circle one is, in fact, simply
dealing with positive and negative points of relationship be¬
tween one planet and another according to the symbolism of
different numbers. The concept of absolutely regular wave
forms round the circle remains the same. Aspect points do not
pop up here and there; if the symbolism of a particular
number applies to a certain class of nativity and if a large
collection of such charts is made and the distribution of one
planet in relationship to another is plotted — giving us our
iron filings again — one can see that the regular beat of the
relevant wave form goes round the whole circle. For example,
if the 4th harmonic is operative in the relationship between
two planets, one will find the distribution of the faster moving
planet in relation to the slower to be as shown in Fig. 40a;
if the 12th harmonic, then it will be as in 40b.

But the reader will say, surely such a state of affairs nec¬
essarily implies that the square aspect — which it is alleged
results from the operation of the 4th harmonic — must always
have an orb of some 22V2° (see Figure 40a). This is totally
contrary to our experience.

Quite true, the 4th harmonic, by itself in terms of aspects
does have an orb of 22 1 /2 <l , that and no other. The explanation

of this apparent contradiction to our accepted experience is
that major harmonics hardly ever operate in isolation and are
in practice nearly always accompanied by a number, and often
a considerable number, of their sub-harmonics.

For example, if, to the 4th, we add only its first two sub¬
harmonics (that is the 8th and 12th), and assuming they are
all positively phased in relation to the points ‘X’ in Figure 41,
we can see that the strength of the square aspect is already
enhanced and the orb narrowed (and is narrowed still further
if more harmonics are added). Yet each harmonic remains
consistently in operation round the whole aspect circle, and if
there are parts of the circle where the combination of har¬
monics throws up peaks of more intense force and others
where the operative forces seem to die away, this is only be¬
cause at some points the harmonics are all acting in unison
and at others they are counteracting each other.

one ‘blanket' definition of an orb except, simply, that for any
harmonic the orb of positive or negative ‘influence’ will be
one quarter of the harmonic length (See Fig. 41). One can¬
not really go further than this because for each combination of
harmonics the orb will be different. Even this simple definition
assumes that we are dealing with harmonics which are phased
either at 0° (positive ‘influence’) or 180* (negative ‘influence’),
as in Fig. 42, but this does not always seem to be the case.
On the contrary, it would seem that sometimes the nodes of
the wave fall at the aspect point so that the applying or separ¬
ating aspect represents the maximum positive or negative value.

See Fig. 43.

This, quite simply, is the sole reason why the so-called
major aspects (the conjunction most of all, then the opposition
the trine and square) an thought of as ‘major’, namely be¬
cause, being primary divisions of the circle, they contain the
most sub-harmonics and because they are the most likely
places in the circle for these sub-harmonics to coincide and re¬
inforce each other.

We can now consider what orbs really are and how they
arc to be defined. The fact is that it is difficult in practice to
avoid adopting a double standard, that is. a theoretically ac¬
curate definition and working definition for practical purposes
in interpreting the chart. Strictly speaking there can be no

It is recognised that such a way of looking at orbs, al¬
though it may be useful to remember, is not very satisfactory
for the person who sits down to interpret the chart. On a
practical level an element of arbitrariness must be brought in
to provide some working rule and the best one can do in such
circumstances is to make sure that the rule is as much in con¬
formity as possible with the harmonic nature of aspects. There¬
fore in Chapter 14 I have attempted to formulate a working
principle which covers the problem of orbs for all aspects, and
the reader is referred to this for a viewpoint which he will
probably find more enlightening in a practical way.

So much for a brief introduction to the theory of harmon¬
ics as applied to aspects. When we come to the question of
demonstrating these principles from actual studies which have
been made, we are faced with one very big difficulty which

has so far restricted all but the most preliminary investigations.
The difficulty we refer to, of course, is that of the apparent
irregularities of the planetary motions. Their periods of retro-
gradation by themselves produce very strong harmonics indeed
if they are studied in relation to aspect patterns in the same
way that we have examined the solar distribution patterns in
the ecliptic. This fact is still often overlooked by those who
make statistical studies of aspects.

To take a simple example, let us look at the case of the
aspects between the Sun and Mars. Reference to the ephemer-
is will soon show that the conjunction between Sun and Mars
is a far more frequent aspect than the opposition. Every two
years, more or less, Sun and Mars are within 5° of an oppo¬
sition for roughly eight days; every two years they are within
5° of a conjunction for, on average, about 38 days. Thus the
conjunctions are over A 1 fa times more common than the oppo¬
sitions. The reason is easy to see.

The situation is shown in Fig. 44. When the Earth and
Mars are in line on the same side of the Sun, there results an
apparent opposition. The Earth, because it is close to Mars
and moves faster than that planet, passes Mars quickly and
Mars appears to go retrograde. Thus the period for which
they are close to a straight line relationship with the Sun is
very brief. When Earth and Mars are on opposite sides of the

Sun, they are far distant from each other and move round the
Sun in the same direction like two wrestlers looking for an
opening. Consequently, this relationship is longer lasting.

]

Thus if a large number of random angular relationships
between Sun and Mars were plotted over a period of time,
there would be far more conjunctions than oppositions and one
would see a 1st harmonic in the aspect circle of over 60%
amplitude. This means that the frequency of the conjunction is
60% greater than the average frequency of all angular relation¬
ships taken together; the frequency of the opposition is 60%
less. This 1st harmonic effect is much smaller in the geocentric
relationship of Sun and Jupiter and smaller still in the relation
of Sun and Saturn. Even so the Sun-Saturn aspect cycle will
show a 1st harmonic roughly in the order of 10% amplitude.

In the case of the solar aspects to the inferior planets
Mercury and Venus there is no longer a full circle of relation¬
ships but a sort of pendulum effect. Mercury and Venus ap¬
pear, viewed from the earth, first on one side of the Sun,
then on the other. In these two cases the conjunctions are
brief in comparison to the duration of their positions when
near their maximum elongations from the Sun. Thus a distri¬
bution pattern in relation to the Sun is formed as in Fig. 45.

FREQUENCY
OF

ASPECTS

A—— DEGREES FROM SUN- 4 pig. 45

If this seems a little complicated when planets are con¬
sidered in aspect to the Sun, whose apparent motion is nearly
regular, it will easily be seen that when the various planets
with their different speeds and stations are considered in re¬
lation to each other, all sorts of harmonic patterns are set up
between them especially when the birth data to which they
relate is drawn from a relatively short period of time, say two
or three decades.

No adequate study has been made of the harmonic pat¬
terns produced by the relationships of the various planets; the
job is essentially one for the computer. Until we have pro¬
grammed a computer to give us the harmonics for the inter¬
relationships of planets for particular periods, we shall not be
able to make much progress in this field. It is easy to see that

one cannot claim significance for the occurrence of over four
times as many Sun-conjunct-Mars aspects as Sun-opposition-
Mars in a particular sample of births, (astronomical factors
alone would produce such a discrepancy in any random sam¬
ple spread over a couple of decades), but it is not so easy to
know exactly w'hat harmonic patterns should be allowed for in
other cases. Perhaps the best we can do is to confine ourselves
to aspects between one of the planets and the Sun (which at
least cuts out the retrograde factor in one of the two bodies)
and to pay special attention to the short wave harmonics since
these are unlikely to be produced by the orbital motions in¬
volved.

Consider therefore the aspects of the Sun to Saturn in the
nativities of 972 nonagenarians, being all those men and wo¬
men in the four volumes of the publication Who Was Who
(1889-1950) whose dates of birth and death were given. 2 All
achieved their 90th year and rated an entry in Who’s Who
during their lifetime, so that their lives had been crowned by
personal achievement and exceptional length of days. Surely
among such people w'e should find the Sun vigorously aspected.
In particular, since everyone knows from Gustav Holst s Plan¬
ets Suite that Saturn is “the bringer of old age,” the aspects
between Sun and Saturn ought to provide us with an inter¬
esting result.

Now', in conventional terms, if there are 972 positions of
the Sun in relation to Saturn, and if we take the number of
cases w'e have of Sun w'ithin 5° of the principle aspect points
— conjunctions, oppositions, trines, squares and sextiles — we
would have a total of eight 10° areas in the 360" circle. We
should expect to find 972 x 10 -f- 360 = 27 cases in each
10° area in a random distribution. Fig. 46 show's in diagrama-
tic form the totals for each of these aspect areas.

I’he sextiles yield a total of 50 aspects, the squares 50,
the trines 57 and the conjunctions and oppositions 60. The
expected total, by contrast, would be 54 or 2 x £7. Thus we
have an observed total of 217 aspects against an expected total
ot 27 x 8 = 216. None of the aspects shows a significantly
high score, especially in regard to the slight astronomical bias
in favour of the conjunction in relation to the opposition. Nar¬
rowing the orb to less than 5® makes no improvement to the
level of significance. An examination in the same terms of the
solar aspects to Mars, Jupiter, Uranus, Neptune and Pluto
yields a very similar result — nothing of the least significance.

It was this observation which led me in 1958 to write the
following: ‘So for these men w'ho had reached the top of their
various professions ol fields of activity, whose lives had been
crowned by success and recognition and by exceptional length
ol days, their natal Suns (representing the ‘life force’) showed
no more than a chance tendency to gather vigour and enter¬
prise irom Mars, or bouyancy and zest from Jupiter, or dili¬
gence from Saturn, or originality from Uranus, or insight and
imagination from Neptune, or intensity and penetration from
Pluto! The maps of so many assorted jellyfish would evidently
have done just as well. 3

1 his is the kind of disappointment or indeed, shock, which
i Ik- student who conscientiously investigates the traditional con-
* <-pts of astrology is liable to receive, although not all investi¬
gations of conventional teachings arc quite so disastrous. Even
ilie resourceful Michel Gauquelin has declared, after making
studies of traditional aspects, that he can find no scientific
loot hold in the astrological doctrine of aspects. Certainly a
M'epiic who set out to show r that astrology was bunk and w r ho

obtained such a result after so much labour, would rub his
hands, publish his findings with joy and say ‘I told you so.'
The usual answer from astrologers is to blame statistics and
say that their science is not accessible to such methods.

For those who love truth this will not do. What wc have
is an example of the cardinal error of all research, the error
of deciding beforehand what the truth of the matter is, and
then setting out to prove that one is right.

The best approach to all research is to ask an open-ended
question. In this case, the question is: ‘Are there such things
as aspects and if so, what are they like?' Or, if one is satisfied
on that score, one should ask in this particular case: ‘What is
the characteristic relationship of Sun and Saturn in the nativi¬
ties of nonagenarians?’ In either case, one leaves it to the re¬
sults to give their reply.

In response to such a question one naturally begins by
listing the angular relationship of Sun to Saturn in each and
every chart, whatever that relationship may be (they are all non¬
agenarians!), arranging them in a 360° grid (see Appendix 1).
This basic flexible arrangement is used for examining the dis¬
tribution in terms of different harmonics.

Ideally one arranges for a complete harmonic analysis by
computer, but, because of the uncertainties described above
concerning orbital irregularities, no aspect distributions have
been analysed in this way. Therefore, one must adopt some
simple tactics to see what can be found. The following is an
example of such methods:

First, since we suspect that major harmonic patterns may
be set up by the geocentric relationship of Sun and Saturn we
will ignore the largest harmonics and start with, say, the 60°
sector. Remember that sectors now are sectors of the aspect
circle. The first sector will be the distribution of Sun in rela¬
tion to Saturn when, it is separating from that planet by 0° to
60% the second sector from 60 9 to 120° and so on round the
circle. For this preliminary skirmish we can conveniently take
our totals for the distribution of Sun in relation to Saturn in

blocks of 5°, giving us 12 totals for each 60° of the aspect cir¬
cle. We then collect our six sets of 12 totals together into one
run of 60°. Here are the actual totals with the resultant graph
shown in Figure 47. The first total (90) is the number of
times the Sun was in the first 5° after the conjunction and all
60° aspects. The second total is the number of times the Sun
falls between the 6th and 10th degrees beyond these aspects;
the third total refers to the 11th-15th degrees, etc.

90 83 103 78 72 69 84 64 98 69 85 77

Looking then at Fig. 47 we can see (1) that there is evi¬
dently a 60° wave, with an amplitude in the order of 10%
which we have inserted in what appears to be roughly the
right place; (2) that in religiously counting up the positions
which fall within 5° of the main aspect points we were in fact
missing all the fun since those are the very places where the
distribution is near to the mean, and (3) that if we compare
the first 30° with the second 30° there is evidently a repeating
pattern with a very high score at the third 5” total in each
half of the distribution.

With this in mind let us go a step further and put the
two halves of Fig. 47 together so as to get a clearer view of
ifir distribution in each 30°. Fig. 48a show's the result and 48b
shows that this pattern is very largely the result of a combi¬
nation of the 2nd and 3rd sub-harmonics of the 30“ period,
that is the combination of a 15° and a 10“ wave with ampli¬
tudes of roughly 7% and 10%. These are the 24th and 36th
harmonics of the aspect circle. Now we are certainly justified
m thinking that there are forces at work in this distribution
whic h are due to something more than chance. The third total,

201, against a mean of 162, is very high indeed. The conclu¬
sion we might draw from this is that the distribution is the
result of unsuspected astronomical factors due to the geocentric
relation of Sun to Saturn. However, if it depicts a significant
astrological relationship, then we need a new view of 'aspects'
which speaks a language based on harmonics.

We said earlier that we could only feel reasonably sure of
having eliminated astronomical factors when vve had found a
very short harmonic. Let us then get out our magnifying
glass, as it were, and ask what happens to, say, the quite
strong L0° wave when we look at the actual single degree to¬
tals in each 10° sector round the aspect circle. This will tell
us the story about short harmonics. For this wc must go back
to our 360-degree totals and add them up in 36 runs of ten
separate degree totals. This sequence of ten totals, which re¬
presents the relationship of Sun to Saturn in each 10° of the
aspect circle, is as follows. The first total represents the num¬
ber of times the Sun was within W on either side of an exact
conjunction or in each tenth degree measured from that point:

89 107 107 101 119 99 9. r > 109 82 64

If we draw these totals in graph form (Fig. 49) we can
see our 10° wave — the 36th harmonic of the aspect circle —
but there are also quite clearly three shorter waves superim¬
posed upon it. We can now sec that Lhe 10° wave is probably

nearer 12% than 10% as we estimated before, and although it
is rather difficult to judge the precise amplitude of our 3rd
sub-harmonic, that also appears to be approaching 12%. This
is a very interesting finding! This short wave is, of course,
3 x 36 or the 108ih harmonic, three waves in each 10°, in
other words, the Indian Navamsa measure of 3 1/3°.

What our subjects are distinctively supposed to have In
common is longevity, but as a matter of fact it is rather more
precise than this. All of them entered their ninetieth year but
because the death rate is very steep at this age the over¬
whelming majority of them died in the next three or four
years. We can say that we have here a large group of people
whose life cycle was just about the same.

The number nine (the Navamsa measure being one-ninth
part of a sign) is distinctively connected with the completion of
<i cycle. It may well be that in setting out to find the Sun-
Saturn relationship in long-lived subjects we have ended by
finding one of the pointers to the length of life — an item of
astrological lore lost to the West but probably better preserved
in India — namely the Sun’s position in the aspect Navamsa
cycle of 3 l/T*

!l is perhaps difficult for the student of orthodox astro¬
logical teachings to accept the idea that the conception of
aspects at 30° or even 15° intervals may be really rather crude
and primitive. But the truth must be that all divisions of the
i n clc have their significance and always the significance is to be
I'Oind m the symbolism of the number by which the circle is divided.

That learned and perceptive astrologer, Cyril Fagan, once
spoke of these Indian techniques based upon small-increment
divisions as “aspectarian verniers” 5 for measuring “micro¬
aspects.” This is only one of the many ways in which the
new approach to astrology in terms of harmonics promises a
reunion of the Eastern and Western traditions in astrology and
indeed, seems likely to illuminate Indian astrology for Indians
as much as Western astrology for Westerners.

Let us return to our example and to the 108th (Navamsa)
harmonic relationship of Sun and Saturn in our nonagenarians.
Have we really satisfied ourselves that this quite vigorous har¬
monic is not a freak result of the Sun’s relationship to the
stations of Saturn repeated over a long period? After reflecting
upon the apparent Sun-Saturn cycle, we might be almost cer¬
tain that this could not possibly be the explanation. But, if it
were not for one thing a lingering doubt might remain. For¬
tunately, there is evidence which settles the matter.

The startling fact is that in our 972 nonagenarians exactly
the same feature appears in the aspects of the Sun to Mars,
Jupiter and Uranus. The other planets have not been investi¬
gated. Fig. 50 shows this sequence of ten aspect-totals for the
solar aspects to the four planets, Uranus, Saturn. Jupiter and
Mars. At the bottom of the diagram the result for all four
sets of aspects are combined — a total of 3,888 aspect positions.

In this figure we have rearranged the sequence of totals so
that the first point in the graph is the Sun V application by
seven degrees to the exact conjunction (or one of the 35 other
points at 10° intervals round the aspect circle). The exact as¬
pect point is indicated. The phasing of the 108th harmonic is
very slightly different from one planet to another and other
harmonics may possibly be present in some cases. Nevertheless
the similarity is such as to give a perfectly clear and convinc¬
ing result in the combined totals as shown in the final graph.

Although one can conceive of such a feature as this 108th
harmonic appearing by virtue of astronomical factors in the re¬
lationship of the Sun to one of the planets, it certainly could
not appear in all of them from this cause, for their motions
are quite different. We can therefore say with confidence that
we have revealed a significant astrological feature. Moreover,
this feature has a very sound if unexpected symbolic aptness.

The main purpose of this chapter has been to show that
the same principles apply to the aspect circle as to the circle
of the houses and of the Zodiac and that (apart from a need
to assimilate the idea of harmonics itself), what is especially
required in astrology is the development of a full range of
number symbolism.

NOTES

1. See Chapter 19.

2. See Addey, John, “The Search for the Scientific Starting Point,’ 7
Astrology, XXXll (1958) nos. 2 & 3. Reprinted in The Harmonic An¬
thology, Green Bay, Win Cambridge Circle, 1976.

3. See reference in Note 2 above. These results have been worked over
by two other people to ensure accuracy.

4. Referring to the full harmonic analysis of the Sun’s distribution in the
ecliptic in these 972 nonagenarians it is interesting to note that, of the
180 harmonics, the 9th is the second strongest. There are many fasci¬
nating insights into number symbolism to be had from these analyses.
In this case there appear to be two especially important harmonic
series: the 9th and the 17th. l'hc strongest amplitude of any harmonic
is the 170th (10x17) at 16.2%. The second strongest is the 9th,
13.8%. The third strongest are the 153rd (9 x 17) at 13.5% and the
171 si (9x19) at 13.5%. The 18th (2x9) is 13.1%. The symbolism
of prime numbers such as 17 is of profound interest.

5. A vernier is an adaptation used bv surveyors for making fine measure
ments of angles.

RECAPITULATION

The reader who has reached this point in the book will
probably be longing for some relief from the positions taken
up by astrological “iron filings” and our attempts to sec be¬
hind these patterns the principles which govern significant
astrological relationships in the horoscope. He deserves such a
respite. In Part Two of the book we shall leave the drudgery
behind for a while and try to demonstrate some of the impli¬
cations, in terms of practical horoscopy, of the principles so
far adduced. But before doing this it is right that wc should
look back briefly at what has been learned so far and try to
sec where it has been leading us.

Astrology is full of circles and circular motions. Three of
these arc usually given precedence: first, there is the circle of
the Zodiac, that is, the circle of the ecliptic in which the po¬
sitions of the planets in their orbits arc determined. Secondly
there is the circle of Lhe houses, that is, the diurnal circle of
the planets as they rise, culminate and set each day. Thirdly
there is the circle of aspects as a planet moves from its con¬
junction with another body round to the opposition and back
again to the conjunction.

In each of these circles the astrologer studies the relationship
of one factor to another and places an interpretation upon that relation¬
ship. Without these relationships and the significance he attach¬
es to them, Lhe astrologer could not even begin to interpret
a horoscope. It is true that each of the planets has its own
symbolism and significance regardless of its relationships in the
chart, but each planet is in every horoscope. What distin¬
guishes each particular horoscope is the relationship of one
factor to another in these circles of reference.

In the first case he attaches a meaning to the planet’s
position in the ecliptic. He says it is in such-and-such a sign,
for example, and in so doing he is saying in effect that it has
a certain relationship to the point 0° Aries. In the second, he
attaches a certain meaning to the house position of the planet,
and in this he is relating this to the Ascendant or some other

point in the diurnal circle. In the third case he ascribes a cer¬
tain meaning to the angular relationship of one planet to anoth¬
er. Thus everything in astrology depends upon how we view
these relationships and the precise basis of the symbolism
which we use to interpret their meaning in terms of qualities.

All these relationships fall within a circle of possible relation¬
ships. Therefore the thing which the astrologer needs to under¬
stand above everything else is the symbolism of the circle and
its divisions. The circle is the most comprehensive of symbols.
In itself it represents the idea of a whole, and in its largest
significance the idea of infinity and eternity.

Everything in the realms of manifestation owes its existence
to the dynamic power of Ideas. Ideas in their highest aspect
are spiritual wholes or unities. Such wholes, existing above
time and space, arc yet the formal causes of everything in
manifestation.

What is unitive above is multiplex below. Thus Ideas ex¬
press themselves objectively through parts, the parts represent¬
ing in their inter-relationships the outworking of the subjective
potentialities of the whole from which they are derived, each
fulfilling or expressing a function or aspect of the parent unity.
The Idea, as a unity, manifests as the entire circle of Lhc or¬
dered relationships of the parts. In the realms of time it mani¬
fests as the whole cycle of the stages of unfoldment of the
Idea by which the inherent potentialities are aciualiscd in the
order of succession.

In the horoscope this scheme of relationships of the one to
the many, of the whole to the parts, and of the parts or as¬
pects of the whole to each other is expressed through the
symbolism of the circle and relationships within the circle. This
scheme functions on many different levels.

To see how the symbolism of the circle is adapted to the
interpretation of different elements in life we must recognise
that all living things and their existences are organised as hi¬
erarchies. Every unity, when it proceeds into manifestation,
unfolds an orderly succession of subordinate principles whereby
it expresses its innate characteristics. FirsL come the most basic
and fundamental movements towards life and then, as these
arc developed and differentiated, a wider and wider range of
powers and principles emerge,

The human soul, w'hich is the unity behind the individual
life, has three basic faculties: the will by which it addresses it¬
self to the good, the “heart” or desire nature by which it ad¬
dresses itself to the beautiful, and the mind or intelligence
whereby it addresses itself to the true. We see these from
babyhood, for the newborn infant first asserts its existence, de¬
sires food and warmth and discriminates, through its senses and
instincts, what it wants from what it does not want.

In time each of these faculties expands and diversifies. The
primary self-assertion of the will develops into a w-ider range of
impulsive, elective and purposive functions, each with its own
subordinate aspects. The basic desire nature responds to an
ever increasing range of attractions, aesthetic susceptibilities
and aspirations of a more and more spiritual nature. So too
with the intelligence; from elementary forms of sense contact
and instinct it moves to more and more deliberative kinds of
knowledge and finally to reason and true intuition.

In all this we see the picture of a unity-in-diversity, a
whole which manifests its life through a hierarchy of powders
and principles in which the lesser, more particular and special¬
ised is subordinated to the greater, more universal and gener¬
al. We see the same thing in the human body where different
kinds of cells are subordinate to different kinds of tissues, tis¬
sues to organs, organs to physiological systems and these to
the life and economy of the w'holc body. We see it again in
society where the individual is part of the family, the family
of the civic, the civic of the national and the national of the
global unit. At each level all sorts of other groups and sub¬
groups operate, consciously or unconsciously, in different fields,
and all are interwoven in the complex life of mankind.

Between each of these hierarchical structures there is an
intimate parallelism. The human body and human society are
constituted as they are because man himself is constituted as
he is. Under each head there arc corresponding elements at
every level. Furthermore, both man and the cosmos are made
“in the image of God”, that is to say they embody the same
powders and principles, the one microcosmically and the other
macrocosmically. Thus there are correspondences between man
and nature at every level.

The ideal way of expressing these correspondences is by
the symbolism of number, for every unity unfolds into multi¬
plicity through identical stages, each in terms of its own nature.
Every monad proceeds to a duad, thenec to a triad, a tetrad,
and so on. It is above all, as Pythogoras and others taught, to
the first ten numbers that wc must look for the basic key t.o
this kind of symbolism. After these ten principles all further
proliferation is a repetition in the sense of new combinations,
upon other levels and in different contexts, of those original
principles. But in all these different contexts and upon all lev¬
els the underlying reality of (he whale and (he parts remains. For
this reason the symbolism of (he circle and its sub-divisions is
adapted to all possible circumstances and to every conceivable
requirement ol astrology as “the algebra of life.

In practical horoscope this symbolism of the circle and its
sub-divisions manifests in the way wc have tried to show in
Part One of this book. Every circle in astrology represents a
particular whole or unity. The primary divisions of each circle
into three or two or five, etc. yields a number of equally
spaced points round ihe circle as in Fig. 19. This represents
the division of the original whole or unity into its appropriate
parts or subordinate qualities. The points themselves represent
the points of maximum expression of the particular subordi¬
nate qualities. The sections of the circle between the points
represent the range of possible relationships of a planet to these
subordinate principles, whether positive or negative, showing
how the planet passes through a whole sub-circle of relation¬
ships within the main circle. For these reasons, Fig. 19 is one
of the most important diagrams in the whole book, as it pro¬
vides the key to almost everything wc have been trying to say.

This gives us the idea of circles within circles. As each
circle and sub-circle is divided and sub-divided into ever small¬
er units, we gradually move symbolically down the scale of a
hierarchy of principles from the more universal to the more
particular. Every student of astrology with any feeling for the
subject already understands this truth in general terms. It is
the basis of many familiar astrological concepts, such as the
Zodiac itself. The principle is emphasised here because it is

important that the student, knowing the principle, should be
as clear as possible in his mind as to how the principle is
expressed in terms of the symbolism of the circle.

Thus we have tried to show in Part One of this book
how astrological positions, when studied in great number, re¬
veal the idea of a fluctuation between positive and negative
phases of divisions of any circle of relationships. It is a funda¬
mental principle that the number by which the circle is di¬
vided holds the key to the interpretation of the relationship
involved.

11 THE NAVAMSA CHART

If one asks a Hindu astrologer to interpret one’s horo¬
scope he will almost always begin by calculating at least two
charts and probably more. First he will have the radical.
Rasi, or sign chart giving the natal positions as ordinarily
understood; but in addition he will calculate the Navamsa or
'ninth division’ chart (pronounced Na VAM-Sha). This chart
is one of 16 sub-charts, the Shodasavargas or sixteen-divisions,
which he can call upon. Strictly speaking there are 15 sub¬
charts for the natal chart is counted as the first of the 16.
Each of these has a special application to the life of the na¬
tive. 1

The way in which the Navamsa or ninth division chart is
calculated is very simple. Each sign of the Zodiac is divided
into nine equal sectors of 3°20’ each. The first sector, extend¬
ing from 0° to 3*20’ Aries, is then allocated to Aries; the
second, from 3°20’ to 6°40’ Aries is allocated to Taurus; the
third, 6°40’ to 10° is given to Gemini, and so on round the
circle. By the time one has reached the end of the sign Aries
one has got nine small Navamsa divisions allocated from Aries
to Sagittarius inclusive. The first 3°20’ of Taurus then goes to
Capricorn, the second to Aquarius and the third, taking us to
10° Taurus, goes to Pisces. Thus the first 40° of the Zodiac
have been made into a new little Zodiac of twelve miniature
signs.

One then starts again with Aries at 10° Taurus and con¬
tinues round the circle, each 40° yielding another set of twelve
signs. Thus, since 40° is one ninth part of 360°. one ends by
having nine little Zodiacs extending in due order through the
original twelve signs. In other words, by dividing each sign
into nine equal divisions and then making these into groups of
twelve signs one is in fact dividing the whole circle into nine
Zodiacs. (See Fig. 51).

So wc arc back with our idea of circles within circles.
Fuller details of methods of calculating the various harmonic

charts are given in the next chapter, but we can use Fig. 51
to show quite simply how the positions in the radical chart
are recalculated so as to give their positions in the Navamsa
chart.

Let us suppose that the natal Sun is in 11°06’ of Aries.
We can see from Fig. 51 that this will fall in a Cancer divis¬
ion of the Navamsa circle for this extends from 10“ to 13° 20’
Aries. How far into that little Cancer sign has the Sun
moved? The division starts at 10® Aries and the natal Sun is
at 11’ 06’ Aries, so it has travelled 1°06’ into the mini-sign.
But the new Zodiac has been created by collapsing the original
Zodiac into nine smaller Zodiacs, so in order to find the new
position of the Sun we must multiply 1*06’ by nine. Thus
9 x 1°06’ gives us 9 D 54’ Cancer as the position of the Sun in
the Navamsa chart.

Suppose the radical Moon was in 7°.50’ Taurus. Refer¬
ence to Fig. 51 shows that this falls in a Pisces sub-division in
the Navamsa circle. How far has it moved into Pisces? The
sub-division starts at 6°40’ Taurus so, at 7’50’ the Moon has
moved 1°10’ into that sub-division. Thus 9 x 1°10’ ~ 10°30’
Pisces, which will be the Moon’s Navamsa position. Therefore
the Sun at 9°54’ Cancer will be in trine to the Moon in
10°30’ Pisces.

If the radical Jupiter was at 17°48 of Gemini it would
have moved 1"08’ into a Pisces sub-division, or more precisely
9 x 1*08’ = 10" 12’ of Pisces. Thus in the Navamsa chart we
have Moon conjunct Jupiter. This is another way of saying
that they are just about 40° apart, from 7°50’ Taurus to
17’48’ Gemini, in the radix.

We can now see that this old tradition in Hindu astrology
of creating sub-cycle charts is really a practical application of
the idea of harmonics. Each division of the circle into a sub¬
ordinate number of cycles or circles has its own significance
derived from the symbolism of the number by which the di¬
vision is made. By dividing up the original circle of the Zodiac
into a number of lesser circles one is, in effect, considering the
distribution of the natal positions within the sub-circle of a
particular harmonic.

It is true perhaps that the Indian astrologer may think of
this technique as one in which each sign is divided by a par¬
ticular number, in this case nine. But in point of fact, what
lie has done first and foremost is to divide the whole circle by
nine and then divide each of those nine divisions into a little
Zodiac of twelve signs. It may be that this secondary division
into twelve signs has a symbolic validity, lor the number
twelve relates to the mundane order of things; thus the subor¬
dinate division by twelve has the effect, so to speak, of earth¬
ing" his original division of the circle by nine, for the pur¬
poses of interpretation.

From another point of view it is arguable that the pur¬
pose of the secondary division into mini-signs is primarly as a
system of nomenclature whereby one identifies points in the
sub-cycles which would not otherwise have a name. In Fig. 52
we have divided our circle into nine parts and the encircling
wave-form shows the resultant cycles of the 9th harmonic. Let
us suppose that in a particular horoscope there are planets
X, Y and Z. They look as though they fall at about the same
point in the 9th harmonic wave so that they would be con¬
junct in the Navamsa chan, but how can wc make an accurate
comparison of their positions? Only by having some system of

measuring exactly where they fall in each sector. The tradi¬
tional Indian practice is to divide each of the nine sectors into
twelve signs so that we can recalculate the positions of X, Y
and Z in a familiar system of coordinates — namely, the Zo¬
diac — and so identify their positions exactly.

Fig. 52

We have said that each of these ‘harmonic charts’ as wc
might call them, has its own symbolism as applied to the life
of the native, based upon the number by which the whole
circle is divided — that is the number of sub-cycles within the
complete circle. Indian astrology has its own traditions regard¬
ing the appropriate significance and symbolic application for
each of its Shodasavarga charts. For example it is said Lhat
one of the primary meanings of the Navamsa chart is that it
describes the marriage partner. This is an interesting allocation and
deserves some comment.

Most of the basic Shodasavarga divisions are related to
departments of life with which one might expect them to be
connected on the basis of zodiacal symbolism. Thus the Hora
or 2nd harmonic chart is said to signify wealth and possessions,
the 3rd (or Dreshkhana) brothers and sisters, the 4th (or Cha-
turthamsa) home and property, the 6th, health and so on. Bui
it is the 7th (or Saptamsa) chart which is said to indicate
children and the 9th or Navamsa which is said to show ihe
marriage partner. Let us, then consider the symbolism of the
number nine.

The reason why Pythagoras and other philosophers of
antiquity attached so much importance to the first nine num¬
bers derives from the teaching that everything unfolds from its
innermost idea, which is pure potentiality, to its outermost
expression, which is its manifest, actualiscd perfection, through
nine stages. * This complete actualized perfection in which
all the parts are finally brought into harmony is called the
cntclechy of a thing. Of ‘entelcchy’ my dictionary says: “In
Aristotelian and Scholastic philosophy a term used to signify
ihe perfect form attained by anything by reason of which it
actually exists and realises its Lrue function; the actual as op¬
posed to its potential cause.”

In Greek mythology the idea of the “entelechy” may be
considered as represented by Apollo. His emblem is the lyre
because he brings all things into perfect harmony. He is like¬
wise said to be the God of Medicine because the purpose of
the medicinal arts is to heal, to make whole and to bring the
parts into harmony. Like his twin sister, Artemis, he was also
handy with a bow and arrow and was sometimes the bringer
of death, signifying the end or completion. Closely associated
with Apollo and celebrated with him at Delphi were the Nine
Muses of whom he represents the unifying principle. Apollo
and the idea of entelechy, the realisation of fullness of form,
arc thus represented by the number ten. The Nine Muses re¬
present the nine forms of inspiration corresponding to the nine
stages of unfoldment by which the Soul is brought to perfec¬
tion. The correspondence with the nine choirs of angels in
Christian thought, associated with the stages of the Soul’s
ascent leading to the mystical marriage with its Ideal, needs
no emphasis.

There are many other parallel examples of this ninefold
order in the myths, legends and religious doctrines of the
world. The point to notice here is the close association of the
number nine with, among other things, the Ideal to be realised
and with Completion. The number nine, though not identical
with the idea of cntclechy, yet represents the gateway to that
lutiilment.

Thus vve see some indication of why the number nine,
and so the Navamsa chart, should be connected with the mar¬
riage partner. Every man and woman, searching consciously
or unconsciously for his or her Ideal in the larger sense, also
tends to chose a marriage partner who, in some way, repre¬
sents this ideal. The student can experiment on his own chart
and that of his married acquaintances to see how well this
Navamsa chart describes the marriage partner. Elsewhere ’
the author uses the charts of Elizabeth Barrett Browning and
Robert Browning as an illustration. My own experience with
the Navamsa chart in this context is that the correspondence
between the Navamsa and the marriage partner and his or
her chart is often very well shown. At other times it is not
very obvious and one has to consider in what way the Na¬
vamsa is descriptive of the marriage partner or, in some other
way, of his or her ‘ideal’.

A phase that is sometimes used of the Navamsa chart is
that it stands in relation to the radical map “as the fruit to
the tree.” The aptness of this phrase in relation to the sym¬
bolism of the number nine as described earlier in the chapter
is obvious. The bringing forth of the appropriate fruit re¬
presents the culmination and expression of the life of the tree.

Thus, where one can give an astrological identity to some
aspect of the life work of an individual (for example, where
one has the horoscope of a firm or an organization of some
sort which is the expression of a man’s ideals or life’s purpose),
that chart will often be found to correspond to his Navamsa
chart.

There are some men who, because of their single-minded
labours for some great purpose or ideal, are later described as
“the father” of this or that. Thus, Ataturk Is said to be the
father of modern Turkey, James Watt is described as the
father of the steam engine and so on. Such cases should always
provide good examples of the relationship between a man’s
Navamsa and the horoscope of whatever embodies the ideal he

worked for or the objective served. Here, for example, (Fig.
53) are some of the positions in the Navamsa chart of Enrico
Fermi together with the positions at the time of the atomic
blast over Hiroshima. Fermi was in charge of the project
which led to the first release of atomic energy in December
1942 and so directly to the manufacture of the atomic bomb/

Enrico Fermi, '‘Father’’ of atomic energy: Navamsa positions (inner
circle) with positions for the Hiroshima atomic blast (outer circle).
Fermi’s radical Pluto 18.40 Gemini, Uranus 13.29 Sagittarius (See
Note 4).

The Navamsa charts are nearly always of great interest in
relation to a man’s life’s work even when they are not super¬
ficially just what one might expect, and they certainly respond
to transits though I have not tested them for directions. For
example, Fig. 54 shows Winston Churchill’s radical' 1 and
Navamsa charts. The Navamsa is not at first sight an obvious
expression of war leadership but closer inspection shows many
apt features. Apart from the tenth house Pluto and the opposi¬
tion of Navamsa Mars to radical Moon, the rising Venus in
Libra (which falls on the radical Mars/Jupiter midpoint) is not
inappropriate. The reason why the Venus/Libra clement is so
often strong in the charts of men of war is because war is in
the nature of an attempt to make an ‘ adjustment ’ in the inter¬
ests of justice. This is a Libran function, the familiar juxtapo¬
sition of the sword and the scales.

Winston Churchill, radix on the left, Navamsa chart on the right

The most interesting feature of the chart is the strength
of the third house. This is thoroughly apt (notice again the
conjunction of Navamsa Mercury with the radical Sun) for in
many respects it was Churchill’s mastery of the written and
spoken word which enabled him to exercise so great a sway in
his time. In his literary output his History of the English Speak¬
ing Peoples is an obviously appropriate “fruit” of this chart. But
it was his oratory which made so great an impact. Perhaps no
one who did not live through the experience can realise or
imagine how great a force Churchill’s wartime speeches were.
Looking back one suddenly realises that one has not really
heard very much oratory from the politicians since, only a
rather uninspiring drone. The 9th harmonic conjunction of
Moon and Saturn in the 3rd is characteristic of this gift for
articulate expression.

On 10 May, 1940 when Churchill took over the national
leadership, the Moon and Mars were opposite this conjunction
at 26° Gemini. His first act was to sit down and write the
famous speech which he delivered to Parliament with Mars
still at 27° Gemini, promising only “blood, toil, tears and
sweat.” “You may ask: What is our policy? It is to wage
war!” It was a speech which riveted the nation’s resolve, It
was of this time, too, that he said he felt as if he were 'walk¬
ing with destiny,’ a nice glimpse of Saturn in the third in
Sagittarius. The transits on 7 May, 1945 when Germany
signed the surrender showed Mars at Aries (Cusp 7). In

July when Churchill was defeated in the general election,
Neptune transitted the Navamsa Ascendant.

Contacts between positions in these sub-charts and radical
positions always strengthen their importance. Thus, with Na¬
vamsa Mars in Aquarius opposite radical Moon, one recalls that
Churchill’s mother died following an amputation after she had
broken her shin . Why should this show in the Navamsa? Pos¬
sibly because it was, for Churchill, an important experience
of death. ^

In this chapter we have done no more than provide an!-
introduction to the idea of the harmonic chart and its signifi-'
cancc, using the 9th harmonic as our example. In Indian'
astrology there are elaborate rules for the interpretation of
these charts. No doubt a close study of the Hindu doctrines
with their sometimes complicated rulership systems will help us
to understand more fully how to interpret and generally get
more out of these charts. A great deal can also be learned
by students from their own studies provided that the principle
behind each chart is understood. Thus our purpose at present
is to give the basic instruction as to their calculation and the
general symbolic content underlying each. In this way astrolo¬
gers can make their own observations and experiments and so
help to fill out our knowledge of the use and applications of
the harmonic chart.

NOTES

L. See Harvey, Charles, “Harmonics and Hindu Astrology,” Astrological
Journal (Astrological Association, London), XII (1970), no. 2. Shortly
to be included in The Harmonic Anthology, Green Bay, WI.: Cambridge
Circle, 1976.

2. See Addey, John, Astrology Reborn, Note 2, Chapter 1, above.

3. Addey, John, Astrology Reborn, p 15.

4. In the first edition of this book. Fig. 53 showed the Navamsa posi¬
tions of Lenin in relation to the U.S.S.R. chart. Serious doubts
about the reliability of those data necessitated a new illustration.
The Navamsa chart of Enrico Fermi (b. 29 Sept. 1901, 19.00
hours. Rome; see Gauquclin collection of birth data) was examined
in relation to the Hiroshima explosion (6 Aug. 1945, 8.15 am) and
this yielded a fair illustration of the principle involved.

5. He was born, according to a letter written by his father on the same
day, at 1:30 a.m. on 30 Nov. 1874, at Blenheim, Oxfordshire. I have
adopted a time about 2 minutes before this and the Ascendant is
calculated for local time.

t •

THE FIFTH HARMONIC CHART

We have seen in. the preceding chapter the general idea
of calculating the harmonic chart and have gained some in¬
sight into the symbolism of the 9th harmonic. In this chapter,
proceeding somewhat arbitrarily, we shall do the same for the
5th harmonic. In the case of the Navamsa chart we divided
the circle into nine smaller Zodiacs. In the case of the 5th
harmonic we are envisaging the circle of the natal chart as
divided into five smaller Zodiacs, each of 72° and each com¬
prising twelve signs each 6° in extent. In Indian astrology this
is known as the Panchamsa chart.

First of all let us deal with the question of how to calcu¬
late from the radical chart the positions in the 5th harmonic
map. The principle is the same for all harmonic charts. There are
three chief ways of dealing with the calculation:

1. The easiest way is to obtain The User’s Manual of the
Astrologer’s Guide to the Harmonics,~ where tables of conversion
are given for each harmonic up to the 13th together with the
method of using them.

2. Alternatively, one can take a large chart form with the
circle marked in degrees and make a conversion tool for one¬
self. Simply divide up the circle into five Zodiacs, each of 72°
as illustrated in Fig. 55, and then divide each Zodiac into 12
signs of 6°. Mark the point where each sign begins and ends.
One can then see where a planet in the original circle of the
signs falls in one of the 5th harmonic Zodiacs. One must then
ask how many degrees and minutes it has moved into its new
5th harmonic sign and multiply this by five. Thus in the dia¬
gram the Sun is shown at 20^23’ Taurus; it has thus moved
2*23’ into the 5th harmonic Sagittarius, which begins at 18°
Taurus. 2*23’ x 5 = 11*55’ Sagittarius, and this is the new
position.

3. The third method lends itself, with one small adapta¬
tion, to use with an electronic calculator. It consists in multi¬
plying the absolute longitude (i.e. from 0° Aries) of the radical
position by the number of the harmonic desired (in this case,
the 5th). The nearest multiple of 360 is then subtracted from
the answer. The remainder gives the new harmonic position in
absolute longitude.

This may sound a little complicated but it is quite simple
in practice. Let us suppose that we wish to translate a radical
Moon position of say, 23*33’ Scorpio into the 5th harmonic:

Radical Moon 23*33’ Scorpio = Long. 233*33’

Multiply by 5 x5

1167*45’

Subtract 3 x 360 (Table Two) 1080

Remainder 87*45’

87°45’ = 27*45’ Gemini = 5th harmonic Moon

Those who have an electronic calculator will need to ex¬
press the radical positions in degrees and decimals of a degree.
For this, remember that 6’ = 0.1*, so the multiples of 6’ will
be easy to see: 12’ = 0.2°, 18’ = 0.3°, 24’ = 0.4° and so on.
For minutes less than 6, the following little table can soon be
memorised (Table One). Table Two gives some multiples of
360. 3

101

Table One

Table Two

6’ = .1"

1. 360

7. 2520

15.

5400

5’ = .0833

2. 720

8. 2880

18.

6480

4’ = .0667

3. 1080

9. 3240

20.

7200

3’ - .05

4. 1440

10. 3600

25.

9000

2 : = .0333

5. 1800

11. 3960

30. 10800

V = .0167

6. 2160

12. 4320

To take one more example: the Sun in Fig. 55 is in
20°23 : Taurus, thus:

Radical Sun 20°23’ Taurus = 50°23’ Longitude
18’ = .3

5’ = .0833 (Table One)

23’ = .3833

So: 50.3833
x 5

251.9165 251 = 11° Sagittarius

.9 = 54’ (9 x 6’)

.0165 — r (Table One)

.9165 = 55’

Therefore, the new position = 11"55’ Sagittarius

When all the radical positions including the Ascendant
and M.C. have been recalculated in the 5th harmonic, these
positions are all put together in one map. Exactly how one
then arranges this map is a matter of personal preference to
the individual astrologer. Probably most students will place the
new ’Ascendant’ (or first house cusp, since it no longer repre¬
sents an actual Ascendant) on the left of the chart as usual,
and then use equal house divisions for entering other positions
in the circle. The M.C. can, of course, fall anywhere in the
circle. It no longer represents an actual Midheaven but is a
symbolic point equivalent to the M.C. in significance. If the
radical Ascendant and M.C. are 72° or 144° apart, they will,
of course, be conjunct in the new chart. So much for the
actual calculation of the 5th harmonic chart. Now' to its sig¬
nificance.

102

Strictly speaking, in order to understand the symbolism of
number, one needs to start at the beginning and to unfold, step
by step, the succeeding principles as they emerge from unity
into multiplicity. To trace this unfoldment at all adequately
really requires a separate work, therefore in these pages we
must be content to deal in a limited way with the symbolism
of a few' numbers in more or less piecemeal fashion. The sym¬
bolism of every number may be derived from an examination
of its composition, that is to say what its parts are and how
the number is produced from them. The smaller the number,
the simpler its composition and the more universal its signifi¬
cance.

The number five is the sum of two plus three and of one
plus four.' 1 This gives us the clue to two of its primary
meanings. In the first place the Pythagoreans said that five
w-as the number of marriage because it represented the union
of the first female number, two, and the first male number,
three. (The number one was regarded as the unity prior to all
division into male and female.) Secondly, as one plus four, five
may be taken to represent man as the artist-soul at work amid
the four elements of nature. Sometimes it is said that five is
the number of man himself and this is true because he is in¬
deed the lord of the realms of manifestation. But this is not
the whole truth for man, made in the Divine Image, contains
all numbers within himself and, in his many aspects and
attributes, exemplifies them all.

Since the number five remains the same number no matter
how we view its composition, it follows that the two interpre¬
tations given above must amount to one and the same thing.
Although theoretical discussion may seem rather tedious, it is
worth exploring this matter carefully because a clear under¬
standing of what is involved will help us to see just what the
5th harmonic chart really signifies and what it does not.

The number two represents the idea of matter, not objective
concrete matter (which belongs to four) but metaphysical mat¬
ter, the idea of matter as the potentiality of manifestation.
And the number three represents form itself, the idea w'hich
‘in-forms’ the matter of a thing and acts as its formal princi-

103

pie or cause. Now if we consider what man as the artist at
work in the world does, he does just this: he puts together form
and matter. This is the characteristic activity of the artist. Every
artist (of every kind of human art — that of the sculptor, the
town planner, the cook, the politician, the doctor) envisages an
idea or formal principle and, wishing to express it, asks him¬
self how he can make it a manifest reality. In order to do
this, he must first discover in his mind what material he needs
and so put together, subjectively, the form and the idea of the
matter. Notice that this process is accomplished by mind, for
it is mind which can subjectively take into itself the idea or
formal principle and the idea of the matter and so unite
them. Hence, note a relationship between five and mind.

Since it has a bearing on what we shall later have to say
about other numbers, it is worth digressing slightly to point
out that when the artist has done this, he has not yet pro¬
duced the finished work of art. He knows what he wants to
express and he knows what materials he needs in order to do
it, but he has not yet done it. To do this he must actively
put together the form (three) with the objective matter (four).
This constitutes the act of creation proper (seven = three +
four). Five is the number of the artist himself and six, which
I call the number of rhythmic activity, represents the work in¬
volved in applying the appropriate ways and means to the
practice of the art. Seven also represents the influx of inspira¬
tion whereby the purely human labour is crowned and made
fruitful by a higher sanction. “Six days shalt thou labour” . .
but . . “remember the Sabbath day, to keep it holy.”

To revert again to the number five, we can say that it
represents the union of male and female and in this sense
marriage as such, and the putting together of form and mat¬
ter and in this sense art. But the practice of art, as we have
indicated, belongs to the number six. The number five and
the 5th harmonic chart will tell us what kind of art and what
kind of marriage. It describes how a person brings together,
subjectively, form and matter, male and female. His marriage
is thus an expression of a larger process with wider implica¬
tions in his life: how he brings together and reconciles the
masculine and feminine (heaven and earth) in himself.

104

The question of exactly how, in terms of astrological sym¬
bolism, the 5th harmonic chart shows one’s relationship to the
order of art is a matter which lies open for investigation. All
these ideas are subject to further research, for we are still at
the beginning of our study of harmonic charts. One way, how¬
ever, is evidently through the involvement of the principal
factors such as Sun, Moon, Ascendant and M.C. (especially
perhaps Sun and M.C.) with the planets which are character¬
istically associated with different forms and fields of activity. In
addition to this, the subsidiary movements, functions and
alignments within a particular field of activity will be shown
by common degree areas being tenanted in the 5th harmonic
charts of those who contribute to that activity. For example,
it would be presumably true to say that Saturn and Uranus
are the planets which ’rule’ astrology as such (although there
are different ‘schools’ and different kinds of approach to the
subject which no doubt involve the sub-influences of other
planets). Thus we should expect Saturn and Uranus to be
strongly linked to the principal factors in the charts of astrol¬
ogers.

Consider then the charts of some leading figures in British
astrology. The late Brigadier Firebrace was the first President
of the Astrological Association, the author was his successor
and Charles Harvey the third President. Ronald Davison has
been President of the Astrological Lodge of London since 1951
and the great Charles Carter, his predecessor, was President
from 1922 to 1951. On the left below are given some of their
radical positions, using only Sun, Moon, Ascendant, M.C.,
Saturn and Uranus. On the right these positions are transposed
to the 5th harmonic:

Brigadier Firebrace

RADICAL 5TH HARMONIC

1. Sun 24.07 Leo 0.35 Aries

2. Moon 6.14 Taurus 1.10 Libra

3. Saturn 23.50 Leo 29.10 Pisces

4. Uranus 19.02 Libra 5.10 Capricorn

5. Asc. 12.12 Capricorn 1.00 Pisces

105

The Author

6. Sun

7. Moon

8. Saturn

9. Uranus

10. Asc.

11. M.C.

Charles Harvey

12. Sun

13. Moon

14. Uranus

15. M.C.

Ronald Davison

16. Sun

17. Moon

18. Saturn

19. Uranus

20. Asc.

Charles Carter

21. Moon

22. Saturn

23. Uranus

24. Asc.

RADICAL

23.51 Gemini
5.49 Gemini
6.08 Virgo
5.40 Pisces
6.00 Leo
11.58 Aries

0.44 Cancer
0.01 Aquarius
24.14 Taurus
6.26 Taurus

19.17 Capricorn
25.52 Gemini
12.10 Gemini
6.32 Aquarius
0.29 Aquarius

7.24 Taurus
17.18 Cancer
12.24 Libra
17.00 Libra

5TH HARMONIC

29.15 Taurus
29.05 Aquarius
0.40 Gemini
28.20 Scorpio
0.00 Capricorn
29.50 Taurus

3.40 Cancer
0.05 Gemini

1.10 Capricorn

2.10 Libra

6.25 Aries
9.20 Gemini
0.50 Aries
2.40 Cancer

2.25 Gemini

7.00 Libra
26.30 Virgo
2.00 Sagittarius
25.00 Sagittarius

To these we ought to add at least one representative of
astrology in the United States. Since Mr. Dane Rudhyar is
one of the best known American astrologers, here are his
positions:

25. Sun

26. Moon

27. Saturn

28. Uranus

29. Asc.

30. M.C.

2.08 Aries
24.38 Aquarius
6.11 Scorpio
18.36 Scorpio
13.30 Sagittarius
12.00 Libra

10.40 Aries
3.10 Libra
0.55 Aries
7.55 Gemini
7.30 Libra
0.00 Sagittarius

If we now collect up these 5th harmonic positions, num¬
bered from 1 to 30, and put them onto one circle of 360°
(Fig. 56) we can see that they all fall near 0° of the cardinal
or mutable signs, mostly within very narrow orbs. About two
thirds of them fall within 2 1 // even after transposition to the
5th harmonic which means that the radical orb to the sensitive
points in the Zodiac is only Vf. One cannot deny that this is
impressive. Of course we have restricted ourselves to certain
positions only, but almost all of the above have other positions
near the appropriate points. For example. Brig. Firebrace,
being a soldier and a diplomat and therefore skilled in the
arts of war and peace, has 5th Mars at 1.15 Capricorn and
Venus at 29.45 Leo, closely involved with his Sun, Moon and
Ascendant.

It is true that we have not listed six out of a possible 36
positions in our tally, but we catch two more (Carter’s Sun
and Harvey’s Saturn) if we include 0° of the fixed signs. Of
the remaining four positions, two (the M.C.’s of Carter and
Firebrace) fall in the 5th chart at 20" of Libra and Aries, re¬
spectively. These degrees are probably significant since there
are two ordinary degree areas usually associated with astrology
(28 s Leo/Aquarius and 22 s Cancer/Capricorn) which, when
transposed to the 5th harmonic, both turn into 20° Aries/Libra.

107

106

A great deal has been written about degree areas including
those related to astrology but no one, to my knowledge, has
ever pointed out this very strong tendency for astrologers to
have planets very close to 0°, 6°, 12°, 18° and 24 9 of the signs.
When transposed to the 5th harmonic these points all come to
0° of the signs. A glance through the above radical positions
will make this clear.

Incidentally it will be seen that in all the above cases
there are close squares and T-squares involved in the 5th har¬
monic positions given. This indicates that the relationship of
those concerned with astrology was one involving hard work,
duties and responsibilities. Possibly those who have facility in
i astrology but whose relationship to it is more one simply of

enjoyment will have the same degree areas and the same con-

f «

i !• tacts with Saturn and Uranus, but with trines and sextiles

predominating.

1 must not leave the impression, in showing this strength
of certain degree areas in the charts of astrologers, that the
degree areas are more important than the planets involved. I
believe it is the 5th harmonic involvement of Saturn and/or
Uranus which is so often the mark of the astrologer possibly
because such contacts have the effect of deepening the mind. If
we switch to other professions or activities we shall find the
Sun, etc. involved with the planets appropriate thereto.

To give a completely different example, consider Lester
Piggott, 5 the English jockey, six-time winner of the Derby
and one of the great performers of our day. He has a quintile
of Jupiter-Neptune (for horses) and a quintile of Mars-Mercury
(for strength and dexterity). These are linked to each other by
semi-quintiles and to the Sun by the 18° aspect, giving the
familiar T-cross in the 5th harmonic chart: Sun square Jupi¬
ter-Neptune and Mars-Mercury. Here we-have an entirely dif¬
ferent but thoroughly appropriate group of planets to show the
type of activity involved. In this way we see how the 5th har¬
monic chart reveals the special art or activity to which a per¬
son is drawn or adapted. It shows his position , as we have said,
in the order of art.

108

There are some radical charts w : hich are very strongly
dominated by the quintile series of aspects; the charts of
Mozart and Hitler are often mentioned in this connection.
These produce 5th harmonic charts which are characterised by
very pronounced complexes of conjunctions and oppositions.
What are we to say of them? Perhaps the most important
thing we should notice is that both destiny and inclination
seem to combine to make such men immensely single-minded in
one field of activity. In these cases the 5th series dominates
everything else and the whole chart is mobilized in one direc¬
tion, leading to power and wholehearted activity in the chosen
field. This would be true of Hitler and Mozart. Apart from
that, of course, the planets involved show- the character and
perhaps something of the flavour of their work. Thus Mozart
has (5th) Ascendant with Sun, Mercury and Mars, Venus with
Moon, and Jupiter with Uranus — very buoyant and sparkling.
Hitler has a rather messy 5th harmonic conjunction of Ascen¬
dant with Saturn, Neptune, Moon, Jupiter and Pluto — a
somewhat obsessive combination.

Just as the 5th harmonic chart describes the nature and
purpose of the art practiced, so in relation to marriage a sim¬
ilar description is given, including any unusual circumstances
surrounding the wedding itself. The marriage partner as such
is not described although there is often a strong link with the
partner’s chart. As an example one might take that of King
Edward VIII who renounced his throne in 1936 in order to
marry Mrs. Wallace Simpson. Ilis radical positions are given
as follows: Sun 2°22’ Cancer, Moon 3°57’ PUccs, Mercury
28°36’ Cancer, Venus 23°18’ Taurus, Mars0°25’ Aries, Jupiter
18°23’ Gemini, Saturn 18°25’ Libra (Sta Dir.), Uranus 11°33’
Scorpio, Neptune 14°00’ Gemini, Pluto 10°43’ Gemini, Ascen¬
dant 3° Aquarius, M.C. 4° Sagittarius,

Fig. 57 shows the 5th harmonic chart set up by equal
house from the new Ascendant. This could scarcely be more
telling. The Sun is square Neptune showing renunciation and
withdrawal; Mars square Saturn forms an exact T-cross with
the sensitive radical Sun in Cancer. The array of four male-
fics, which would be described as ‘elevated' in a radical chart,

109

do not help. Venus (trine Uranus) is in the 7th house, how¬
ever, showing the personal happiness which came to him
through his marriage but note that Venus in Sagittarius (for¬
eign countries) is ruler of the 12th house (of exile) and like¬
wise Jupiter, lord of the 7th, is near cusp 12. After his mar¬
riage, he was, of course, more or less obliged to live abroad
for the rest of his life. This one might say is how marriage
affected him personally. If the chart is set up by equal house
from the new M.C., showing more particularly how the mar¬
riage affected his position in the world, Pluto now falls near
cusp 5 (which represents, like Leo, the idea of kingship) and
Mars and Neptune are also in the 5th house, being square
the Sun, now lord of M.C. Altogether a very apt chart.

So far in this chapter I have managed to avoid using the
word ‘creativity’ in relation to the symbolism of the 5th har¬
monic, but not without a struggle. In every aspect of number
symbolism one finds oneself* called upon, to make fine distinc¬
tions. Two things are often so closely associated that one may
easily fail to distinguish between them and so let them pass as
one and the same thing. We are up against such a difficulty
here.

110

Earlier in the chapter, we said that seven was the num¬
ber which represented the idea of creation. Yet wc have re¬
peatedly said that five is the number of man the artist and
that his characteristic function lies in putting together form
and matter. Is this not creativity? In a sense it is and I think
it is legitimate to regard five as in some senses the number of
creativity. Yet it would seem that the better keyword for the
number five, in this context, is ‘power’, including the power
to create, or as we shall see later, to destroy. (The question of
whether five or seven should be regarded as the number of
creativity amounts to this: do wc say that a man is creative if
he has lots of good ideas as to how things should be done or
made (two + three), or do we reserve this adjective for the
man who not only has the good idea but actually puts it into
practice (three + four) and so produces something?)

An analogy may be drawn from marriage and sexual un¬
ion. An important symbolic element in the marriage ceremony
is the placing of a ring on the finger and the consummation
of the marriage likewise involves the idea of penetration. In
sexual union the numbers five, six and seven are all involved
in the ‘act of creation’: the coming together of male and fe¬
male and the act of penetration (five), the rhythms of sexual
union (six, the number of rhythmic activity) and the orgasm
of creation (seven) which requires a more distinct element of,
in this case erotic, inspiration.

On this basis five may be said to represent the urge to
power which is the prelude of creation. This desire to domi¬
nate some kind of material applies to all forms of artistic activi¬
ty but the use of the words ‘potent’ and ‘impotent’ in a sex¬
ual context usually refers to this aspect of sexual union and
reinforces what we have been saying. This undoubted connec¬
tion of the number five with the idea of power brings us to
another aspect of the 5th harmonic chart, and that is its rele¬
vance in assessing sexual proclivities and aberrations. We shall
refer to this again in Chapter 14 where wc consider what new
light harmonics shed upon the meaning of aspects, but it
hardly needs pointing out that the urge to power will be in¬
volved in sado-masochistic tendencies and the like. That power
which is potentially creative can also be used destructively.

Power as such is good, and likewise the urge to obtain
power, for nothing can be accomplished without it and every

111

man rightly exercises power in some sphere. To ask what kind
of power one exercises is simply another way of asking what
kind of art or arts one practices and how they are performed.
Nevertheless it seems to be true that those who rise to power
in the world in the conventional sense tend to have strong
appropriate positions in the 5th harmonic chart. At the time
of writing Gerald Ford recently took office as President of the
United States. His accession to this high office was unusual in
that he was the first and only President not to have been
voted into office either as President or Vice-President. Thus
fortune, as it were, dropped the Presidency into his lap and
the element of popularity also evidently played a part. It is
not surprising, therefore, to find that his 5th harmonic chart
shows a close conjunction of Jupiter and Venus (radical aspect
144°02’) in very close trine to Uranus conjunct Pluto (radical
aspect 143°54’). Both conjunctions form a grand trine with the
5th harmonic Ascendant and a sextile to the M.C. (see Fig.
58). 0

To sum up we have suggested that the 5th harmonic chart
shows the union of form and matter and of male and female.
It is therefore relevant to the nature and purpose of one’s
marriage, often linking up with the actual marriage horoscope
and indicating any special circumstances connected with the
marriage ceremony or unusual events of the wedding day. Sec¬
ondly, we have suggested that as the sum of one and four the
5th represents man's exercise of rulership or power over matter
and the manifested world. It is an indication of whatever ele¬
ment of lordship he may exercise in life and it especially
shows what art or activity he commands. This aspect of the
number five, incidentally, has an obvious connection with the

112

5th house and has, in general, a solar connotation which can
often be traced in mythology and traditional rites and customs
among mankind. Often one’s special art or activity relates to
one’s vocation or occupation, but where this is performed
merely to secure a livelihood and docs not represent any crea¬
tive impulse, the 5th harmonic chart refers more obviously to
one’s hobby. For example, in the case of President Ford the
grand trine at about 0° of the water signs links up with his
enjoyment of swimming. There are, of course, other aspects of
the number five which arc related to the foregoing but which
we have not specifically dealt with. Others we have only
touched upon, such as its relationship to mind and mental
characteristics. 7

NOTES

1. These 6° divisions were formerly known in the West as 'faces’.

2. The Catalog User Manual and Harmonic Index is the companion volume
to the Catalog of Harmonics in \\illiamsen, James S. and Ruth h..
Astrologer’s Guide to Harmonics, Green Bay, Wi.: Cambridge Circle,
1975.

3. Tables for converting minutes and seconds into decimal parts of de¬
grees and vise versa are contained in the Catalog User Manual of the
Astrologer’s Guide to the Harmonics, see Note 2 above.

4. For a further study of symbolism of the number five see Addey, John,
“Fivefold divisions and sub-divisions in Astrology,” Astrological Journal
(Astrological Association, London), Xll (1970), no. 2. Also included
in The Harmonic Anthology, Green Bay, Wi.: Cambridge Circle, 1976.

5. Born 5 Nov. 1935. I have no time but believe it is on record.

6. A letter from the White House to Ann Davis of Cherry Hill, N.J.,
states that Gerald Ford (then Leslie Lynch King) was bom at 12:43
a.m. on 14 July, 1913, Omaha, Nebraska. 1 have adopted a birth
time just after 12:41. The full radical positions are given in Note 6,
Chapter 16.

7. For further interesting observations on the number five and its sym¬
bolism see Jones, Daphne, “A Pythagorean Approach to Astrology,”
Astrological Journal (Astrological Association, London), XV (1973),
no, 4.

113

OTHER HARMONIC CHARTS

The studcnL who has grasped the principle of the harmon¬
ic chart will by now have realised that there lies concealed
within the natal map an endless series of sub-charts each with
its own range of symbolic content and application. Just as we
have in the last two chapters divided the original circle of the
Zodiac into nine parts in the one case and five in the other,
so it can be divided by any other number or combination of
numbers and the resultant chart interpreted in the light of the
symbolism of the numbers involved. The full exploration of
these sub-charts is a task which lies in the future. Our main
purpose in this book is to indicate the general principle, show¬
ing how to deal with the calculations and providing a few
pointers to the symbolism involved.

The general principle itself is not at all new for not only
is it embodied in the Shodasavargas of Hindu astrology, hut
also the recent introduction in the West of the so-called 90°
dial and the 45° dial, popularised by the Eberlin school of
astrology, is simply an application of this principle. In other
words the 90° dial (in which the planetary' positions in each
90° arc put into one circle) has the effect of showing relation¬
ships in the 4th harmonic and the 45° dial, similarly, in the
8th harmonic. I believe that these two dials have proved so
popular and useful because the numbers four and eight have a
special reference to outward events and conditions. Or if pre¬
ferred, they refer to the stimulus which circumstances provide
to the actualising of inner potentialities as a result of the chal¬
lenge of events.

In this sense the number four is connected with the ‘ma¬
terial cause’, to use a term from classical philosophy. In terms
of the life process this means that when two factors are in a
square relationship or arc brought into a square relationship
by some directional movement, they show the appearance of
‘external’ conditions in the life which provide the possibility of
realising inner potentialities and making them manifest. It is
only by the practice of the different virtues that one achieves
self-mastery, but one cannot realise the virtues of courage or
patience or temperance or anything else in a vacuum, but

114

only in circumstances which truly require us to be courageous,
patient, etc., hence the importance of the number four in
introducing us to hard conditions which alone enable us to
aetualise certain qualities.

This element belongs not only to the square aspect, as
such, but appears wherever there is a division of the circle by
a number which has four as one of its factors. Thus a square
aspect in a 90 5 dial or 4th harmonic chart is a ‘16th’ aspect,
or a square of the square, in the radical chart. The num¬
ber twelve tras both three and four as factors and therefore
the 30° aspect has in it something of the difficult nature of the
number four and something of the enjoyable nature of the
number three. Similarly, the manifested or mundane world
in which we live, of which the number twelve is symbolic, is
both a hard school in which wc have to learn to unfold our
potentialities and yet, at the same time, a magnificent game
which is a source of enjoyment.

The reason why the number four, as represented by the
square aspect for example, seems to us a difficult or unpleasant
feature of life is not so much because it involves an effort of
will, for all positive actions are good and enjoyable in them¬
selves. Rather it is because of the element of uncertainty which it
brings with it. It challenges us to do something which we do not
know whether we can do or not — until we have done it! Then
if we have met the challenge successfully, we are just as
pleased in retrospect with our squares as we are with our
trines! Perhaps more so, for there seems to be something of
solid value about the results.

The number three and so the 3rd harmonic chart repre¬
sents form as opposed to matter and it is the formal principle
of a thing which makes it what it is and imparts to it its spe¬
cial qualities. Without going into the esoteric complexities of
the inner constitution of Man, we can say in very general
terms that every individual man has a formative principle
which is the source of his own unique existence and character¬
istics. A great deal could be written about this subject but we
will content ourselves here with noticing that all defects of
health which are not inherited necessarily arise from defects in
this formative principle. For this reason the 3rd harmonic chart

115

has much to say about the health, although, because we tend
to think of health in bodily terms we usually look to the num¬
ber six for such information. Notice that the number two gives
us the objective expression of a thing, thus two times three or
six tells us about the health as expressed objectively in the life
of the body. This is something with wdiich we are already fa¬
miliar through the significance of the sixth house and the sixth
sign.

The number seven and the 7th harmonic chart are inter¬
esting, if only because seven has been somewhat neglected in
conventional astrology. This is not altogether surprising for it
is a difficult number to pin down. It is an awkward number
to deal with in terms of divisions of the circle and also some¬
what elusive to interpret. We have already suggested that it
has some connection with sacred matters, with one’s creations
and creativity and with inspiration and one’s receptivity there¬
to. To this we may also add that it is evidently connected
with the unitive and mystical aspect of things and with whole¬
ness and the idea of fulfillment and completion, although not
in the same sense as applies to the numbers nine or ten.

Inspiration is, by definition, something which is breathed
into the life from without (or from ‘above’ if one prefers that
term), thus apparently giving to the limited human powers
and faculties an added dimension. In this sense, inspiration as
such lies outside the horoscope. Yet we shall probably be on
the right track if we think of the number seven as representing
the kind and degree of one’s receptivity to inspiration. The
direction in which it is sought and our capacity to focus it in
our work and even to impart it to others may also be repre¬
sented by seven and indicated in the 7th harmonic chart.

The horoscope of Winston Churchill, for example, in
Chapter 11, shows the Sun in close septile aspect to Mars. The
septile aspect, one-seventh of the circle, is 5T25.7’ approxi¬
mately, and Churchill’s Sun-Mars is 5T08’. If we regard ma¬
jor aspects as those which divide the circle by the numbers
from one to ten (or twelve), then this is easily the strongest of
Churchill’s solar aspects. We can see that this accords well
with his life for it was the condition of war which inspired
Churchill and brought out his special genius, and although his

116

wartime leadership has been criticised on some scores, no one
seems to question that he was able to impart a dynamic in¬
spiration to the nation and to the allied cause. (A close septile
in the natal map gives a conjunction, of course, in the 7th
harmonic chart).

The fact that aspects in the septile and semi-septile series
are difficult to spot unless one is looking for them has meant
that they have seldom received the attention they deserve, yet
the charts of creative people very often seem devoid of any¬
thing really noteworthy unless the fifth and seventh series of
aspects are observed. The Astrological Association’s collection
of 18 maps of artists, with biographical notes, in their Brief
Biographies 1 series provides some interesting studies. We shall
have more to say of these in the next chapter when consider¬
ing what new light harmonics throw on theVhole subject of
aspects.

The best way of being sure that one does see all these in¬
teresting aspect complexes in the maps of creative artists or
anyone else is of course to set up the 5th and 7th harmonic
charts. When this is done one not only sees the 5th and 7th
series of aspects and their subdivisions in regard to the natal
charts, but one also often finds that the charts of artists in a
particular tradition — such as, say, impressionist painters — are
linked by common degree areas and the aspects of particular
planets. This occurs in just the same way as we have shown
in relation to the positions of astrologers in the 5th harmonic
chart (see Chapter 12).

David Hamblin, a member of the Astrological Association,
has suggested, for example, that composers in the romantic
tradition tend to have distinct groupings in the 7th harmonic
chart which resolve into conjunctions in the vicinity of 0° Can¬
cer in the 28th harmonic. He points out that the first three
composers in the collection of Brief Biographies referred to above,
Beethoven, Berlioz and Debussy, all show complexes in the
neighbourhood of 20°-25° of the cardinal signs in the 7th har¬
monic chart, as shown in Fig. 59. These yield conjunctions
near 0° Cancer in the 28th, or the 4th of the 7th. It is not
suggested that these positions show musical ability, as such.

117

but rather that they indicate a certain sympathy in the con*
tent of the music of these composers, that they belong to a
certain epoch and that their art is rooted, proximately or re¬
motely, in the romantic revival. Of the other three composers
given in this collection, Delius, Ravel and Schumann, Schu¬
mann has Mercury, Uranus and Neptune, Ravel has Uranus
and Neptune, and Delius has the Moon in these areas.

There are two things of particular interest here. First and
foremost, note that it is part of the philosophy of the doctrine
of harmonics in astrology that one should ask: Into what har¬
monic must the chart be reduced to bring all the planets concerned into
a conjunction? Thus ah the squares in the 7th harmonic shown
in Fig. 59 are brought together in the 28th harmonic (four
times seven). This suggests the recurring manifestation (four)
of a certain type of creative work (seven) or musical form.

The second thing to note in this case is that it is the
major and outer planets which are so much involved, especial¬
ly Uranus and Neptune. This suggests, what every astrologer
knows intuitively, that there are what might be called ‘histori¬
cal’ rhythms underlying the births of the great exponents of
particular art forms. Since all temporal rhythms follow the
same principle whether long or short, the use of the word
‘historical’ here is purely relative, indicating longer time inter¬
vals due to the slower movement of the distant planets. This
link between an artist’s creations and the 7th harmonic chart
agrees, incidentally, with the Indian tradition which relates
the Saptamsa (or 7th chart) to one’s children. This is a topic

118

we have not touched upon but the student can verify for him¬
self by comparing the 7th harmonic chart of parents and off¬
spring.

To refer to a different aspect of this matter I believe that
the contacts in the 7th harmonic chart provide some indication
of the conditions required to stimulate creative work and also
of the character of the creative labour itself. One might take
the case of Sun conjunction or opposition Saturn in the 7th
harmonic. There is evidently a paradox here which often ap¬
pears where Saturn is involved in the radix with the self-ex¬
pressive powers. Saturn is the planet which distinctively gives
actual form and in relation to the expressive powers (for exam¬
ple where Saturn occupies the third house) one can almost
always see one of two things happening: either Saturn seems
to impose an obstacle, making self-expression difficult in some
way, and so producing taciturnity (or even a stammer or some
other impediment to communication such as deafness), or else
it enables the native to give form and definition to his thoughts
with exceptional ease and fluency, producing the chatterbox or
gift-of-the-gab type.

So in relation to the act of creation, the Sun with Saturn
in the 7th chart either makes creation a real labour or bestows
exceptional ease or fluency. In the case of Beethoven (7th Sun
opposite Saturn in Scorpio) the extreme turmoil of his creative
labours is well known. Cezanne (7th Sun conjunct Saturn) also
laboured over his painting; he abandoned one portrait after
over a hundred sittings. In contrast, Schubert (7th Sun opposi¬
tion Saturn) possessed a degree of fluency in composition
which was quite exceptional; his ideas readily clothed them¬
selves in musical form. Here we see the two sides of Saturn’s
characteristic action.

In relation to the kind of stimulus or the circumstances
needed to induce inspired action of some kind one might con¬
sider the chart of Jim Clark, the world champion racing dri¬
ver (see Fig. 61, Chapter 14). Here we sec Jupiter to Venus
5l l /2°, giving a conjunction in the 7th harmonic. This might
seem a curious contact but when we find exactly tne same as¬
pect, Jupiter-Venus 51 1 /2°, in another world champion racing
driver, Jackie Stewart, we are driven to ask what sort of ele¬
ment in the personal make-up this contact indicates. One of

119

the important things about Venus-Jupiter contacts is that they
give a strong emotional charge which tends to seek thrills and
excitement. Can we therefore say that, whatever the connota¬
tion of other Venus-Jupiter contacts, in the septile range they
can give inspired judgments in conditions of speed and excite¬
ment? Jupiter and Venus are both planets of judgment, the
one through the judicial sign, Sagittarius, the other from the
sign of the balance. Think of the many sports in which this
could be an advantage.

We can see from this that aspects in the septile series are
connected, to use a modern phrase, with what “turns one on’’
or with the conditions in which one becomes receptive to some
form of inspiration. This, as we have said earlier, links the
7th harmonic with sexual activity, for one of the strongest
forms of inspiration in everyday life is the erotic inspiration.
This provides a horoscopic key to certain factors in the psy¬
chology of sex.

According to his biographers, for example, Ruskin was
jj one who suffered from sexual impotence. Here we have Mars-

j Saturn 51W so that Saturn would be conjunct Mars in the

l 7th chart. It is a well known aspect of sexual psychology that

f some people find it difficult to respond sexually unless they

« can, at least in some degree, act out the appearance of domi-

! nating or being dominated and even of inflicting or receiving

| pain or the semblence thereof. Perhaps such an element would

' be needed in the case of Ruskin’s Mars septile Saturn, but in

| his case the standards of his day, together with the refinement

of his own nature or other elements in the chart, would per¬

haps make this difficult or impossible. This aspect of the 7th
harmonic chart is mentioned for its relevance to a wide range
of phenomena in this field. 2

Finally, we suggested that the 7th harmonic was connected
with the mystical or unitive aspect of things. For example,
a Sun-Jupiter septile often tends to give an interest in mysti¬
cal philosophy. Mercury-Saturn might give an interest in the
mystical or symbolic aspect of numbers. In fact whenever a
person seems to be impelled by what is called the “mystique 1 ’
of a particular subject, I believe one can look for appropriate
contacts in the 7th chart.

120

It is precisely this ability to sense the mysterious “whole”
behind the parts of a subject which above all imparts inspira¬
tion; indeed, from one point of view, inspiration is no more
than the capacity to embrace intellectually the formative idea
or principle behind a thing and so to participate in the dy¬
namic energy which that idea imparts. This operates in every
field. “Courage,” said Clemenceau, “e’est des idees.” Shades
of Churchill’s Sun-Mars septile.

It is this connection between the number seven and the
“whole” which links it also with the idea of completion and
especially with recurring cycles of completion in time. There
are many fascinating examples of this tendency for temporal
processes to culminate in cycles of seven days, seven years,
etc., or their multiples, but this belongs to another subject.

To sum up, we have tried to show in this chapter that
the technique of reducing the natal chart to the different har¬
monics within the chart is a valuable adjunct to practical horo-
scopy. Each number has its own symbolism and therefore
each harmonic chart has a particular sphere of application.
This is a field of study which, like many others opened up
by harmonics, lies wide open for investigation. The great prob¬
lem, as we have often said, is the need for a much more
sound and comprehensive understanding of number symbolism
than is usually provided by the general run of books on nu¬
merology.

An understanding of the symbolism of particular numbers
can always be had from studying their composition. This
makes prime numbers very important for all numbers can be de¬
composed into prime factors. We already have some grasp of
the significance of the lower prime numbers but how is one to
arrive at tha symbolism of such numbers as 17, 19, 23, 29,
31 and so on?

First, of course, one can always consider how a number is
arrived at by addition. We have already given the examples
of five and seven as the sums of two and three and three and
four, respectively. But to help those who may be interested in
exploring this field further, the following working principle
suggests itself to the writer.

121

Numbers follow one upon another in orderly sequence.
Each one embraces all that has gone before it and adds one
more. Every prime number, with the exception of the num¬
bers one, two and three which stand apart, is equivalent to a
non-prime plus one. In this sense each number gives an ele¬
ment of unity to what has gone immediately before. Thus, if
we regard the number four as representing the four elements
of the natural world, we can consider man as the fifth element
in the universe who gives rulership and a certain crowning un¬
ity to it. We illustrated the same principle in relation to a
non-prime when considering Apollo and the Nine Muses. The
number ten follows upon and represents the unifying principle
of the nine which preceded it.

In Note 4 following Chapter 9 wc pointed out that the
seventeenth harmonic and its multiples were dominant elements
of the harmonics shown in the solar distribution of nonagen¬
arians. The strongest harmonic was the 170th (10 x 17) and
the third strongest the 153rd (9 x 17). Now the subjects of
these nativities all had a very similar life span. Wc have
already noticed the connection between the numbers nine and
ten and the completion of a cycle of unfoldment. Is it a coin¬
cidence that the number seventeen stands in the same relation¬
ship to the number sixteen (4 2 ) as ten does to nine (3 2 )? In
other words if ten represents the completion of the out-working
of the formal principle symbolized by three through all its
terms (3 2 ), then seventeen would represent the unifying prin¬
ciple of the outworking of the number four (4 2 ), the principle
of manifestation.

This will no doubt strike some readers as being somewhat
speculative. It is given nonetheless as a suggestion which
appears to be sound in principle to help those who may be
interested in the symbolism of prime numbers. The suggestion
is that we can deduce something of the idea behind each
prime number by considering the number it follows and then
asking what the structure of that number is, through its factor¬
isation. The succeeding prime number is regarded as having
certain rulership over the whole sequence of preceding numbers.

122

This chapter has been concerned with techniques of con¬
structing and interpreting harmonic charts. Through these and
similar methods wc have found a growing range of derivative
charts each based upon the radix but having its own specific
content and application.

NOTES

1. Russell, Lesley. Brief Biographies for Astrological Study (I. Arts), London:
Astrological Association, 1973. This work contains portraits (by Adrian
Turgd), drawn charts and potted biographies of artists, composers,
poets and writers.

2. Since writing this chapter a student has lent me a collection of charts
showing sexual imbalance and in every case the .ith or 7th harmonic
chart, and usually both, had strong relevant features.

123

NEW LIGHT ON ASPECTS

The student will not have failed to observe that in the
course of the previous chapters on the various harmonic charts
there was an increasing tendency to short-cut the actual calcu¬
lation of the harmonic chart by simply pointing to a particular
type of aspect in the radix, Thus if two planets are 72® or
144° apart in the natal map we know that they will be in
conjunction in the 5th harmonic; if they are 36° or 108° apart
we know that they will be opposition in the 5th. If the planets
are 51 l /'f, 103® or 154® apart we know that they will be in
conjunction in the 7th, and so on. Thus, in a sense, all that
we have said about the meaning of these harmonic charts we
have at the same time been saying about the meaning of
aspects.

This is all part of the unifying effect of the harmonic con¬
cept in viewing the component parts of the language of astrol¬
ogy. The more the student assimilates the idea of harmonics in
astrology the more clearly he will see that all the factors he
uses, whether divisions of the ecliptic circle, divisions of the
diurnal circle or divisions of the aspect circle, are based upon
exactly the same principles and, what is more, that what ap¬
plies to one must and will apply equally to the others.

If the student agrees that there are “degree areas” which
have a special connotation in the zodiacal circle he will begin
to realize that there are degree areas in the aspect circle
whereby certain unusual angular relationships between planets
have a certain specific association quite apart from the con¬
ventional aspect points. He will understand, too, that by the
same token there will be degree areas in the diurnal circle. If
he acknowledges that divisions of the aspect circle by the num¬
bers three, four, six, eight, etc., are related to effects based
on the symbolism of those numbers, he will begin to consider
what effects might be related to aspect divisions of the circle
which conventional astrological teaching ignores. He will ask,
furthermore, if such unusual divisions will not apply also to
points in the zodiacal and the diurnal circles.

124

Having noticed, say, that Churchill has the Sun one-
seventh part of the circle away from Mars and that this has
a certain appropriateness based on the symbolism of the num¬
ber seven, he may ask himself if there is not some significance
in the fact that Churchill also had Pluto at 2l°20’ of Taurus,
almost exactly one-seventh of the ecliptic circle from 0® Aries.
Having noticed that the number five is connected with power
and authority he may wonder if President Ford’s radical Sa¬
turn at 13® Gemini, almost a fifth of the zodiacal circle from
0® Aries, is not a pointer to the position of authority to which
he was raised, especially when it is noticed that the harmonic
chart for his 60th year (see Fig. 73) shows Saturn once more
in this identical position with an exact trine from the Sun.

In these and many other ways the doctrine of harmonics
has the effect of unifying and enlarging our understanding
through the analogies it reveals between the different facets of
astrological symbolism. Of course these analogies are already
recognised by the thoughtful astrologer, but a fuller exploration
of the harmonic idea has the effect of bringing them into
sharper focus.

Our purpose in this chapter is to pursue a little further
the idea of divisions of the circle in terms of aspects. In doing
this we shall not repeat all that was said about the symbolism
of those numbers already discussed in the preceding three
chapters, but those who are interested in gaining a deeper
understanding of such aspects as the quintile, septile and no-
vile can re-read at their leisure what has been said about the
5th, 7th and 9th harmonic charts fully assured that these
accounts will illuminate the nature of the corresponding aspects.

We mentioned that the number five was symbolic of the
power both to create and to destroy (mentioning the charts of
Mozart and Hitler as examples of each kind of action), so
there is no need to labour the fact that the quintile, biquintile
semiquintile and sesquiquintile aspects are frequently impor¬
tant features of the charts of those who enjoy the feeling of
power in some form or other (such as racing drivers, dictators,
etc.) or seek power (such as revolutionaries) or exercise power
or leadership (such as statesmen or others in authority) or lust
after and abuse power (such as gangsters and some other sorts
of criminals).

125

The Swiss astrologer, Dr. Hans-Jorg Walter, has made a
number of excellent studies of the quintile aspect. For example
in the Ebertin Kosmobio logical Yearbook 1974 he examines a con¬
siderable number of charts which are heavily loaded with
quintiles including those of the French revoluntionaries Robes¬
pierre and Danton, statesmen and politicians such as Poincare'
the racing driver Jackie Stewart, the Italian soldier-poet-
patriot Gabriele D’Annunzio, the gangster Caryl Chessman,
the murder victim Michael John Gregston and others. Else¬
where Walter gives the charts of Italian racing driver Alberto
Asccri and John George Haig, a famous ‘lust-murderer’, to use
the graphic German term. In the latter case not only was the
natal chart strongly characterised by quintiles but also the
charts for the times of his crimes and eventually for his exe¬
cution, carried out on the same day as the executions of a
group of Nazi war criminals. This certainly exemplifies the
destructive side of the quintile series. Happily the constructive
use of power is more common than its abuse and as well as
the more ordinate of the examples given above there arc plen¬
ty of examples of the quintile series to be found among crea¬
tive artists, writers and scientists, for example Einstein.

One very important derivative of the quintile series which
is almost entirely ignored, as a rule, is the third subharmonic
of the quintile, which gives us the aspect of 24° and its mul¬
tiples. This is the 15th harmonic, the third of the fifth or the
fifth.of the third. Fig. 60 show's the aspect angles involved. It
w'ill be seen that this series includes the angles of 72, 120, 144
with which w r e are familiar but also the angles 24°, 48®, 96®
and 168® which are not customarily used or understood. How¬
ever these are certainly important and can now be given a
quite definite meaning in the horoscope.

126

These aspects are indicative of the enjoyment of and facility
in some form of activity as shown by the planets involved. In
other words they show us what kind of power or what art or
activities (five) a person delights (three) in exercising. One can
think of them as trines in the 5th harmonic map and interpret
them in the light of what was said about that chart. This
must be seen in a w'ide context, for example a 24° aspect be¬
tween Moon and Venus might indicate someone who enjoys
cultivating the social graces, the art of the hostess, the art of
forming sympathetic and agreeable relationships, understanding
people and generally making the wheels of life turn smoothly.
This is a most important art.

Looking through the 18 nativities of artists, poets, musi¬
cians, etc. in the collection of Brief Biographies (I. The Arts)
published by the Astrological Association 1 we find many
examples of these aspects. One of the commonest is between
Venus and Jupiter which in its highest form represents the ex¬
citement of or the response to intellectual beauty as expressed
in artistic activity.

Here we have:

Beethoven Venus-Jupitcr 23®16’

Delius Venus-Jupiter 168° 33’

Schumann Venus/Mercury/Des. -Jupiter 48°58’

Blake Venus-Jupiter 47°58’

Van Gogh Venus-Moon/Jupiter 95°33’

Baudelaire Venus/Jupiter-Uranus/Neptune 95®12‘

James Joyce Sun/Venus-Jupiter/Neptune 95"21’

Besides these we have Shelley (Venus-Jupiter 72® 16’,
mediated by a 24® aspect to Mercury) and others w'here there
are Venus-Jupiter oppositions and squares in the 15th harmon¬
ic chart or where the two planets are related in this aspect
series through the meditation of another planet — in fact very
few of the 18 cases do not have some contact of this class.

127

To take quite a different kind of ‘art form’. Fig. 61
shows the chart of Jim Clark, the former world champion
racing driver (bom 4 March 1936, 3:25 p.m., Wester Kilmany,
Scotland). Here we have an interesting chain of 24° aspects
linking MC/Uranus-Mars - Sun - Mercury/Descendant which
gives, again, a good indication through the planets involved of
the sort of activity in which he found enjoyment and facility.

Horoscope of Jim Clark, former world champion racing driver, born
4 March 1936, 3:25 p.m. Wester Kilmany, Scotland (birth certificate)

It does not matter whether a person finds his enjoyment
in travelling to distant places (Neil Armstrong, Moon-Jupiter
167°13\ Mars-Jupiter 23°47’) or being an evangelist (Billy
Graham, Jupiter-Neptune 23°3T) or thinking (Bertrand Russell
Sun-Mercury 24°38\ Mercury-Mars 24°2T, M.’C.-Jupiter
24V2°) or fighting and planning military strategy (Churchill
Moon-Mars 46°57’, Mars-Neptune 168°07’) or astrology (Dane
Rudhyar, Asc.-Uranus 23°54’, M.C.-Saturn 24°11’), or simply
reorganising everything (Einstein, M.C.-Uranus 168“27’). These
aspects seldom fail to give some pointer to the sort of activity
enjoyed and they are well worth keeping an eye on.

128

Many students are misled by the term ‘minor’ aspect into
thinking that such aspects as this one are of small importance
in chart interpretation. I believe this to be quite mistaken; one
can reliably give them full weight in the interpretative field
provided that the orbs one allows are reduced in proportion to the size
of the angle. On these terms such aspects are just as rare and
just as significant as the so-called ‘major’ aspects.

At this point it is worth stopping to answer a question
which by now must be running through the mind of the read¬
er. What ‘orbs’ should one allow for this kind of aspect — and
for that matter, all other aspects? This question is worth care¬
ful discussion. In Chapter 9 we have shown that in actuality
the orb will be a variable quantity according to what har¬
monics are involved in any particular case, but for practical
purposes we need to find a working rule which will serve as a
guide in the ordinary course of chart interpretation. If we
combine practical experience with the picture we now have of
how these things work, I suggest that we can arrive at a good
working principle which covers all cases, even though it neces¬
sarily has an element of arbitrariness which cannot be entirely
disposed of except in the terms indicated in Chapter 9.

We know that in every harmonic, whether it be the 4th
harmonic of 90* or the 120th of 3°, one is really dealing with
one complete cycle. We can envisage the situation as shown in
Fig. 62a. In each harmonic any two factors pass into and out
of relationship with each other on the pattern of a wave form.
In 62a, planet Y is moving towards planet X. Throughout
the harmonic it has some sort of relationship to X, positive or
negative, but it is only at the top of the wave where the wave
flattens off that it briefly reaches and holds its maximum in¬
tensity and becomes a clearly distinguishable combination to
be reckoned with. Expressed in circular form the situation is
as shown in 62b.

129

In other words, if we suppose that no aspects were al¬
lowed except the conjunction, what orb should we allow in the
full circle of 360°? Let us suppose that we decided upon 12°,
remembering that al this stage we do not recognize any other aspect. It
would then follow that in the 2nd harmonic (i.e., the opposi¬
tion), when our wave is only 180° in length, our orb would
be only 6°, that is our original orb of 12° divided by 2. In the
3rd harmonic, the trine, the orb would then be 4° (12 -5- 3),
3® for the square (12 -r- 4), about 2 1 /a° for the quintile, 1® for
the semi-sextile and quincunx and 48’ for the 24° aspect.

Perhaps the consensus of opinion would be that 4® was
too small an orb for the trine and that 5® would be nearer
the mark. Then we must enlarge our original orb for the full
circle to 15®; this will give us 7W* for the opposition, 5® for
the trine, nearly 4° for the square, 3® for the quintile, nearly
2“ for the semi-square and 1® for the 24° aspect series or 15th
part of the circle.

The virtue of stating the problem and its solution in these
terms is that it brings home to us, unequivocally, the simple
proposition that the orb must diminish in direct proportion to the
number of the harmonic , that is the number by which we have
divided the circle to get our aspect. If one considers that 3® is
too much for the quintile and 1° too much for the 24° aspect,
then it must follow that 5® is too much for the trine. One
cannot have it both ways, and so one must arrive at a com¬
promise which one can assent to as applicable to all divisions.
If this general principle is accepted, the problem resolves itself
into a simple question of what basic orb one is prepared to
allow in the full circle. Tested against experience, as one goes
down the scale through the smaller and smaller aspects, the
12® to 15® 1 have suggested above seem about right.

It is always rather difficult to get people to change their
minds about something which has been instilled into them by
a hundred textbooks. However, the above presents a clear and
consistent basis for the determination of orbs in practice and,
with the proviso mentioned below, can be taken I believe as a sen¬
sible guide. An opposition with an orb of 8“ or 9® really is a
very weak one and so is a trine of 6® or 7®; such things may

be legitimately regarded as background influences but they are
not aspects to which one can sensibly give much weight in
interpretative practice. It is better to stick to the smaller orbs.

Let us then, for interest’s sake, list again the orbs which
would be permissible for the different aspects on the basis of

of 12°

and of 15® in

the full circle,

i.e. for the

conjunc

Angle

A sped

Division By

Orb (I)

Orb (2)

0®

Conjunction

12°

15®

180®

Opposition

6®

7® 30’

120“

Trine

4®

5°

90®

Square

3®

3® 45’

72°

Quintile

2® 24’

3®

60®

Sextilc

2°

2*30’

51V

2 ® Scptilc

1®43‘

2® 08’

45®

Semi-Square

1®30"

1°53’

40°

Xovilc

T20’

1°4()’

36®

Decile

1°12’

1°30’

30°

Semi-Scxtilc

1®

1°15'

24°

Quin-Decile

0®48‘

1“

18®

Vigmtilc

0°36’

0°45’

Needless to say any multiple of one of these aspects which
does not coincide with a more primary aspect counts as having
the same orb as its basic division. The orb of the Quincunx,
for example, is regarded as the same as that of the Semi-
Sextile of which it is the 5th multiple.

To make a list of this kind has its advantages and dis¬
advantages. One great advantage is that it enables one to
check one’s accepted notions of orbs for consistency. It is incon¬
sistent to want to have an 8® orb for a square and then refuse
to allow, say, a 3® orb for the 36“ or the 108® aspects. If the
latter is too wide (as I believe is the case) then so is the form¬
er, Undoubtedly what most students will quarrel with in our
list is the very wide orb which is allowed for the conjunction.
This is certainly something to give one pause for thought if
not misgivings, but it is worth while to try to look at such
things with new eyes occasionally. The reasonably acceptable
consistency in the rest of the list suggests that we should try

131

130

to sec what it is that is special about the conjunction and how
this wide orb should be viewed. Wc must remember, first,
that the conjunction is the most powerful and universal of as¬
pects, forming as it does a part of every aspect series and thus
having a proportionately wider connotation. Secondly, as ex¬
plained in Chapter 9, the force of the major aspects can be
viewed as deriving from the fact that they represent the points
where many harmonics are in practice Liable to coincide and,
so to speak, reinforce each other. In this sense the conjunction
which is the 1st harmonic aspect is unique in having a very
wide orb beyond that allowed to its nearest neighbor, the oppo¬
sition or 2nd harmonic. In other words, in allowing 12° for
the conjunction we must notice that only the first 6° is sup¬
ported by even one more harmonic, so that after the first 6"
the influence is relatively weak and general in character. Per¬
haps these observations will placate some of the criticism which
this feature of our List of orbs is likely to arouse,

The disadvantage of such a list is that it may cause one
to become inflexible. We spoke, earlier, about a ‘proviso’ in
applying this principle to determine what orbs should be al¬
lowed. The proviso is this. Every map is different and every
aspect is a case on its own. It is not that an aspect suddenly
ends when it reaches the limits of the orbs such as we have
listed, but that as a rule aspects with wider orbs will sink into
the background and become rather faint voices, so to speak,
in the chorus of the horoscope. But vve must recognise that
some aspects are stronger (and some weaker) by virtue of their
position in the horoscope. Some, though wide, w'ill agree with
other factors in the horoscope and so increase the existing ten¬
dencies, while others will be quite at variance with more im¬
portant factors and so will be entirely overshadowed. The good
astrologer already knows this.

More important still perhaps is the fact that some horo¬
scopes actually seem to be very short of aspects, and this is
not necessarily an enfeebling condition. It does mean, however,
that the few aspects that are there become the channels of the
whole life force and even those which are wide by ordinary
standards become important. Such charts are often easier to
interpret because of the concentration into a few well-defined
lines of development.

132

Consider for example the horoscope of the poet Shelley 2
shown in Fig. 63. One seldom sees a chart with so few as¬
pects. There are trines and an opposition to Pluto but the
really important aspects are the immensely powerful quintiles
between Sun-conjunct-Venus and Mars-conjunct-Jupiter which
gave him his tremendous mental power and turbulent poetic
fervour, making him something of a ‘rebel angel’ — and the
highly inspirational septile of Mercury-Neptune. To these we
must certainly add the wide 24° and 48° involvement of Mer¬
cury with the quintile group, for even though the orb is wider
than we have listed as appropriate to this aspect, in a map of
this sort it clearly plays a key role in providing an outlet for
the energy of this quintile. The same can be said in more
general terms of the wide bi-quintile aspects and quincunxes
to the Moon in Pisces.

133

Another advantage of having a definite principle upon
which to judge orbs is that it enables one to move with confi¬
dence into the sphere of micro-aspects which result from the
division of the circle by numbers above, say, 20. One such as¬
pect which must be important is the 27th part of the circle
(3 x 3 x 3). although we have no clear views as to the inter¬
pretation of this at present. This is an angle of 13 1/3° and Its
multiples. One would hesitate to apply this aspect because it
occurs 2(i times, in addition to the conjunction, in the circle.
Hut, provided one applies the rule given above concerning
orbs, its occurrence will be neither more nor less common in a
horoscope than any other aspect. In this case the orb will be
about 12° -s- 27 - 27 ! or 15° -r- 27 = 33' — say half a de¬
gree. As with all other aspects. Us action will be most pro¬
nounced where the orb is smaller.

Another issue which is likely to become a focus of interest
in the light of the idea of harmonics is the symbolism of as¬
pects based upon prime number divisions of the circle, such as
11, 13, 17 and so on. These will call for a greater measure of
research into number symbolism than seems to have been car¬
ried out in a truly philosophical manner in modern times,
although there may well be valuable studies of which the
writer has no knowledge.

In relation to these numbers one is often dependent upon
suggestive glimpses of earlier ideas. For example the old philos¬
ophers said that eleven was a number of 'excess' because it
went beyond die perfection of the number ten. I cannot say
what value there is in this idea although a student has drawn
my attention to two charts of alcoholics where the Moon-Nep-
tune angle fell in the eleventh scries of aspects (multiples of
32°44' approximately).

The number 13 is also interesting. It represents the one in
the midst of the twelve and so suggests the idea of spiritual(P) lord-
ship. Keith Critchlow in his valuable study of Order in Space 3
paints out that twelve spheres of equal size will exactly fit
round a central sphere of the same size so that all arc exactly
touching their neighbours. The aspects in the thirteenth series
are as follows:

27°42’ 55°23’ 83*05’ 110*46’ 138*28' 166*09' (orb about 1*)

134

Searching for representations of the number 13 in art,
literature, etc., one thinks of the Last Supper. This used to
be a favorite theme of artists, and perhaps still is, for Annigoni
is currently engaged on a mural of this scene. Leonardo da
Vinci’s painting is usually given pre-eminence because he evi¬
dently gave more thought to the whole subject. Interestingly,
Leonardo has a '13th’ aspect between Saturn and Venus
(138°2T — orb 7’). The aspects of Saturn and Venus are al¬
ways important in the maps of artists because they relate to
the effort to give shape and form to the beautiful. Considering
that I have only a small handful of charts in which to look
for examples there seem to be a lot of 13ths about between
these two planets: Blake 27°32’ (orb 10’), Mozart 27°30’ (orb
12’), Rupert Brook 55°52’ (orb 29’). Zola 82*00’ (orb 1*05’).
Could this be connected with the element of assymetry in art?
The number 13, after all, cannot be divided by 2 and is a
prime.

Closely associated with the Last Supper is the idea of
betrayal, Edward Elgar 4 treats this theme in his oratorio
The Apostles. 5 He has Saturn-Neptune 110*35’ (orb 7’) and
Thomas Hardy, 0 whose stories constantly show a preoccupa¬
tion with betrayal, also has Saturn-Neptune 55*52’ (orb 29').
Emily Bronte, another doom merchant, has Saturn-Neptune
83°33 ! (orb 28’). Van Gogh had the Sun on the mid-point of
Neptune and Uranus about 27 l A° from each; one thinks of
his religious mania. Perhaps it is a pity to emphasize a rather
negative factor such as the idea of betrayal when there are no
doubt important virtues associated with this scries of aspects
loo. The apparent association is mentioned as a basis for fur¬
ther investigation by others.

It is worth pointing out in passing that nowadays, when
many people are in a position to have charts calculated by
computer, it is a good idea to choose a programme which
simply lists the angles between each pair of planets as shown
below. This is no trouble for the computer and it enables one
to glance through the angles in search of aspects in a partic¬
ular series such as the one we have been speaking of, or
others which are difficult to spot such as the septiles. Compu¬
ter programmes which list the conventional aspects are not

135

:: This page is a typeset facsimile of a computer printout

nearly so useful. (I know that many people like to drasv lines
on the horoscope to indicate squares, trines, etc., but I have
always had reservations about this practice for the same reason.
In drawing attention to certain aspects it may also draw the
attention away from others which are often most important,
especially the quintile and septile series).

We can if we wish move directly into the world of micro-
harmonics proper. Strictly speaking, in terms of aspects the
circle is infinitely divisible and we are limited only by the
limits of observational accuracy. This is obviously something
for the more advanced student to consider, but, when the
German astrologer Theodore Landscheidt 7 speaks of the 1024th
harmonic (2 10 ), we need not feel that we are being too out¬
landish in looking for such intervals as the 125th (5x5x5).

Elsewhere" I have tried to show the nature of the link be¬
tween this (the 125th) harmonic and the senses, among other
things. If it is true that the 5th harmonic has a special con¬
nection with the mental or gnostic faculties — those by which
we know — then one can see that the senses, which represent
the outermost aspect of this system of faculties, might well be
shown by a subordinate division in the 5th series. Thus for
particular physical characteristics one may have to look some
way down the harmonic hierarchy. Ronald F. Harvey, whose
fascinating book The Grammar of Astrology 9 is teeming with
fertile suggestions for the philosophically and scientific minded
astrologer and who, as an osteopath by profession, has the
knowledge and experience to judge of medical issues, has
drawn my attention to numerous cases of high-numbered har¬
monics as they appear to relate to physiological questions.

To revert to the 125th harmonic, this gives an angle of
2°52.tF — a micro-aspect, one might say. 1 have tested this in
ten cases of blindness 10 with allegedly accurate birthtimes by
calculating the 125th harmonic chart 1 Tor each and looking for
afflictions to Mercury, which must certainly have relevance to
the sight. Only one out of the ten cases 12 failed to yield close
squares or oppositions from malefics in the circle of the 125th
harmonic. Here are the results in the other nine cases:

137

1. Mercury square Mars (orb 1’)

square Neptune (orb 3’)

2. Mercury square Saturn (orb 1’)

3. Mercury square Saturn (orb less than 1’)

4. Mercury opposition Neptune (orb less than 2’)

sesquiquadrate Saturn (orb 1’)

5. Mercury square Mars (orb 1’)

opposition Saturn (orb less than 1’)

6. Mercury square Mars (exact)

opposition Saturn (orb less than 2’)

7. Mercury opposition Uranus (orb less than 2’)

also in aspect to Mars square Saturn (orb

less than 1’)

8. Mercury square Neptune (orb L’)

semi-square Mars (orb 1’)

9. Mercury semi-square Mars (orb almost exact)

opposition Saturn (orb 2’)

It will be appreciated that with regard to these ‘aspects’
one is dealing with a complete circle of 2*52.8’ or 173’ ap¬
proximately, so that squares in this circle will represent an
interval of about 43’. In other words an orb of 1’ is equiva¬
lent to an orb of 2° in a full circle of 360®. The above test
cannot be considered exhaustive but it is convincing as far as
it goes. It suggests that in looking for pronounced physical de¬
fects one may have to examine high-numbered harmonic inter¬
vals.

One recognises that some astrologers will view an aspect-
angle of 2°52.8’, let alone a quarter of that, with a jaundiced
eye. Presumably not many will find room for it in practice.
However for those who are interested in researching specialised
problems in astrology this topic of micro-aspects deserves
mention.

Before ending this chapter, reference should be made to
tire “Catalog of Harmonics” in the Astrologer’s Guide to Har¬
monics 13 compiled by James and Betty Williamsen and pub¬
lished by the Cambridge Circle. Anyone who has read this
chapter and considered the implications of aspects based upon
divisions of the circle by all sorts of unusual numbers will
rightly ask: How arc we to deal with all the aspect-intervals

138

thrown up by such divisions, and how are we to research un¬
usual aspect series when the labour of dividing the circle by
all sorts of numbers and then finding the intervals at which
such divisions repeat round the circle is so prohibitive a task?

For many years after I had realised the importance of
harmonics and harmonic intervals in relation to a wide range
of astrological problems. I had the hope that one day some¬
one would use a computer to compile a complete catalogue of
harmonic intervals of the circle and their multiples right down
to, say, the 180th harmonic (2°). It was not until I met Dr.
Williamsen, then a Fellow of Kings College, Cambridge, at
the Astrological Association’s annual conference at Cambridge
in September 1971, however, that I found someone who would
tackle this project. Early in 1972, with the help of John
Barnden, he produced a complete list of all harmonics and
their multiples. At about the same time Michael Heleus of
Florida and Michael Munkasey of New York were also ad¬
dressing themselves to the same problem, each adopting a very
slightly different approach although basically the same. For
the record I believe Michael Heleus was the first to produce
such a catalogue but all three were produced independently
within a time-span of two or three months. Michael Heleus
has since performed some interesting experiments reducing the
orbital intervals of planets, combined with harmonic relation¬
ships, to the musical scale. 14 Michael Munkasey, too, has con¬
tinued to pioneer this field.

Dr. Williamsen’s catalogue has now been published in an
adapted format designed to facilitate easy reference and re¬
search. It is worth reproducing a specimen page to ^show how
it works (see below).

Every degree of the circle from 0° to 359° is given one
complete page, as shown. Suppose two planets are approxi¬
mately 100° apart. One can turn to the page giving the har¬
monic intervals which fall in this degree. In the first column
are listed all those fractions of the circle which fall exactly at
109° (i.e. 5/18ths, 10/36ths, etc.). Next to these are listed for
quick reference all those which fall beyond 1(H)® but before 101°.
Then, after the double line, the fractions between 100 p and
101° as they occur are listed in due order. Thus 100 p 07’06”
(or 100.1183 s ) is 47/169ths of the circle and so on.

139

EXACTUf BEYOND | 100° and 100° and * aXACTTLY HLYOND I 100° and 100°«md

100°0’0 1 ‘ lOOOO'O" I Min Sec HAifrONIC . DECIMAL 8 I00 j 0 , 0' 1 lOO^VQ' 1 Kin ^cc HAIfrtOHIC DECBtAL

C- >-t so \£>

<-1 G\ J- LTS

C\0 Mf-
co <7s ON Os

cn me me me t— oj -=r

h4\5ma^)OiAC lA lAfOCVO Pi
r-4 H r-t r—i rH rH .H t*~ CM iH r~I t-1 <“H <p

fnc os cm AQ hj r— f- c sc en

-J J m CV| <M H J AfOJ ft!

J- US U*\ i/S LG u*\ s

H H H rl

<—« gj cv ms so so t— c—cp ex o\ O

.H CS US t— Q OJ US CO

hhhhSww cm

IAA C— CVI H (VI

O Q co dj h a

r-t 3 LrtCO C\l -4

US W\ Lf\ US SO \D

Q\ rH PS US SO OO

Co ir\ on r-i r^-1~7 ~

® On S ^ rH VO O S'vo PO uS H f-oo, GO >

. . . . H r- H H y£> r)r)HHHa!)r 4 fHH H H VO rH G>

vS’5 r ' cj - ri vd"

C\J w J“4 cn CM H m ir\ m ,-t ^ oj

I H H H

:6 w h‘"' ^

H n rH wH *H *H r-\

t on m on m on on i

CO ^04

r-l PS US f— CKH (H H H rl

If one were researching the 25th harmonic and wanted to
know if two planets 100°30’ apart were involved in this series,
one could look in the first and second columns where one
would see at a glance that the interval of 7/25ths fell on this
page of the ''Catalog;” further inspection would show that it
fell at 100°48’, which is well within the orb.

Of course this catalogue is intended partly as a tool for
research; most of the fractions given are as yet quite unex¬
plored and their meaning undefined. Nevertheless some inter¬
esting connections have been found between unusual harmonics
and specific conditions and it is obviously desirable that all
fractions should be fully listed. Altogether the “Catalog” lists
over 16,000 harmonic intervals.

There is another point which should be mentioned. This
catalogue lists all angles from 0° to 360° and not only 0° to
180°. For many purposes the latter would be adequate but in
the long run Dr. Williamsen is justified in treating every angle
as a fraction of the whole circle and not only of the half circle.
Thus in the specimen list of Einstein’s planetary angles given
above, the angles arc listed from 0° to 180° taking the smallest
angle between each two planets. As long as one is interested
only in the denominator of the fraction concerned, this is ade-
quate. Thus if Saturn is at 0° Aries and the Sun at 10° Can¬
cer their aspect angle will be 100°. They would also be 100°
apart (measured by the smaller angle) if the Sun was at 20°
Sagittarius, but strictly speaking, in the latter case the Sun
lias travelled 260° round the circle from Saturn and not 100°.
In ihc first case the Saturn-Sun angle is 5/18ths, in the sec¬
ond it is 13/T8ths.

This raises an issue in relation to harmonics to which we
have so far made no direct reference. If we divide the circle
into twelve parts we say, speaking in terms of the houses, that
the first twelfth refers to the personal qualities and character¬
istics. the second twelfth to possessions, the third to brothers
and sisters, the fourth to the home, etc. So, too, with the
successive steps of every number scries, each represents a dis¬
tinct aspect of that number-principle considered as a one-in-
manyuess. This is something which has not been explored to

140

141

NOTES

any great extent in terms of most numbers although we are
familiar with the constituent elements of the Two Principle (as
embodied in the idea of polarity), the Three Principle (as em¬
bodied in the cardinal-fixed-mutable concept), the Four Prin¬
ciple (as represented by the four dements) and the Twelve
Principle. I have also written on the Five Principle and its
constituent parts.” But in the long run there is a need for
more studies of this kind in relation to numbers,

The User's Manual '"of the “Catalog/’ issued separately,
provides a great deal more information for the research stu¬
dent. Included are the arc-lengths for every aspect separately,
how the harmonic intervals are concentrated at different points
in the cirde, and so on.

In summary, a clear recognition of the relationship be¬
tween the symbolism of number and divisions of the aspect-
circle, combined with a definite norm for deciding upon orbs,
enables one to move freely and think creatively about the
whole field of aspect relationships. Major aspects are more im¬
portant in the sense that they are more general and more
comprehensive in their significance, but minor and unusual
aspects can reliably be given full weight when the orbs are
kept proportionately small and when their meaning has been
defined and understood. The former reveal the character and
balance of the horoscope in general terms. The latter can con¬
tribute most valuable insights into the precise direction and
flavour of the chart. Such minor aspects will often supply the
key to those things which make one person so different from
another, his special aptitudes and not only in what he does
but how he goes about it.

NOTES

1. Russell, Lesley, Britj Biographies far Astrological Study- (I Arts}, London:
Astrological Association. 1973.

2. This chart is for the recorded time of 10:00 a.in. on 4 Aug. 1792.
llorsham, Sussex, but I assume that the correct Ascendant falls at the
end of Aries, and that birth occurred 15 or 20 minutes earlier.

3. Keith Crilchlow, Order in Space, London: Thames & Hudson, 1969.

4. Born 2 June 1857.

5. Elgar was once asked how he produced the terrifying sound in The
Apostles where judas goes out to hang himself. Elgar replied that he
simply visualized Judas in the extremity of his remorse and heard it on
the muted horn — a good example of how the dynamic power of
ideas, when contemplated, inspires its own appropriate expression
through the artist.

6. Born 2 June 1840.

7. Lanrischcidtb point is that whilst the Moon’s motion is such that it
forms several aspects every day, Jupiter, Saturn and the outer planets
will only form frequent ’aspects’ if one uses very small intervals, the
1024th being 2T approximately in length.

8. Addcy, John, Astrology Reborn, Green Bay. VVi.: Cambridge Circle,
1975. p. 20f; also see reference in Chapter 12, Note 4.

9. Harvey, Ronald F., The Grammar of Astrology. Green Bay, VVi.: Cam¬
bridge Circle, forthcoming.

10 Of these ten cases the first was a blind piano tuner who came to the
author’s house and was able to give an exact birth time (4 Jan. 1906,
11:40 p.m., London). The second is that of Helen Keller (horn 27
June 1880 about 4:1X1 p.m., Tuscumbia, Alabama, U.S.A.). The re¬
maining examples of blindness were a collection of cases of this afflic¬
tion found in an old copy of the British Journal of Astrology (a publication
long since defunct) which was available at the time. Unfortunately
I no longer have the birth dates and times but the charts were calcu¬
lated and discussed by E. H- Bailey, the editor, who wps an astrologer
of the old school and a stickler for accuracy, so I believe the positions
can be regarded as reliable.

11. It is really necessary to have for this the User Manual in the Astrolo¬
ger’s Guide to the Harmonics, see Chapter 12, Note 2 above.

12. This was the chart of an Indian boy. I am a little skeptical about
Indian birthtimes which seem often to depend more on “rectification”
than accurate observation.

13. Williamsen, James S. and Ruth E., Astrologer’s Guide to the Harmonics,
see Chapter 12, Note 2 above.

14. Helcus, Michael C., “Astrosonlcs,” Astrological Journal (Astrological
Association, London), XVII (1975), no. 2.

15. Addey, John “Fivefold Divisions and sub-divisions in Astrology,”
see Chapter 12, Note 4 for full details.

16. Williamsen, James S. and Ruth E., User Manual of the Astrologer’s
Guide to the Harmonics, see Chapter 12, Note 2 above.

143

142

HARMONICS AND DEGREE AREAS

The allocation of special meanings to certain degree areas
in the Zodiac has a long history in astrology and is a familiar
idea to all students. 1 The subject has been variously treated
by writers in the past according to the thought of their day.
In former times word-pictures were devised to catch, as it
were, the symbolic content on different levels of a particular
degree or degree area; in modern times empirical studies have
been made of horoscopes with a view to discovering what
common feature or attribute is associated with planets occupy¬
ing a given degree area. These studies have ranged from the
somewhat over-imaginative to the thoroughly perceptive and
scientific.

Strictly speaking we ought to distinguish between the sig¬
nificance of degree areas and of the symbolism of the 360 de¬
grees as such. The latter obviously derives from the number 360
in its outworking. It is with the former that we arc chiefly
concerned in this chapter. As a rule there has been no under¬
standing of how these “degree area influences'’ arise, and
writers have been content to point out that certain areas of
the Zodiac arc clearly associated with certain qualities whilst
admitting that they do not know why this should be so.

In the light of what we have learned about harmonics we
are in a position to explain the basis of at least those degree-
area influences which repeat at certain regular intervals round
the Zodiac, as for example degree areas which are in opposi¬
tion or trine and which therefore could not be associated with
certain fixed stars (even if fixed star influences were deemed
valid). In a nutshell, degree-ana influences always arise by vir¬
tue of the coincidence of certain harmonics. Thus, we say that
people with a certain very specific aptitude or talent must, in
order to possess that aptitude, have certain pre-requisite quali¬
ties; for example, a successful tennis player must have quick
reactions, a muscular system which is not liable to sprains and
strains, a good judgment of the position of objects moving in
space, a competitive spirit, a delicate sense of touch and

144

timing and so on. We can then say that the harmonics asso¬
ciated with these separate qualities will tend to combine in a
certain way to produce degree-areas which are very character¬
istic of those in whom all these qualities are combined.

Some of these degree areas are undoubtedly based upon
very complex harmonic combinations; however, we can illu¬
strate the principle quite simply with, say, three harmonics
which we must suppose are associated with three separate ten¬
dencies. Thus in Fig. 64 we have the 1st, 3rd and 8th har¬
monics of a given sector of the ecliptic. In the example of the
successful tennis player given above, the first harmonic here
might refer to the more general characteristic, a competitive
spirit perhaps, the third to the sense of touch and timing and
the shortest wave to the most specific attribute, perhaps the
ability to judge moving objects in space. We can easily see
that there is one point in this combination of regular waves
which gives a high ‘plus’ rating in relation to any aptitude
which requires all three tendencies in combination. This quite
simply is the basis of all degree area meanings. If the funda¬
mental in Fig. 64 is 180 degrees in length then our degree
area will occur twice in the Zodiac at opposite points, if 120
degrees there will be three sensitive areas in trine, and so on.

We can study an actual example of a degree area influ¬
ence at work in diagrams already used in Chapter 7. Fig. 28
shows the distribution of the Sun in the nativities of 7,302
doctors and we can see that certain very high peaks occur in
the solar distribution, the highest actually falling in 22° Taurus.

145

We arc inclined to think of special degree areas as falling,
very often, at opposite points in the zodiacal circle (for
example Garter, in his Encyclopedia of Psychological Astrology 2
gives many such polarities, as: 3° Cancer-Capricorn — sight,
17° Arics-Libra = oratorical ability); but sometimes the sensi¬
tive areas are in square or in trine (e.g. Carter gives 5° of
the fire signs — hair). In the case of medical ability he mentions
22° of the negative signs.

Now any factor which falls at 22° negative signs must re¬
cur at regular intervals of 60°, We can therefore look at our
60° distribution pattern (Fig. 32) extracted from the general
solar distribution and see there that the peak distribution in
each 60° does in fact fall between 19° and 23° of the negative
signs. In Fig. 32 we can see that the basis of this high-scor¬
ing area is, in the first place, the coincidence of the 60° wave
and the 30° wave, but on top of those, there must be other
harmonics which refer to qualities or tendencies common to
doctors and so we have our degree area for ‘medical ability*
at 22° of the negative signs.

There are of course two ways of arriving at our degree
influence meanings. One is the empirical or inductive approach
where actual horoscopes are examined either singly or in quan¬
tity (these two methods are complementary). The other is the
deductive approach in which the meanings of particular har¬
monics are deduced from the first principles of number sym¬
bolism, that is from the ideas which lie behind numbers. As
always in scientific inquiry, it is good to use both inductive
and deductive methods in conjunction, each checking and rein¬
forcing the other.

In the light of these general principles there are certain
things we can say about degree areas which are not generally
recognised.

1. For every positive degree area which promotes a certain
attribute, there is usually another one—a negative de¬
gree area so to speak—which militates against that
attribute. Thus in Fig, 64 as well as in the high peak
about one quarter of the way along the wave complex,
there is a deep trough three quarters of the way along.
These negative degree areas are just as important as
the positive ones although they have never, in my
knowledge, been made a subject of study.

146

2. Sensitive zodiacal areas relative to a certain quality do
not only occur infrequently in the Zodiac say at inter¬
vals of 180°, 120° or 90°. They may be much more fre¬
quent, although when this happens the ‘area’ involved
at each point will be narrower. Thus in writing about
the positions of astrologers (Chapter 12) we drew atten¬
tion to the tendency of important positions in their
maps to fall at 6° intervals from 0° Aries. If we ask
where the Sun, Moon, Ascendant, M.C., Uranus and
Saturn of the six astrologers listed (in Chapter 12) are
placed in each half-degree of the recurring 6° sectors of
the Zodiac then Fig. 65 shows the answer.

Here we can see a clear 6° rhythm with peaks at 0°,
6°, 12°, 18° and 24° of the signs and a ‘low’ at 3°, 9°,
15°, 21“ and 27°. Actually the highest half-degree total
falls in the last quarter-degree before the 6° intervals
and the following quarter-degree. This half-degree area
(1 /12th of the 6° span) yields 15 positions out of the
total of 36.

Needless to say some of these 6“ intervals are more im¬
portant than others in this context, for the obvious rea¬
son that the 6° rhythm (the 60th harmonic) is involved
with other harmonics. This can be inferred from the

147

fact that some of the clusters shown in Fig. 56 are much
stronger than others. Another example of this repetition
of sensitive zodiacal points is to be seen in our refer¬
ence to David Hamblin’s work on musicians’ charts in
the 7th and 28th harmonics.

3. It is to be noted that sometimes a strong positive de¬
gree area will at one point in the Zodiac be matched
by a strongly negative area at the opposite point. This
happens when the dominant harmonics are odd num¬
bered, for such harmonics always produce a ‘high’
opposite to a ’low’. When even numbered harmonics
are dominant there will be a ‘high’ opposite to a
‘high’ in the circle and a ‘low’ opposite a low’. When
odd and even numbered harmonics are mixed, one will
frequently see a ‘high’ opposite a ‘low’ with peaks on
either side of it. This can be seen at the point opposite
to the peaks at 22° Taurus and 12° Cancer, for ex¬
ample, in Fig. 28.

4. It is sometimes asked how wide a degree area is in the
Zodiac and how rapidly the ‘influence’ falls away on
either side. We can now see there is no one answer to
this question for the possible combinations of harmonics
which produce a degree area are many and various.
Sometimes the area is quite wide, sometimes very nar¬
row, sometimes the effect dies away gradually, some¬
times rapidly. Everything depends upon what harmonics
ajre involved and how they are related.

Finally in this chapter, there is one very important corol¬
lary concerning what has been said about degree areas in the
zodiacal circle. Because exactly the same principles apply to all
circles in astrology the idea of 'degree areas' is just as valid in the
aspect and diurnal circles as in the Zodiac. This is a matter to
which very little thought has been given; one never hears of
degree areas in the mundane circle apart from conventional
house positions, and very seldom in the aspect circle apart
from conventional aspects, although these are, strictly speaking,
just like degree areas in that circle of reference.

An example of the former may be found in Gauquelin’s
sports champions. If we stick to house positions only, one
merely notices in his Mars distribution for outstanding athletes
that there is a high score in the 12th and 9th houses; how¬
ever the truth of the matter is much more striking than this.
The really high score is not just in the 12th and 9th houses
but in the 3rd decanale above the Ascendant and the third
decanate past the M. C. Fig. 66 shows in 10° sector totals the
distribution of Mars in the 90^ of oblique ascension from
Ascendant to M.C. (top line) and again from M.C. to De¬
scendant (bottom line). Here we see the extraordinary leap
between 20° and SO 0 past the exact angle.

The two 9CP sectors yield the following totals of Mars positions:
Degrees past the angle

0 10 10-20 20-30 30-40 40 5Q 50-60 60-70 70-80 80-90

139 133 180 123 103 99 95 107 96

That this should show up so powerfully despite the admitted
element of approximation in the birth time is extraordinary.
This leads one to think that there may be a very narrow
‘mundane’ degree area here for Mars in relation to sporting
prowess, perhaps about 23° to 26° after the angle. If, as we
suggest in a later chapter, Gauquelin’s birth times tend to be
registered late, then this degree area may be nearer the angle,
but in any case it is clearly not connected with the house
cusp as such.

148

149

There is usually a strong symbolic connection between a
feature such as this and the psychology' of the case. In this in¬
stance the only way in which such a sudden high peak could
be obtained is by the extreme concentration or coincidence of
many harmonics at one point; in just the same way the really
outstanding sports champion must have the capacity to concen¬
trate all his energies (Mars) for an intense effort. Looking at
Fig. 66 one is reminded of an electro-cardiogram where the
different rhythms of the heart coincide at intervals to give the
sudden leap of the heart beat. Perhaps the heart could be
called the athlete of the body.

The point to notice especially here is that this feature
appears as a degree area in the diurnal circle , not in the Zodiac,
and that it does not fall at an angle or on a cusp any more
than zodiacal degree areas fall exactly at the four cardinal
points or even exactly at the beginnings or middles of signs.
Degree areas can fall anywhere in the circle.

In precisely the same way the important angular relation¬
ships in the aspect circle are not only at the conventional
aspect points at 30° intervals but may fall anywhere in the
aspect circle. We can reasonably assume, however, that the
conventional points have a priority of importance. If we look
again at the diagram showing the Sun’s relationship to Saturn
among nonagenarians (Fig. 48) we can see that the significant
relationships do not fall at the conventional aspect points but
between 10° and 15° past the conventional aspect.

NOTES

1. This chapter is based on Addey, John, “The Nature and Origin of
Degree Influence,” Astrological Journal (Astrological Association, Lon¬
don), XII (1970), no. 1; to be reprinted in The Harmonic Anthology ,
Green Bay, WI.: Cambridge Circle, 1976.

2. Carter, C. E. O., The Encyclopedia oj Psychological Astrology, London:
Theosophical Publishing House, 4th ed., 1954, pp. 197-199,

150

HARMONICS IN PROGRESSIONS,
TRANSITS AND OTHER
DIRECTION PROCEDURES

We have discussed some of the various applications of
harmonics in the natal chart but so far no reference has been
made to harmonics as they appear in relation to the unfold-
ment of the radix through progressions, transits and the like.
It would be very surprising, however, if a principle which
applied universally in the one case did not apply equally in
the other.

First of all let us think about what happens as the events
of life unfold. The course of life is not a chaos and although
some events may appear to happen ‘out of the blue’ as it
were, we are really always dealing with orderly sequences of
experience. A man may have a period when he is feeling the
pinch financially, this leads him to seek promotion or a better
paid job and this again, if he is successful, brings new respon¬
sibility and readjustments. It also brings a new prosperity
which may enable him, say, to put down the money on a
house. On a different level a child may appear to have a ra¬
ther sluggish period of poor health, this makes her vulnerable
to infections at school, she catches measles, but after a quick
recovery she suddenly blossoms out and is found to be bursting
with life and energy. It does not always happen like that but
this is not an uncommon experience; it is as if the fever had
had a cathartic effect. Or again, the corresponding first stage
of such an experience may be something in the nature of a
a nervous breakdown, when life seems to confront someone
with an overwhelming dilemma which he does not know how
to deal with. However, as Jung has shown, such situations are
sometimes resolved almost imperceptibly. Some symbolic act
or experience, which happens almost unobserved; releases the
tension; suddenly the dilemma no longer looks like a dilemma
and equilibrium is restored and confidence regained.

Now when these experiences are looked back upon, what
is it that is actually remembered? In the last case it is the
dreadful experience of a nervous breakdown which is recalled
and if the native is an astrologer it is that “event” for which

151

he will later look in his directions. The child’s mother remem¬
bers the time when her daughter was so ill with measles and
searches for suitable directions for that, forgetting the earlier
period of poor health and perhaps not associating her daugh¬
ter’s renewed energies with the measles. The little girl looks
back upon the time she took on a fresh lease on life and came
top of her class. The man who suddenly steps up in the
world may regard his promotion as the natural culmination of
much effort (and long overdue anyway!) and chiefly remembers
the day when he and his wife could at last have a house of
their own.

This lengthy preamble is intended to show that the course
of our lives is not so much a series of isolated events as a
flowing sequence of unfoldment and that whereas one person
will focus on one stage of the sequence, another will see a
different stage as the important event.

Now in terms of progressions it would seem to be the case
that as progressed aspects form we can often relate the sequence
of events to the applying, exact and separating stages of an
aspect. Thus in Fig. 67 if we think of planet A forming a
progressed aspect with planet B, point x may represent stage
one (the ‘hard up’ period of the man in our first example, the
little girl’s poor health, and the nervous breakdown), point y
may indicate stage two (promotion, measles, the unnoticed
resolution of conflict) and point z will show the consequent
improvement (the new house, the fresh lease on life, confidence
restored). The period from x to y and y to z may be a
month or six months or two years.

152

In each case the process is the development of one prin¬
ciple or type of aspect through various stages: in the first case
it is evidently a Saturn aspect which is at work; x = Saturn
denied (penury), y = Saturn resurgent (promotion, responsibil¬
ity), z = Saturn enjoyed (bricks and mortar). If Saturn is
planet B in this example and the Moon is planet A, then in
the case of the young lady with measles, planet B is probably
Mars and planet A is perhaps the Sun, for hers is a more
Mars type of experience: x = Mars denied (impurities clog the
system and the fires of life burn poorly), y = Mars resurgent
(cathartic fever), z = Mars released (the energies burn bright¬
ly again). And so on. Notice that in each case 4 y’ is, so to
speak, a nodal event with a distinct ‘before’ and ‘after 1 stage.
The nodal event (promotion, measles) is often short and sharp
in contrast to the before and after stage.

I do not of course suggest that the applying aspect is
always a denial or repression of the planetary principle in¬
volved. Sometimes the excess comes first and the deficiency
comes after the aspect; in fact all four possibilities shown in
diagrams 42-43 can apply; it is a question of what stages of
experience we are passing through.

This brings us to the point we have been leading up to.
The different principles and forces at work in life arc constant¬
ly moving between polarities or positive and negative, full and
empty, tension and release. This is why I believe the notion of
progressed aspects which suddenly pop up from time to time
and then are done with is basically a false one. As a pro¬
gressed planet A moves around the circle forming an ever-
changing relationship to planet B we are always dealing with
a regular flux between positive and negative poles of experi¬
ence. If the gentleman who was feeling the financial squeeze
and looking for promotion thinks he is going to feel rich for¬
ever he has got another think coming; but he probably knows
as w r ell as we do that in a year or two’s time he will be
feeling poor again. If he is a student of Parkinson’s Laws he
will know that expenditure expands to meet income; if he is of
a philosophical turn of mind he will know about Yin and Yang,
and will realise with Lao Tse that:

‘If there is contraction, then before there was expansion.

If there is weakness, then before there was strength.’

153

And so the rhythm of life moves on. In short we need to
think less about exact aspect points and more about the ebb
and flow of progressed motions, trying to determine the types
of life rhythms related to different planetary configurations in
the progressed chart. It would seem to be the coincidence of
these rhythms at certain intervals which brings the most sig¬
nificant situations and these do not always coincide with the
conventional aspect points. 1

Enough theory; let us have some practice. What progres¬
sions, for example, should be look for at the time of marriage?
The investigative astrologer is always on the lookout for suit¬
able data and often he must take it where he can find it. The
Directory of the Turf (1970 edition) 2 gives the dates of birth and
marriage of the jockeys of the day and by extracting these in
relation to all married flat-race jockeys 3 we have a collection
of 116 cases where the actual dates of birth and marriage are
given. From these we are able to calculate the progressions for
the age of marriage in years and months, assuming birth to
have taken place at noon—a small marginal approximation.

But what are we to look for? Of course the textbooks
have a rather simple approach to such questions and may sug¬
gest something like Sun progressed in aspect to Venus. The
positions of the progressed Sun in relation to Venus radical at
marriage in these 116 cases are shown in Fig. 68. We can
see that what is chiefly reflected is the general distribution re¬
lationship of Sun and Venus exactly as illustrated in Fig. 45.
There is no suggestion that progressed Sun in conjunction with
or in aspect to Venus coincides with marriage. We need to
think a little more carefully.

.lUkJk l..u.. ikLuwi .u »dk„.

10 20 30 40 50 60 70 80

Fig. 68

DEGREES OF Op FROM 9r

The point about marriage perhaps is that it is a permanent
relationship, a definite formal agreement binding upon both par¬
ties; it introduces an dement of stability into their lives and
confers a measure of security of relationship and affection. In
the past at least the woman gained some financial security and
the man financial responsibility. The relationship between Venus
and money is well brought out in Carter’s Astrological Aspects. 4

There is no need to go any further, all that we have said
points to a Venus-Saturn relationship. The phenomenon of the
young man or woman who has been rather wild but suddenly
becomes more steady, serious and responsible at the time of
marriage is a commonplace, Saturn is not exalted in Libra for
nothing; this is the time when one’s affections crystalise as it
were, upon one person. Now if there is any sense to be made
of the symbolism of planetary relationships then there must be
a characteristic Venus-Saturn relationship of some kind involved
here.

But what kind of Venus-Saturn relationship and what kind
of direction should we use? The usual day-for-a-year method of
progressions is well attested and certainly justifies an examina¬
tion but symbolic measures such as the One Degree (equals
one year) may be better. We must not start with the precon¬
ceived idea of what this Venus-Saturn relationship will be;
that way we shall be limited by what we think we know in¬
stead of discovering what we do not know. So our question
must be: “What is the relationship of progressed Venus to
Saturn at the time of marriage?”

After calculating the secondary progressions for marriage,
we must tabulate the relationship in degrees from Saturn to
Venus progressed (we measure from the slower planet to the
faster). For this we again use the grid, illustrated and ex¬
plained in Appendix I, upon which we record the angular
distance from Saturn to Venus in every one of our 116 cases,
hi this way we shall get the best picture possible of the actual
relationship of Venus to Saturn at marriage without any pre¬
conceived ideas about what we shall find.

154

155

Now because Venus may be anywhere in the whole as¬
pect circle in relationship to Saturn, we shall naturally find
these progressed positions of Venus scattered round the whole
circle and this is in fact what we find. In the 30° after the
conjunction there are 8 cases of progressed Venus, between
30° and 60° there are 8 again and so on round the circle. No
sector has more than 12 cases and none less than 6. This sort
of thin spread of cases does not lend itself wel] to a full har¬
monic analysis even if we were able to perform one, so we
must resort to the sort of simple tactics which we have used
before, that is collapsing the distribution of progressed Venus
positions into one 30° sector by collecting the degree totals for
all twelve sectors into one 30“ run.

Here are the totals, by degree of separation from the 30°
aspects:

deg. sep. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

total 4063 10 5452343321

deg. sep 15 16 17 IS 19 20 21 22 23 24 25 26 27 28 29
total 245225764831237

To be clear what these figures mean: the first total (4)
shows that there are four cases where Venus is exactly at one
of the twelve aspects to Saturn at 30° intervals, i.e. w r ithin
V2 0 on either side of the conjunction, semi-sextile, sex tile,
square, etc. The second total (0) means that there are no
cases of Venus separating by 1° from these aspect points. Then
there are six cases of Venus separating by 2°, three cases sep¬
arating by 3°, ten separating by 4° and so on, while at the
end of the line of figures we have three cases of Venus ap¬
plying by 2” to an exact aspect and seven cases applying by T.

In order to check our line of figures for a 1st harmonic
(actually the 12th harmonic of the whole circle) we can ask if
it is possible to divide them into two halves of 15° each so
that one half is significantly higher than the other. A little
addition shows us that the middle portion of the line of figures
has lower scores on the whole than the two ends. If we start
at the seventh total (4) then we have 15 consecutive totals
which add up to 47, whereas the next 15 toials (starting at 7,
the 21st degree of separation) add up to 69. This suggests the

156

presence of a 1st harmonic with the peak near the exact as¬
pect point. Continuing our investigation we can point to two
harmonics which are even stronger. These are the 2nd and
5th of this series, the wave of 15° and that of 6".

In order to demonstrate this, casting our minds back to
what we learned in earlier chapters, we can put our totals
down in runs of 15° and of 6°, thus:

4063 10 545234332124 5 225764831 237

245225764831237 4 0 6 3 10 5

6 4 11 5 12 10 11 11 6 11 7 4 5 5 8 4 5 2 3 4 3

18 21 20 28 27 33 32 28 28 24 22 16 14 18 19 (3* Moving toial) 3 2 1 2 4 5

2 2 5 7 6 4
21 12 15 17 27 24

Taking the 15° run first, we have made a 3° moving total
of this series, the results of which are shown in graph form in
Fig. 69. Here we can see a vigorous 15° wave with a rise and
fall of about eight on a mean of 23; in other words the amp¬
litude is (8/23) x 100 or nearly 35%. Fig. 70 shows the graph
of the 6“ w r ave from the totals above. Here we can see
another good result with a rise and fall of about 6V2 on a
mean of nearly 20, giving an amplitude of (6V2/2O) x 100 or
nearly 33%.

A'.HCTS

Notice that in these two harmonics the peak and the
(rough are more or less equally spaced and the totals for the
the peaks are more than twice those of the troughs. This gives
us a measure of confidence in the result. On the evidence of
ilirse totals, we therefore have three harmonics which when
put together show a relationship of Venus to Saturn in each

157

30 degrees of the aspect circle at the time of marriage in this
particular sample of cases. The 30° wave which we will very
conservatively call 10%, the 15° w T ave (35%) and the 6 wave
(33%) are drawn together in Fig. 71, to show our combined
characteristic distribution.

Fig. 71

It must be emphasised that this graph is simply a general
description of this particular result and is neither more or less
reliable than the sample we have taken. The sample is small
and applies to men only and furthermore to a sample of men
of a similar type, jockeys. Thus it is not claimed for one mo¬
ment that this graph is universally applicable; what we have
done is to demonstrate a method of procedure which if applied
on a larger scale might well show us that there is a typical
Saturn-Venus relationship at the time of marriage. Indeed as
astrologers we must assume this to be the case. The relation¬
ship may be different for men and women, it may be different
for different types of people, and it may vary from epoch to
epoch, but these differences should be identifiable. In any
case the principles involved in the relationship remain the
same, only the circumstances of their applications differ. Of
course, in starting with 30® sectors of the aspect circle we have
already partly prejudged the issue; for a fuller investigation
one would need to examine the distribution in other sectors.

What we have demonstrated is that, whatever people may
believe about exact (textbook) aspects, these 116 cases taken
from life tell a different story. There are points where the
Venus-Saturn relationship is strongly associated with marriage,
for example, when Venus is separating by about 4W from, or
applying by 7° to, a conventional Saturn aspect, and there
are positions when it is not. But the relationship is more
complex than is generally assumed. 5

Even if the result of this little investigation proves to be a
misleading one, yet the method of approach to the problem is
surely the right one. It is interesting to note in passing that if,
instead of taking the secondary progressed Venus, we take
Venus by one degree measure for these cases, the 6" wave
holds good as shown in Fig. 70, with similar amplitude and
phase, despite the considerable difference in motion between,
these two measures. Similarly the progressed Sun in relation to
Venus (as given in Fig. 68) also shows a strong 6° rhythm.
Six degrees is 1/5 of a sign and we have already pointed out
the association of the number five with marriage. One of the
unsatisfactory things about the insistence upon the 30° aspects
in relation to an event such as marriage is that the interval
between such aspects is too large for an event which usually
takes place during a relatively short age age-span; it is much
more likely that a 6® rhythm for Venus progressed, something
like a five-year cycle, would suit the case better. In any case
we must allow this brief coverage of progressed aspects to il¬
lustrate what we believe to be the principles involved.

What of transits? Evidently the same principles apply.
One illustration must serve to show what is involved. Some
years ago Mr. W. H. Somerford of Urmston, Manchester sub¬
mitted an entry for the Astrological Association’s annual Astrol¬
ogy Prize which was never published but is of unusual inter¬
est. Mr. Somerford extracted from Burke’s Peerage, Baronetage
and Knightage (103rd edition, 1963) all cases of only sons where
the date of death of the father and the date of birth of the
only son, and therefore the age of inheritance, were given.
This amounted to 205 cases. He provided in his study the
natal, progressed and transiting positions of the Sun at the
time of inheritance and the position of the lunation preceding
the event. Lunations are simply double transits of Sun and
Moon.

158

159

The death of a parent is an important psychological event
for most people and this must be enhanced in the case of only
sons, especially when the event marks the inheritance of lands,
title and wealth with their accompanying responsibilities.

There is a tendency for astrologers to think of transits as
operating within quite narrow orbs, and the transiting posi¬
tion of the Sun in relation to Sun radical would not, in any
case, rank very high in the books of most students. But
Somerford’s ‘iron filings’ scattered over this particular astro¬
logical magnet show that the low-numbered harmonics, the
long waves with wide orbs, are strongly operative in the case
of transits, just as they are in other ways.

At the time of the father’s death these transiting Sun posi¬
tions showed a strong 4th harmonic relationship to the radical
Sun, and this was even stronger in the case of lunations
(the positions of which are of course closely related to the
transiting Sun). Fig. 72 shows the distribution of the lunations
which preceded the father’s death, relative to the radical Suii,
in each 90® sector. In other words we are asking where the
monthly conjunction of Sun and Moon preceding the father’s
death fell in relationship to the radical Sun or to the points

Frequency of lunations prior to the father s death falling in each 15 of
40° sectors from the radical sun in the charts of 205 only sons.

160

This 4th harmonic shows an amplitude of about 38%! It
is very much stronger than any of the other shorter harmonics
involved in the position of transiting Sun. Somerford did not
include any strictly planetary positions in his study but an
examination of these shows good harmonics for transiting
positions. This is a very interesting collection of data.

Before ending this chapter there are two additional points
that should be made, the first one is important, the second
somewhat speculative. First, it is worth spelling out what will
be obvious to most students, namely that the idea of har¬
monics when applied to directional methods points very clearly
to the importance of what are called ‘symbolic measures'.
Many of these have been suggested and indeed demonstrated
to be valid by various authorities. The criticism which can
be made of symbolics however is that most astrologers tend to
apply any symbolic measure to any kind of event. But since
there is an almost endless variety of symbolic measures to
choose from, it follows that the astrologer will always be able
to find some sort of aspect to go with any event he chooses.
This is unsatisfactory.

Every division of the circle has a specific meaning derived
from the number by which the division is made, and each
symbolic measure, if it is to be used intelligently, should be
applied in the field to which it belongs and no other (although
there are of course some measures which are more general in
their right application and others which are more particular).
The study of number symbolism in relation to harmonics will,
I believe, help to clarify the right use of symbolic measures
and so greatly enhance predictive potential.

The second and somewhat speculative suggestion is this:
we have shown in earlier chapters how to calculate a har¬
monic chart, and though we were chiefly concerned with the
lower numbers, the principle applies to the harmonic chart
for any number. Now there is a possibility that the harmonic
charts in succession may apply to each year of life, i.e., the
2nd harmonic chart to the second year of life, the 3rd to the
third year, the 40th to the fortieth year and so on. The
interesting thing about this suggestion is that it conforms to an
acknowledged fact about the unfolding life process. The change
from one harmonic chart to the next in the low numbers

161

(that is in the early years of life) is considerable and similarly
our development in one year of childhood experience is also
considerable. Later in life we become progressively more set¬
tled in our ways and character and so the change from year to
year, say from the 40th to the 41st harmonic chart, is rela¬
tively small yet perceptible. A little experiment with this
technique has given mixed but promising results. Perhaps the
problem lies in identifying more clearly just what we mean
by ‘unfoldment’ in this context.

To illustrate how this works: suppose the Ascendant is
20° from Jupiter. Then, since 20° is 1/18 part of a circle, the
18th harmonic chart w r ill show Ascendant conjunct Jupiter.
This will occur again in the 36th, the 54th and the 72nd har¬
monic charts and the theory is, of course, that these years of
life will have the appropriate Jupiter conjunct Ascendant fla¬
vour. This tendency of similar events and circumstances to
recur at ages which are multiples of the age at which they
first occurred has often been noticed. This technique of using
the successive harmonic charts not only gives a rationale to the
idea but also shows how the particular configuration, such as
Ascendant conjunct Jupiter in the example given, will fit into
the whole picture of the rest of the chart for a given recurrence
of the aspect. It is usually quite impossible to see this whole
picture without using the harmonic chart.

This may prove to be a valuable addition to the predic¬
tive branch of astrology. The difficulty is that if we wish to
check past years of our life the labour involved in calculating
the charts for the appropriate years may be troublesome. How¬
ever, a simple check on the ages on which major conjunctions
will materialise can be made with the help of the “Catalog”
in the Astrologer's Guide to Harmonics.

Let us suppose that the angle from Ascendant to Jupiter
is a rather unpromising one, say 78° 16’, and we want to know
at what age, if any, this will occur as a conjunction in a har¬
monic chart. We can look up 78° 16’ in the catalogue and
there we find that it is just 5/23rds of the circle. Thus we
know that Ascendant conjunct Jupiter would appear in the
23rd harmonic chart and again in the 46th. This may sound

162

complicated but a little practice will, as always, show its po¬
tentialities. It is worth adding, however, that two planets will
not always appear as a conjunction in any harmonic chart
during one’s lifetime. Their relationship must be such that it
forms some whole fraction of the circle, the denominator of
which is less than or equivalent to a normal life span.

My view is that though this general technique is almost
certainly valid it must apply to some rather basic, stable pro¬
cess underlying the life, rather than transient events as such,
though these may provide triggers for the deeper process. To
give an example, Fig. 73 shows the 60th harmonic chart of
President Ford, based on a birth time shortly after 12:41 a.m.
on 14 July 1913. The radical positions are given below . 6
Gerald Ford unexpectedly stepped up to the Vice-Presidency
of the United States on 13 October 1973 (aged 6 OV 4 ) at a
time when the Presidency was tottering. He became President
in the following year. As will be seen, the 60th chart is a
striking one and has a number of extremely interesting features.
(If a slightly later birth time Is taken. Ascendant and M.C.
will move forward sharply In the 60th. By 12:42 a.m. M.C.
would be opposition Sun and Ascendant would be later in
.Aries. This shows the potential value in rectification of these
charts.)

Positions for the 60th harmonic chart of President Gerald Ford. {Gerald
Ford was 60 when he became vice-president of the U.S.A.)

163

To sum up, wc have tried to show that the principle of
harmonic fluctuations applies as much to progressed and trans¬
iting positions as to radical positions and that the prevailing
concepts of astrology are, in this respect, ripe for review. It
will be objected that if one takes away the preeminent impor¬
tance of exact progressed aspects (and it is certainly not sug¬
gested that these are unimportant) then the whole business of
prediction from the natal chart is put into the melting pot. To
those who are satisfied with the reliability of present predictive
methods this will seem like a good argument. But after many
years as an astrologer I have yet to find a man whose chart
was rectified to the same Ascendant by any two good astrolo¬
gers, whilst I have known some who have had their charts
‘rectified’ to a different Ascendant by each of a dozen leading
practitioners. The inadequacy of these methods speaks for
itself.

NOTES

1. Most students are familiar with biorhythms, the theory that there are
three rhythms which start at birth, a 211 day rhythm referring to body
states, a 28 day rhythm relating to feelings and a 33 day rhythm re¬
lating to mental states. Much has been made of this idea but al¬
though the general concept is fully in accord with what we have been
saying, it will be obvious to students of astrology that life rhythms are
of immense variety and that the three mentioned, if true, will surely
be lost amid many others. In this sense one might regard biorhythms
as something like Sun-sign astrology, not without a grain of truth but
inadequate on their own.

2. Directory of the Turf. London: Stud and Stable, Ltd-, 1970, 4th ed.

3. Flat race jockeys can lie distinguished by their lighter riding weight,
as given.

4. Carter, G.E.O,, The Astrological Aspects, London: L.N. Fowler & Co.,
Ltd., 1969 , 9th ed. This book has always been recognised as one of
the outstanding modern works on astrology.

5. It so happens that the writer’s son was recently married and after
writing this paragraph I decided to look where his progressed Venus
was at the time. It was exactly 4* past the conjunction with Saturn.

6. Gerald Ford zodiacal positions: Ascendant 12°12' Taurus, M.C. 24*1’
Capricorn, Sun 21° 12’ Cancer, Moon 3°56’ Sagittarius, Mercury 16°8’
Leo, Venus 5°52’ Gemini, Mars 19°35’ Taurus, J upiter 1T50’ Capri¬
corn (Rx), Saturn 13° 13’ Gemini, Uranus 6°9’ Aquarius (Rx), Nep¬
tune 25*34’ Cancer, Pluto <r3’ Cancer.

PART THREE
PROBLEMS

SOME WAVE COMPLEXES

Astrology today has inherited a large body of doctrine
from a bygone age. There is no doubt that in general terms
the basis of thought upon which this traditional knowledge
rests is a sound one, but it is equally certain that in many
respects the application of the underlying principles has be¬
come confused. In the effort to make the science easily man¬
ageable (and this tends to happen in every field), rule-of-
thumb methods are laid down, principles are over-simplified
and modified, and textbooks which are primarily written to
help the beginner to get his bearings become the standard
yardsticks of astrological teaching.

The result of all this is that, with the passage of time, the
really fundamental principles tend to be lost sight of and the
codified system of rules becomes first the main focus of atten¬
tion and then the subject of dispute. There is not a single de¬
partment of practical horoscopy — the Zodiac, the houses, as¬
pects, directional methods (to mention only the main topics) —
which does not present a host of uncertainties. The fact that
many students are scarcely aware that these uncertainties exist
only makes things worse. And the trouble, first and last, is
that fundamentals are ignored and the efforts of researchers
which should go towards the needed clarification of basic prin¬
ciples are directed towards justifying the conventional code of
rules.

In earlier chapters of this book we have tried to clarify
some of the principles which should govern our understanding
of astrological positions in the various circles of relationship
with which the astrologer deals. There are however many basic
issues which remain obscure, and although we cannot deal
with all of these in a textbook which is intended only to be
introductory, there are a number which can be mentioned.
Some of these refer to the standard issues of dispute in astrol¬
ogy today, for example the problem of the Tropical and Sid¬
ereal Zodiacs, and some are more concerned with the pursuit
of a clearer understanding of the workings of the principle of

167

harmonics, for example what determines the phasing of the
waves shown in our harmonic distributions. We certainly can¬
not produce all the answers but at least we can attempt to
indicate the nature of some of the problems and set the ball
rolling towards some of the answers, at any rate to the extent
of considering what criteria, or what sorts of criteria, we
should be looking for if we are to find solutions.

(It might be kind to indicate at this point that Chapters
17 and 18 contain a good deal of semi-technical material. I
hope the reader will tackle them in the end but he may pre¬
fer to go on to the later chapters which are of more general
interest and return to this part at a second reading).

As a first step towards discussing some of our problems,
one of the things which will help us most is a brief considera¬
tion of some of the theoretical formations of certain wave
complexes or combinations. This may seem a strange starting
point for further inquiry but the relevance of the topic to
some of our problems will become apparent and in any case
the student should know something about this matter-.

We have already noticed one type of wave complex which
we may call the ‘kick’ effect, when a number of harmonics all
come into phase at one point to produce a sudden leap like
the heart beat. The example given was that of the Mars dis¬
tribution for athletes shown in Fig. 66 . We suggested that this
effect might occur in the charts of those who were required to
make sudden spurts or concentrations of effort.

Another wave complex which will be encountered again
and again by anyone who investigates planetary distributions
in astrology is the ‘beat’ effect. When two adjacent harmonics,
say the 5th and 6th, appear strongly in a distribution pattern,

\ >| the result is that the two series of waves will alternately coin-

S ' tide with, and then contradict, each other. Thus in Fig. 74

we can see that in the centre of the diagram the two series of
waves are moving in unison, whereas at the edges the)' are
out of step. The result of this is to produce, when the two
wave series are combined, a ‘beat’ effect with a strong oscilla¬
tion in the centre when the two are reinforcing each other
and then a ‘dying away’ effect where the two are working

< 1

168

against each other. This is ihc same phenomenon which one
hears sometimes with a bell (such as Big Ben on the radio-—
the bell shape notoriously produces harmonics which are close
together), where after the initial stroke of the bell, one can
hear reverberations (BOOM . . . BOOM . . . boom . . .) as
the sound waves pass into and out of phase with each other.

Fig. 74

\otiee that if Fig. 74 represents the forces at work in the
whole circle then there will be one place in the circle where the
waves are in phase and one place (opposite) where they will
cancel each other out. If the period represented is a half cir¬
cle (180°), so that the two harmonics arc really the 10 th and
12 th of the full circle, there will be two opposite places in the
circle where they are in phase and two, in square to these,
where they are out of phase.

This is an effect which one often meets; for example Fig.
75 shows the distribution of the Sun in the Zodiac by deeana-
tes in the nativities of 391 delinquent children who were
I nought before the courts in Australia . 1 Ivan Hyde, who
published this data, could find no significant deviation of the
solar distributions w'hen he examined the totals for each sign
of the Zodiac, naturally, since the high score in the first dc-
«a nates of Aries and Libra vvere immediately cancelled out by

169

low scores In the 2nd and 3rd decanates. It was not until he
examined the solar distribution by smaller sectors that the two
opposing peaks became apparent. This illustrates well the mis¬
take which some investigators make, of assuming that the signs
of the Zodiac are necessarily the significant divisions. Notice
the high peaks at the beginning of each half of the Zodiac
and the flattening off half way between.

DisLributurn of the Sun in the Zodiac by dccanatcs in the charts of 3 l Jl
delinquent children, showing the “beat” effect of adjacent harmonics
in the half-circle.

In this example there are two opposite places in the cir¬
cle where the ‘beat’ effect occurs, so that harmonics involved
(adjacent in the half circle) must be two places apart in the
Whole circle. They may in fact be the 10th and 12th as in the
previous example shown in Fig. 74. It must be pointed out
however that this effect can also arise in a different way (see
Fig. 38). Of course, one can get a clearer picture of what is
happening by putting the totals for the two halves of the
Zodiac together.

It may be a coincidence but I have noticed that just as
there is something discordant about the note of a bell or two
adjacent notes on the piano, so this effect seems to appear
where there is an element of discord in the subject of the
study — in this case delinquents. One is doubtful if this sug¬
gestion could he sustained, and yet it seems highly probable
that there must be analogies between the characteristics of
sound wave complexes and the psychological qualities which
correspond to our planetary distribution patterns. Thus some

instruments such as the clarinet produce a full, rounded note
which is reflected in a rounded sound-wave complex, whereas
others such as the ‘shrill passionate voice of the violin' pro¬
duce a rather spikey sound-wave.

This ‘spikey’ zig-zag effect occurs where the fundamental
is accompanied by odd numbered sub-harmonics phased so
that their peaks and troughs coincide with the original peak
and trough of the fundamental. This tends to make the peaks
and troughs into sharper and sharper points as more and more
odd numbered harmonics are added (Fig. 76a). Where a fun¬
damental and its odd numbered sub-harmonics coincide not at
the peaks but at the descending and ascending nodes, one ob¬
tains a square, fortified or turreted effect (Fig. 76b). This sug¬
gests something stable, defensive or resistant. This effect, which
incidentally represents the only situation where one could get a
‘box’ type Zodiac result with alternate signs high and low and
dear sharp changes at the boundaries is one which I have
never seen in practice though it exists in theory. Would a
collection of ‘defensive’ types (policemen, goalkeepers') show this
turreted fortification-type distribution pattern? An interesting
type of wave complex of which one can produce examples is
the saw-tooth effect. This occurs where a harmonic and all its
sub-harmonics coincide at the ascending node (See Fig. 76c).
Notice that if the descending rather than the ascending nodes
coincide the saw-tooth will face in the opposite direction.

171

A good example of the saw-tooth in modified form is to
be found in one of Gauquelin’s experiments. This was one of
the experiments he conducted to show the association between
certain characteristic distributions of particular planets and
specific psychological types. (Full details can be obtained from
the appropriate text. 2 ) In relation to his collection of the
nativities of successful scientists he inquired what psychological
attributes were considered to be characteristic of the typical
scientist. This he did, first by examining a number of studies
of the scientific temperament made by psychologists, second by
asking a section of the educated public to list the words they
would use to describe the scientific type, and third by using a
dictionary of synonyms to enlarge the derived lists of character
traits. He then made use of a dictionary' of antonyms to list
the character traits which were opposite to those that allegedly
describe the typical scientist. Thus he obtained two lists of de¬
scriptive words, one deemed to be characteristic of the typical
scientific, one descriptive of the opposite, temperament.

He then went through the biographical notices which de¬
scribed individual scientists in his collection. Each time one of
his character-trait words was used of one of the scientists, the
position of each of the planets for that person counted once.
Gauquelin thus obtained two sets of planetary positions for
each planet, one which correlated with the words descriptive
of the typical scientist, one set which correlated with the op¬
posite characteristics.

As it happens Gauquelin was chiefly interested in the po¬
sition of Saturn, but he provides the diurnal distribution in 18
sectors for other planets, too. Fig. 77a, then, gives the distri¬
bution of the Moon for the characteristics listed as those of the
typical scientist; 77b gives the lunar distribution for the char¬
acteristics opposite to those of the typical scientist. Here w r e can
see the basic ingredients of the saw-toothed effect, with a very
steep rise (77a) between the extreme ‘low’ in the last 20° be¬
fore the I.G. and the extreme high in the 20° just after the
I.C. This must be produced, as in Fig. 76c, by the coincidence
of the ascending nodes of a number of harmonics at the I.C.
The opposite result is yielded by the opposite character traits
(77b) and this must be produced by the coincidence of de¬
scending nodes at the I.C,

If we are to extend, somewhat shakily, our analogy be¬
tween wave shapes and personality types we should have to
say, perhaps, that the scientific mind should be incisive and
that hence the saw-tooth has some aptness. However the scien-
t ist ought presumably to be using a scalpel rather than a saw
so perhaps the analogy breaks down!

Notice that the peak positions for the Moon in relation to
(lie scientific temperament is in the third house, and this con¬
forms to traditional ideas. Of greater interest, however, is the
t.m that the peak actually comes just after the I.C., that is to
s.iy at the ‘back’ of the 3rd house, the region near the cusp
having only an average score. This confirms what we have
bent saying throughout this book: so many of the arguments
m present-day astrology (in this case, whether the strongest
pomt of a house is in the centre or near the cusp) are simply
bcing carried on in out-worn and irrelevant terms which do not
\pruk the language of astrological reality and can never produce clear
• waters.

172

173

Of course it is fully acknowledged that whoever wishes to
practice astrology must adopt a code of manageable rules, and
therefore the existing rule book must be used until a better
one can be devised. This does not justify the objections, how¬
ever, of those who say that investigations of astrological laws
through the study of large collections of data are of no use
because they are not immediately applicable to the individual
chart. The object of such studies is to enable us to clarify as¬
trological principles so that a manageable code of precepts
which is nearer to the truth can be formulated for the guidance
of those who interpret the birth chart.

We have already shown in earlier chapters that this new
understanding of how astrology works, from the practical view¬
point, is emerging and is already providing new insights, for
example into the interpretative value of aspects. But even
where it is not yet possible to reduce the observed astrological
effects to coherent laws, nevertheless the empirical study of the
effects helps to give the astrologer a sense of what kind of laws
he is dealing with and so inculcate a better feeling for the
subject.

All the same, the inductive method based upon observa¬
tion and experiment can never by itself lead to final solutions.
There should always be an interplay between such methods
and the deductive or philosophical approach, so that observed
effects are related to first principles and such principles vised
again as guides to the understanding of the more phenomenal
side of our science. In the last resort it is ideal philosophy
and the vision of spiritual law's which will give a secure foun¬
dation to our knowledge of all the out workings of astrological
effects. The writings of the German mystic, Jacob Boehme,
are said to have been a direct inspiration to scientists as di¬
verse as Samuel Hahnemann in his formulation of the laws of
Homoeopathy and Isaac Newton in his intuition of the law ot
gravity. It is only in the light of universal spiritual laws that
the details of astrological science can be perfectly tonnulaied.
Although so much of this book has evidently been concerned
with conclusions based upon observational methods, this is be¬
cause present circumstances call for such an approach. Only in

this way can the real nature of the effects which the astrologer
studies be more distinctly seen and so more intelligently and
securely, related to their originating principles.

NOTES

1. See Spic.it (magazine of Sidereal Astrology), Jan. 1970 and April 1970.

2. Gauquelin, Michel and Francoise, Birth and Planetary Data Gathered
Since tf)4. , ) y Scries C, Vol. 3, The Saturn Temperament 8i Men of
Science, see Chapter 4, Note 2 for full details.

17.5

WHAT DETERMINES PHASE?

If wc are to reduce our observations of wave distribution
patterns to coherent ana manageable laws we must try to
draw some general conclusions about the principles by which
astrological effects are related to planetary positions. Some of
these are self evident. The amplitude of the observed harmonics
is, as we said at the outset, related to the intensity of the effects
studied. Gauquelin has himself demonstrated this to be true.
In studying the distribution of Mars in the nativities of sports
champions he found certain parts of the diurnal circle which
were more frequently occupied by Mars, and we have shown
that this is because the distribution of Mars was dominated by
certain harmonics. But when he took not merely any successful
sportsmen but only those of supreme achievement, he found that the
parts of the circle where the peak distribution occurred were
even more frequently tenanted by Mars and, similarly, the places
in the circle which were avoided by Mars in the generality of
sportsmen were even more frequently avoided in the charts of
the greatest sports champions.

This is simply another way of saying that the amplitude
of the harmonics of Mars’ distribution was more vigorous in
the supreme athletes and this, again, is simply another way of
saying that Mars was even more strongly attracted to certain
points in the circle and away from other points. This is
straight-forward enough and merely confirms the general prin¬
ciple of harmonic divisions of the circle.

But the great problem is: What determines the phaseP How'
are we to decide at what points in the circle the maximum
effect occurs in any particular case? Of course we can continue
to collect large quantities of data and make our harmonic
analyses of the planetary distributions, but we cannot do this
forever and for every particular instance. The collections arc
laboriously made in order that by studying them we can ar¬
rive at general principles which will allow us to make astrological
interpretations about planetary positions, even those which have
never been examined in quantity. Ultimately we shall, without
doubt, succeed in arriving at these principles; at present the

176

question of phase remains unsettled however and some discus¬
sion of it is called for.

We are always dealing with the relationship between two
points. In the diurnal circle we are considering the relationship
of a planet to the horizon or to the meridian (in practice the
Ascendant or M.C.). We ask: Where in relation to the Ascen¬
dant does the peak distribution of a planet occur in each har¬
monic? In the zodiacal circle we ask similarly: Where does the
peak distribution occur in each harmonic in relation to 0°
Aries — the point of intersection of the ecliptic and celestial
equator? (The Siderealists consider that the correct point of
reference is elsewhere, but we will consider this later.) In con¬
sidering aspects in terms of harmonics we ask: Where does the
peak distribution of one planet occur in relation to another
planet? In the case of the diurnal and zodiacal circles we can¬
not be absolutely sure that we are correct in taking the Ascen¬
dant and 0° Aries as our measuring points, we only assume we
arc correct. In the case of one planet in relation to another
no question arises about the positions of the two points in¬
volved (unless by any chance we should be using heliocentric
co-ordinates).

In considering what determines the phasing of the peak
distribution there are two likely hypotheses. The first may be
thought of as attributing to the aspected point, whether the
planet or some other point, a sort of projective power. Thus in
Fig. 78, if we regard the circle as representing the 360° of
any harmonic (not necessarily that of the 1st harmonic only),
then if the phase is given as 240°, we are saying that the
aspected point or planet symbolically projects as it were a
maximum effect to a point two-thirds of the way around the
circle, and that that is the point at which the moving planet,
as it passes around the circle, will produce the strongest effect
in relation to a particular quality.

177

I'hc second hypothesis is. on the face of it, more in con¬
formity with the philosophy of harmonies. It states that the
conjunction of the moving planet with the aspected point is al¬
ways what counts, and that it is always at the conjunction,
say, of one planet to another, or a planet with the Ascendant,
that the maximum effect, positive or negative, occurs, d his is
another way of saying that the phase angle of any harmonic
in any significant relationship between two factors always tends
to be 0° or 180°. Either planet A in conjunction with planet B
(or with the Ascendant, etc.) is positive (0° phase) and promoles
a certain quality, or else A with 15 is negative (180° phase) and
militates against a certain quality (see Fig. 79). I or example.
Mars in conjunction with the Ascendant may promote the
quality of aggressiveness: this would be associated with a
Mars/ Ascendant harmonic with a phase of 0°. But. Mars con¬
junct Ascendant might militate against the quality of forcbear-
ancc; thus the phase will be 180° in relation to that character¬
istic.

A w '"i 6 Mi ;kim! iv;• A vvi'h B is ve

Fig. 79

» There is something very attractive, from the philosophical

viewpoint, about this hypothesis; it reduces things to a bare
i simplicity which is in conformity with many other scientific

^ and philosophical ideas. It involves a simple contrast between

i positive and negative, being and non-being. The / Ching is

built up on this contrast between polarities of Yin and Yang,
and the 64 hexagrams simply represent the two alternatives
raised to the power of 6. 1

Two objections to this hypothesis immediately present
themselves. First, even allowing for the undoubted fact that
the phase angles observed in empirical studies can only be
approximations, nevertheless we have evidently found cases

178

where harmonics arc phased at 90° or 270°, i.e., with the
peak intensity before the exact aspect and the trough after¬
wards (or vice versa) with the exact conjunction representing
the node. Secondly we have Gauquelin’s results to consider
where the characteristic peaks come after the Ascendant and
M.C.. i.e. in the astrologers’ 12th and 9th houses. This again
suggests that the Ascendant and M.C. play a nodal role, or
at least that the peak does not coincide with die "angle’ of the
chart.

In this connection we must remember that, with all odd-
numbered harmonics, if the peak reaches the exact positive
or negative phase at say, the Ascendant then the points in
square (i.e. the M.C. and I.C. if we are prepared to speak in
terms of mundane squares), will be occupied by a node. Simi¬
larly, in zodiacal terms, any odd-numbered harmonic which
peaks at 0° Aries will have a node at 0° Cancer-Capricorn.
But this would not account for Gauquelin’s peaks in both the
12th and 9th houses. We are left to conclude either that our
second hypothesis, where the conjunction of two factors always
represents the positive or negative phase, cannot be sustained,
or that Gauqueliivs division of the mundane circle is in some
way misconceived, incorporating as it docs both M.C. and
Ascendant in one circle of reference though they arc seldom
in exact longitudinal square. There are certain things about
Gauquclin s results which make one believe that his use. in
effect, of the circle of oblique ascension (where M.C. and
Ascendant are 90° apart, i.e. in mundane square) must be
right, but there are other features of these results which raise
misgivings about his divisions of the diurnal circle. This is
something which has yet to be explored.

'T here is also the idea to be considered that the most sig¬
nificant astrological point in the East may not be the Ascen¬
dant but another point. We accept the significance of the
{joint on the ecliptic which is cut by the meridian running
North-South and passing through the Zenith of the observer
and the North and South Poles. Why should we not look for
equal importance to the points on the ecliptic cut by the
Prime Vertical, the corresponding meridian which runs East-
W est through the observer’s Zenith (and which therefore yields
i he ecliptic {joints which are due East and due West — the

179

so-called Anti-Vertex and Vertex), or the ecliptic points cut by
the l : ,ast-West meridian which runs from the eastern and west¬
ern points of the horizon but passes through the North and
South Poles? These again are matters which have been partial¬
ly explored in astrology but have not been related to diurnal
harmonics.

Let us see what happens if we examine Gauquelin s re¬
sults carefully in the light of our second hypothesis. Is it or is
it not true that the important harmonics yielded hy Gauquelin ’.5 re¬
searches tend to be phased either at 0° or 180 relative to. say,
the Ascendant? In other words docs the Ascendant mark either
the peak or the trough in Gauquelin’s outstanding harmonics?

We must remind the reader again (it has already been
pointed out but perhaps not sufficiently emphasised) that
“Ascendant” in this context means the planet’s own point
of rising. This often differs from the Ascendant as such,
but throughout this chapter “Ascendant” means the planet s
own point of rising.

That Gauquelin’s results are highly significant, arc becom¬
ing more significant as he proceeds and will one day be recog¬
nised as such by the scientific world, all this is beyond doubt.
That they will eventually be seen to rest upon the general
theory of harmonics is also, in our view, beyond doubt.
So let us see what we can make of them in relation to our
hypothesis about phasing. It is sometimes better to stick to a
good hypothesis which does not quite appear to fit the ob¬
served facts than to abandon it in favour of 'facts' which may
prove to be distorted by misconceived observational methods.

THE EXPERIMENT

1. Material. Our material consists of the Astrological Associa¬
tion’s harmonic analysis of all Gauquelin s planetary' distri¬
butions by 36 sections in the diurnal circle. 2 that is to say of
Moon, Venus, Mars, Jupiter and Saturn positions for 2088
sports champions, 2552 physicians, 1095 scientists, 3046 mili¬
tary men, 1473 painters, 1409 actors and 1352 writers." The
smaller collections of politicians and musicians arc omitted for
reasons stated below.

180

Each of these collections consists of two groups: 1) nativi¬
ties collected in France and 2) nativities collected in other
countries (Germany, Belgium, Holland and Italy). The object
of our exercise is first to ask which of the harmonics revealed
by the harmonic analysis of these planetary distributions are of
outstanding significance, and then to see where their phase
angles lie in relation to the (planet’s) Ascendant.

2. The Estimate of Significant Harmonics. The science of calculat¬
ing the significance of particular harmonics in analyses of
this sort is a branch of mathematics which has received rela¬
tively little attention, although a number of writers have tack¬
led the problem. I have provided an appendix dealing with
some of the problems of harmonic analysis and for those inter¬
ested, this chapter should be read in conjunction with that
appendix.

First we must notice that the amplitudes given in har¬
monic analyses will vary with the size of the sample analysed.
The larger the number of cases in one’s sample and the high¬
er the sector totals the more stable and reliable will be the
result and the less erratic will be the amplitudes yielded. The
smaller the sample, the higher and more erratic will the amp¬
litudes tend to be. It is for this reason that politicians and
musicians are omitted from this test, in each case one of the
two groups was too small a sample.

I do not know' of any formula which gives the precise re¬
lationship between sample size and expected mean amplitude, al¬
though I am told that this is proportional to the square root
of the sample size. However, it is possible to determine an
approximate expected mean amplitude by taking such harmon¬
ic analyses as we have and calculating the mean amplitudes in
those. Thus Fig. 80 shows the actual mean amplitude in thir¬
teen sets of harmonic analyses of various results. The small
crosses represent mean amplitudes of Gauquelin’s results, each
one being the mean of 85 amplitudes. The three heavier cross¬
es are from analyses of solar positions in the nativities of 710
judges of the high court, 1974 British clergy and 7302 doctors
of medicine, each of these being the mean amplitude of 179
harmonics.

181

Insofar as it must be assumed that some of the harmonics
involved have significantly high amplitudes due to their astro¬
logical connotation, an empirically obtained graph such as
this should yield a curve which gives somewhat too high a
mean amplitude. However, because the significant harmonics
may be relatively few among a large number of others the
result may be taken as a fair practical guide. At any rate it
will not be too low.

In order that the reader can see exactly what is involved,
let us give the harmonic analysis of the distribution of Mars
in Gauquelin’s 3046 military men:

Mars — Military Men (3046)

French (1035)

Other Countries (2011)

Combi

•ml

Hn rmon ic

Amplitude

Phase

Amplitude

Phase

Amplitude

Phase

6 9

216

4-5

259

4.0

240

7.5

0t6

260

2.5

357

13.3

10.3

11.5

7.9

242

0.8

263

3.2

246

4.9

3.5

3.7

4.9

2.)

234

0.8

230

10.0

106

5.2

284

0.2

202

7.5

194

9.0

146

7.9

160

4.9

249

5.6

223

5.2

231

12.3

297

3.7

5.5

317

3.9

3.8

343

190

5.7

1.2

334

120

5.1

1 7

336

165

l .5

296

2.8

137

1.3

145

4.8

6.0

5.5

4.5

6.)

137

2.8

142

4.5

102

7.0

151

5.7

140

2-9

3.5

270

1.3

270

182

We have three sets, ‘French’, ‘Other Countries’ and
‘Combined’. It has been customary to omit the 1st harmonic
from these results because, in some, astronomical factors are
liable to give an artificially high result. If we total the ampli¬
tudes for the other 17 harmonics for the combined sets and
find the mean, the result is 4.0. Comparing this with our
graph (Fig. 80) we find that the expected mean amplitude for a
sample size of 3046 is almost 3.4. Thus our mean for this set
is higher than expected; this is not surprising since we have
chosen a factor (Mars — military men) which one would ex¬
pect to contain some significantly strong harmonics.

Having now provided ourselves with some means of assess¬
ing what the expected mean amplitude will be for a given sam¬
ple size, we can ask what criterion we must adopt for singling
out those harmonics which are significant. In doing this we
arc obviously looking for those harmonics which are not only
strong in terms of amplitude but also those that are consistent
in phasing as between the nativities collected in France and
those collected in other countries.

For example, in the table showing the harmonics for
Mars in the maps of military men given above we can see
not only that the 4th harmonic is very strong for both ‘French’
.Mid ‘Other Countries’ but also the phase agreement is close as
between the two sets. It is because the two sets have this close
agreement in phasing that the Combined’ amplitude is strong,
lor no matter how strong the amplitudes of the two sets are
separately, if the phase agreement is wide then they would
mid to cancel each other out.

Alter considering our position, the following admittedly
arbitrary criteria have been adopted for the choice of harmon-
u s to be considered as significant:

1. The observed amplitude must be 50% above the
expected mean for the sample size far each set separately.

'1. 1 he amplitude must be 100% above that expected for
the combined total of the two sets together.

3. The phase angle of the two sets must be within 30°.

I I ms. to pursue our example of Mars — military men, the
li« tuh set consists of 1035 cases and the expected amplitude

183

for this size of sample (see graph) is 5.7; the amplitude ob¬
tained for the 4th harmonic, 13.3, is over 50% above that
expected. The Other Countries set consists of 2011 cases —
expected amplitude 4.1; again the 4th harmonic (amplitude:
10.5) qualifies. For the Combined cases (3046) the expected
amplitude is 3.4, so the observed amplitude (11.5) which must
be double this, easily qualifies. Finally, the phase angles, 52°
for the French and 53° for Other Countries, fall within 30° of
each other. Thus, by the criteria we have adopted the 4th
harmonic for Mars in military men qualifies as significant. As
can be seen it is the only one in this set which does qualify.

Before setting out the list of harmonics found to be signif¬
icant there is one other qualification we must make. As already
mentioned, investigations of the reliability of harmonic analysis
by researchers of the Astrological Association have shown that
the standard methods of Fourier analysis only yield reasonably
reliable results up to that harmonic which is one-sixth of the
sector-totals used for the analysis (see appendix). Gauquelin
gives 36 sector-totals so we can only depend upon the reason¬
ably close accuracy of the amplitude and phase given for the
harmonics up to and including the 6th. Since we omit the 1st
harmonic for astronomical reasons we shall only have regard to
the harmonics from the 2nd to the 6th, inclusive.

3. Harmonics Found to Be Significant. On the basis of the criteria
given above the following is a list of harmonics found to be
significant. Notice that against the combined phase angle there
is a second figure given in brackets. This represents the phase
angle measured from a different point and will be explained
presently.

OTHER

FRENCH COUNTRIES COMBINED

Expected Ampli- Ampli- Ampli-

Ampli¬

tude

Harmonic

rude

phase

tude

Phase

rude

Phase

Milita ry Men

1035 French

5.7

Mars

2011 O.C.

4.1

4Lh

13.3

10,5

11.5

52(16)

3046 Corah.

3.4

Sports Cfiampians

M ars

11(344)

1094 French

5.6

3rd

15.1

10.0

356

12.4

994 O.C.

5.8

V onus

2088 Comb.

4.1

5ih

8.8

LS3

10.2

162

9.3

172(127)

184

Expected

Ampli

Ampli-

tude

Harmonic

tude

Phase

tude

Phase

tude

Phase

Physicians

132) l-rench

5 0

Saturn

1231 O.C.

5.2

4th

8 9

10.3

9.3

49(13)

2552 Comb.

3.7

Samlisli

381 French

8.4

Jupiter

714 O.C.

6.5

3rd

13.4

221

12.9

195

12.8

205(178)

1095 Comb.

Painters

1133 French

5.4

340 O.C.

8.7

Saturn

1473 Comb.

4.8

4th

16.3

253

16.5

244

16.3

251(215)

4 r/rjFV

783 French

J upiter

026 O.C.

7.0

4th

15.4

10.4

13.0

46(10)

1409 Comb

4 9

H'ritrrs

813 French

6.4

Saturn

539 O.C.

7.5

4 th

11.7

200

11.7

229

11.3

211(176)

1352 Comb.

5.0

In this list we have eight harmonics which are evidently signif¬
icant. Without a doubt our qualifying mark for what consti¬
tutes significance is a very stiff one indeed, and it has certain¬
ly demanded the exclusion of a number of harmonics which
one can feel confident are in fact significant. Some of these
are listed below.

In order to give some substance to our qualifying standard
it should be said that Colin Bishop of the Astrological Associ¬
ation generated four sets of 36 random totals on a strictly
comparable basis to Gauquelin’s results. Each of these was
subjected to harmonic analysis exactly as in the table (Mars —
military men) above. This gave 72 harmonic amplitudes and
phase angles (18 harmonics x 4 sets) based on random data.
As these results had no reference to observations in the diurnal
circle it was legitimate to compare each harmonic amplitude
and phase with every other , yielding 2556 pairs of harmonics for
comparison-f 72 x 71) 2. Although these harmonic analyses

looked superficially very like Gauquelin’s results, only seven
pairs of harmonics out of 2556 pairs reached our qualifying
standard of significance, or one pair in 365. 'From Gauquelin’s
results we have obtained eight significant pairs out of 175,
or one pair in 22.

185

As the above eight significant harmonics do not provide
us with the abundance of evidence which we should like, it is
worth listing the main harmonics which did not qualify but
missed either because the amplitude for one of the two sets
separately was not quite high enough, or because the phase
agreement was not quite close enough. Here are the near
misses’, eleven in number, in which one can feel some confi¬
dence:

French

O.C.

Combined

Military Men
Sports Champions
Physicians

scientists

A'filers

j upiter 4th
Mars 4th
Mars 3rd
Mars 4lh
Saturn 3rd
Venus 5th
Moon 3rd
Saturn 4th
Moon 4tit
Mars 6th
Venus 4th

17.9

8.6

1ft

10.6

44(8)

17.4

9.3

115

12.1

76(40)

9.5

8.1

11(344)

11.7

5.3

6.4

38(2)

9.3

6.0

358

7.7

1(334)

11.6

181

11.6

185

11 6

1B3(137)

14.0

144

7.9

177

9.7

161(134)

6.0

21.2

15.9

47(11)

8.8

14,0

10.3

59(23)

9.8

10.6

9.9

81(27)

16.4

4.3

11.5

52(16)

:ant Harmonics.

now

come to con-

sider where the phase angles of these outstandingly strong
harmonics lie.

It occassionally happens in scientific work that some kind
of mistake or accident leads to the discovery of something
which might otherwise remain unnoticed and this is what
happened in this case. Due to a misunderstanding of instruc¬
tions the phase-angles were originally calculated so that they
were measured from the centre of Gauquelin’s Sector One (i.e.,
the first 10" above the Ascendant) instead of from the Ascen¬
dant. In other words they were measured form a point 5"
above the Ascendant.

When these were examined there was indeed a tendency
for the phase-angles to fall into two groups, those phased
roughly towards phase 0" and those phase roughly towards
180", although they were rather to one side of these points.
When the mistake in measuring was discovered and put right
the phase-angles, instead of moving nearer to 0" or 180",
moved in the opposite direction. This led me to ask from
what point it was necessary to measure the phase-angles so that they
were phased at (f or 18(T.

A little experimenting revealed that the point needed was
some distance above the Ascendant, say between 8" and 10°.
Therefore, in the foregoing lists of outstanding harmonics 1
have listed, against the ‘Combined’ phase-angle, what the
phase would be if measured from a point 9° above the Ascen¬
dant. Fig. 81 shows, on the left, how the phase angles fall
when they are measured from the Ascendant, and on the right
how they fall when measured from a point 9° above the
Ascendant.

Phase angles measured from the Ascendant (left) and from a point
9“ above the Ascendant (right) showing the tendency for the strongest
harmonics in Gauquelin’s results to be phased at 0° or 180 s in the
latter case. (The eight most significant harmonics are marked with a dot.)

First, let us be clear what this diagram shows. The lines
on the left-hand circle do not show how far the planet was
above the horizon, but how far along the particular harmonic
it had travelled, treating the whole circle as the length of
that harmonic. In other words the 360° of the circle repre¬
sents the 360° of each and every harmonic.

For example the 4th harmonic of Jupiter in military men
has a phase of 44“ when measured from the Ascendant, but
of 8° when measured from a point 9° above the Ascendant.
(See Fig. 82)

186

187

Now in both parts of Fig. 81 we can see that the phase-
angles for our significant harmonics spray out in opposite
directions, but it is at a point approximately 9° above the
Ascendant that they tend to be phased at 0° or 180°. What is
the significance of this extraordinary finding? There seem to be
three possible explanations;

1. Gauquelin’s way of treating mundane positions in
oblique ascension has produced some unexplained distortion in
the result. On the face of it this does not seem likely but it
remains a possibility.

2. The significant point we should be taking note of is
not the Ascendant but some other point which lies near the
Ascendant.

3. Perhaps the most likely explanation is the simplest one
and it has the advantage of putting the blame for everything
on a well-known scapegoat; father! In European countries the
responsibility for registering the birth within so many days
rests with the parents, thus it normally falls to the lot of the
father. In other words the time of birth as registered tends to
be significantly late! IP is equivalent to about 36 minutes of
time and this seems rather a lot but our point may be a little
less than 9°. bringing the time lag nearer to half an hour.

It is certainly a common observation among astrologers
that the reported time of birth tends if anything to be a
little after the true time. We must remember that most of
these births took place long before the days when fathers
were allowed into the delivery room and so they were depen¬
dent upon a report which might reach them after some delay.
Being male chauvinists they would naturally not appreciate
the reason for any delay.

188

If we can judge strictly by our nineteen strongest harmon¬
ics listed above we can also give the different groups of fathers
a reliability rating. The fathers of future scientists performed
best being about 10-15 minutes late. The fathers of future
physicians came next, about 20 minutes late; sport champions
25 minutes; actors, military men and writers about three-
quarters of an hour, and the fathers of painters just over one
hour. This may be a misleading assessment, based as it is on
a few harmonics, but no one to our knowledge has made a
scientific study of the degree of impairment to the faculties
of men who have just heard that they have become fathers or
of the mental process by which fathers decide on the time to
be registered.

A very interesting and informative article by Francoise
Gauquelin in the Journal of Interdisciplinary Cycle Research 4
presents a study made from hgr wide experience of the evi¬
dence as to the reliability of registered birth times. She implies
that the professional classes tend to be more accurate with
their information than the lower orders, that birth times
registered in this century are considerably more accurate than
in the last and becoming steadily more so, and that the
Germans tend to be more accurate than the South Europeans. 5
It would be interesting to know if the German nativities in
Gauquelin’s collections showed harmonics phased closer to the
Ascendant than in France and Italy. The relatively good
showing of sports champions may be due to the fact that they
are the latest generation to appear in Gauquelin’s results and
therefore benefit from the improved accuracy of registration in
the 20th century.

To sum up, Fig. 81, showing the phasing of Gauquelin’s
strongest planetary positions, leaves little doubt that the phase-
angles tend to fall into two opposing groups. This lends some
support to the idea that it is the conjunction of two factors,
in this case the planet and its Ascendant, which marks, in any
harmonic, the point of strongest 'influence’, positive or nega¬
tive. This tends to give phase-angles of 0“ or 180 6 . If this is
true and it is the Ascendant which is the significant point in
this context, then Gauquelin’s recorded birth times tend to be
late by about half an hour and the much discussed strength of
the 12th and 9th houses in Gauquelin’s results becomes sus¬
pect. In any case the peak of this effect, as observed, does not

189

He in the middle of the 12th and 9th houses but between 7°
and 11° past the angle. In order to see the sort of thing that
happens when the phasing slips in this way one has only to
look at Fig, 24 where the positive phase of the 4th and the
negative phase of the 12th, which coincide, have got into the
12 th house and raised the score there to a very considerable
degree.

Finally, we must make it clear what is implicit when we
speak of harmonics being positively and negatively phased.
The 3rd harmonic of Jupiter for example is negatively phased
at the Ascendant for scientists (Fig. 83a). Since Jupiter 3rd
represents the idea of exuberant enjoyment this suggests that this
characteristic is not commonly found in the temperament of
the scientist; compare, for example, the annual dinner of a
rugby football club, a Jupiter 3rd event, with the annual
dinner of a scientific society, a more staid occasion. But the
3rd harmonic of Mars is positively phased at the Ascendant
for sportsmen (Fig. 83b) and this suggests that the enjoyment
of competition and the exercise of strength is a characteristic
of these people.

In brief, then, there is evidence that the conjunction of
two factors tends to produce the strongest effect, positive or
negative, in any harmonic relationship. We cannot regard
this as conclusive however, and the possibility that there may
be a symbolic basis for phasing at any point in the cycle of a
harmonic remains. If this is so then we may evidently expect
the four ‘cardinal’ phase-angles, 0°, 90®, 180°, and 2TIP, to
take some precedence in potency. One piece of evidence in

190

particular must not be overlooked; this concerns the phasing
of the lunar harmonics in Gau quel in’s test on the scientific
character-trait words, described in the last chapter (Fig. 77).
This shows the coincidence of ascending and descending nodes
at the I. C., which alone leads us to include 90 and 270 as
important symbolic phase-angles.

NOTES

1 For discussion of this idea, see Graham, Charles M,, The Concept of
Cycle in Contemporary Science, Astrology and I Ching, Green Hay, Wi.:
Cambridge Circle, 1976

2. See Chapter 4, Note 6.

3. Gauquelin, Michel and Franchise, Birth and Planetary Data Gathered
Since 1949, Series C, Vol. 1, See Chapter 4, Note 2 for full details.

4. Gauquelin, Francoise, "Terrestrial Modulations of the Daily Cycle of
Birth," see Chapter 4, Note 4,

5. A quick check on 500 cases from each country shows over 80% of
French births to be registered on the hour but less than 50% of Ger¬
man births. Over ’,i of German births arc registered at quarter to or
quarter past the hour, suggesting a real attempt at accuracy.

191

TROPICAL OR SIDEREAL?

One of the great controversies of the astrological scene in
the past 50 years has been between the Tropicalists and
Siderealists. The former contend that the Zodiac begins at the
Vernal Point (the intersection of ecliptic and celestial equator)
and moves with the precession of the equinoxes. As opposed to
this, the Siderealists contend that Ptolemy (or someone) made
a disastrous mistake in ever taking note, for astrological pur¬
poses, of precession and that the true Zodiac reposes in
unchanging splendour in the circle of the constellations, pro¬
viding the only true basis for astrological interpretation,

Cyril Fagan, undoubtedly a very knowledgeable and
perceptive exponent of astrological lore, was the great cham¬
pion of the Sidereal Zodiac. He sought to demonstrate that
this was the Zodiac used in the astro logically enlightened per¬
iods of antiquity. 1 Fagan was supported by Donald Bradley,
the brilliant American researcher, who sought to justify the
Sidereal Zodiac through statistical studies, 2 the scholar Rupert
Gleadow, who fought the battle on the interpretive front;’
Brig. R. C. Firebracc, who edited the Sidereal magazine
Spica for many years, and others. Fagan, Bradley, Gleadow
and Firebracc all died during 1973-74.

In the West the great majority of students use the Tropi¬
cal Zodiac but in the East the Sidereal Zodiac is still the
accepted yardstick. Those who have read this book so far may
feel that too much has been expected of the signs of the
Zodiac and that this twelvefold division has been given undue
prominence in comparison to other divisions.

Perhaps the most telling indication that something, some¬
where, is wrong, is the very fact that this controversy about
the ‘right’ Zodiac can exist at all. I summed up the position
in 1968 as follows, when reviewing Rupert Gleadow s book
Your Character in the Zodiac in which he gives his interpretations,
in terms of character, of the signs of the Sidereal Zodiac:

'‘The traditional tropical view of the signs is that
each sign provides, in most respects, a striking and
distinct contrast to those adjacent to it. In the inter¬
pretation under review, (i.e. Gleadow’s) these distinc¬
tions may be muted but they are still there. Pisces
still ‘dislikes taking decisions’, is ‘kind and good na-
tured’, ‘undisciplined’, etc., whilst Aries is still ‘often
full of energy' and decision’, ‘unaware of the feelings
of others’, ‘straightforward and direct’, and so on.

“Sagittarius still ‘can’t help enjoying life while Cap¬
ricorn cannot help thinking it all very uncalled for’.
Sagittarius still ‘hopes for the best’ while Capricorn
still ‘prepares for the worst’.

"Yet the two Zodiacs are now said to be out of step
by more than V* of a sign, so that we have a situa¬
tion in which one group of people are looking at a
man and seeing someone who is prompt and decisive
and another group who look at the same man and
see an easy-going character much given to procrasti¬
nation. It is just as if intelligent people were to sit
round solemnly arguing whether a certain colour were
black or white.

“Now I have found it a good rule in life to assume
that when an intelligent person (and I know such
people on both sides of this controversy) has made a
careful study of something, iL is unwise lightly to set
his opinions on that subject aside. And when a situa¬
tion arises in which informed judgments inexplicitly
arrive at exactly contrary conclusions about the same
thing, I believe one can nearly always look for some
kind of confusion in the point at issue.” 4

In the light of the concept of harmonics one can see
where some of this confusion arises. Part of it evidently comes
simply from the over-emphasis of the twelve-fold division and
the neglect of other valid divisions which must be just as
strong if in a seme less basic. But another distorting factor
comes from that view of the ecliptic which sees it, astro-
logically, as twelve box-type sectors, each sign having a uniform
quality from start to finish, instead of as a complex of wave
forms.

192

193

It is this last error which undermines—indeed, invalidates—
the work of Bradley and others who have followed in his
footsteps, seeking to justify the Sidereal Zodiac on the basis of
the greater statistical significance of solar emplacements in the
Sidereal signs as opposed to the Tropical. The theoretical basis
of such work by Bradley and others is as follows-, the Zodiac
is envisaged as twelve equal sectors of the ecliptic with distinct
boundaries and a more or less uniform significance of each
sign from the first degree to the last—like twelve boxes placed
end to end. Thus, on the assumption that each sign will
favour say, certain vocations, one has only to collect a large
number of astrological positions for members of a certain pro¬
fession and ask where abouls in the ecliptic one must make one j
twelve equal divisions or boundaries so as to obtain the most significant
divergence of sign-totals and this will tell one where the bound¬
aries lie and so where the Zodiac starts and ends.

On this assumption Bradley and others have made their
collections of nativities of different groups of people, found the
total of solar positions for each degree of the ecliptic, and
then tried out thirty possible Zodiacs, one starting from the
vernal point 0® Aries, one from 1° Aries, 2° Aries, 3° Aries
and so on up to 29° Aries, thus sliding the Zodiac along the
ecliptic, as it were, to find at what point it produces the most
significantly high and low scores for Sun-position totals.

As long as the Zodiac is viewed as twelve boxes this
method should succeed. There will come a point in the process
where the twelve divisions ‘click into place’, so to speak,
with the true zodiacal divisions. But the zodiacal influences are
not box-like divisions but are represented by the ebb and flow
of harmonics in the ecliptic circle, and this requires a different
approach.

One can illustrate the situation in various ways. For ex¬
ample we have seen in an earlier chapter that the strongest
single solar harmonic in the Zodiac in the largest collection
of nativities we have, that of 7302 physicians, collected and
analysed by Gleadow and Firebrace, is the 12th harmonic,
the 30° wave (see Fig. 29).

Now if one goes along this Zodiac giving a total of Sun
positions for each sign of the Zodiac one is always exactly can¬
celling out this harmonic by adding together, in each 30°, the

positive and negative halves of the wave. And it does not matter
where abouts one makes one’s divisions—one can have 30
possible Zodiacs or a thousand—there will always be a positive
and negative half of a wave in each 30°. So Bradley, by the
methods he used and the model he formed for so many
subsequent siderealist investigations, was throwing away the
strongest element in this solar distribution, and a good many
others besides.

But if this is so, how have the Sidercalists been able to
come up with what they call “consistently’' good results in
favour of the Sidereal Zodiac? The first answer is that such
results do not consistently favour the Sidereal Zodiac; their re¬
sults are mixed and only favour the Sidereal division on bal¬
ance. But the real reason for this is deeper yet. Suppose we
consider a zodiacal distribution where the 5th and 7th har¬
monics dominate, with the 5th harmonic having a phase of
180° at 0° Cancer (0° at 0° Capricorn) and the 7th having a
phase of 180° at 0° Aries (0° at 0° Libra), both Tropical.
Fig. 84 shows the result. The waves both have a primary
phase in relation to the cardinal points of the Tropical Zjodiac,
yet this combination of odd-numbered harmonics produces a
distribution with the highest and lowest scores in Sidereal signs
as delineated by the Bradley-Fagan ayanamsa.

In Fig. 84 we have shown the first six signs only. The
parts of the distribution which coincide with Sidereal Gemini
and Leo arc entirely below the mean and Sidereal Cancer
entirely above. In the Tropical Zodiac these ‘high’ and ‘lows’
do not so exactly coincide with the sign boundaries. The
graph will be inverted for the second six signs so that the
most outstanding results for the whole Zodiac will be ‘highs’
in Sidereal Cancer, Sagittarius and Aquarius and ‘lows’ in
Sidereal Gemini, Leo and Capricorn. Not one of the Tropical
signs will produce such “good” (i.e. significant) results. Yet the
marking points for the harmonics involved are the cardinal points of
the Tropical gfodiac, and this will happen again and again
and indeed, I believe, tends to happen when odd-numbered
monies are involved either by themselves or mixed with even-
numbered harmonics.

194

195

Sid,

MOON 1 RAINFALL

__|_I_ 1 _1-

y U 5 / ^

TROPICAL SIGNS

Fig. 84

Showing how harmonics with a primary phasing measured from 0°
Aries (Tropical) will often produce the highest distribution scores in
those parts of the ecliptic which correspond to the Sidereal signs.

This all comes about basically because the 'influences’ of
the ecliptic circle have been over-simplified into a twelvefold
Zodiac with distinct boundaries instead of the all-various har¬
monics of the circle. Bradley should have guessed as much and
perhaps, by the end, did. His work on meteorological studies,
now accepted by the scientific world so far as the Moon and
rainfall are concerned, are clearly based on the harmonics of
cosmic periods — in this case the synodic lunar period.

Fig. 85 shows rainfall precipitation over 50 years in the
United States as related to the synodic lunar period, as dem¬
onstrated by Bradley. 5 One is left in no doubt of the domi¬
nance of the 2nd harmonic as a related factor. Bradley also did
work showing the relationship of Venus and Jupiter to rainfall
precipitation, no less convincing than that relating to the
Moon. This, however, has not generally been accepted; a nice
example of how scientists are conditioned by their metaphysical
conceptions of what is possible! This work was based partly on
the Capricorn Sidereal ingress positions of Venus and Jupiter,
but there are other possible ‘marking points’ in that vicinity
which could provide a basis for his results.

196

NM FO FM LQ NU

To come back to the question of the Zodiac, the import¬
ant issue is not one of the Zodiac as such but of the signifi¬
cant focus or foci in the ecliptic from which effects, as repre¬
sented by the harmonics in this circle, are generated. To put
it simply, we are looking for a point or points in the circle of
the ecliptic which have a substantial identity capable of pro¬
ducing effects. Fixed stars could possibly answer the require¬
ment but in that case we would have many points, all pro¬
ducing effects. Unless we are prepared to contemplate such a
medley of zodiacal influences all producing harmonics (which
is not impossible), this is an answer which we must tentatively
eliminate.

It is much more likely that such effects are generated
from the point where two great circles intersect or from some
kindred factor identifiable to astronomy. For such points there
are several contenders. First we have the points of intersection
of the ecliptic and celestial equator—the Tropical points 0®
Aries and 0 6 Libra. This must be the most likely choice. A
second alternative is the Solar apex, the point in the constel¬
lations toward which the Sun and its system of planets is mov¬
ing (and this is said to be at about 2°6’ Capricorn). A similar
possibility is the Galactic Centre, positioned evidently at about
26°3r Sagittarius, 6 at present. A third possibility is the inter¬
section of ecliptic and galactic Equator.

197

All these coulcl be significant measuring points in the
ecliptic, all except the first arc Sidereal and all, incidentally,
arc more likely candidates than the point 0° Aries of the Side¬
real Zodiac postulated by the Bradley-Fagan ayanamsa. This
point appears to have no astronomical identity at all, unless
it is claimed to reside in one of the Fixed Stars, as used to be
claimed for Spica until it was agreed that this star did not
measure up to requirements.

But it is to the Tropical marking points, the equinoxes,
that we come back as being the most likely generators of har¬
monics in the ecliptic, at least so far as the Sun is concerned.
We can easily put this to the test for we have many collec¬
tions of data which include solar distributions. The question
therefore is, quite simply, do the solar harmonics in the collec¬
tions of data gathered to date tend to have a primary phasing
(i.c. 0°, 90°, 180°, 27(F) at the equinoxial point 0° Aries?

The Astrological Association holds harmonic analyses of
the solar distribution for the following collections of data: 7302
physicians, 2875 artists. 2492 American clergy, 1974 British
clergy-, 1024 cases of poliomyelitus, 977 nonagenarians and
710 judges of the High Court. 7 If then we take all of the first
60 solar harmonics in these collections which have an ampli¬
tude at least double that expected for the sample size (see
graph, Fig. 80), we can sec to what extent they do have a
primary phasing in relation to the equinoxial and solisticial
points (i.e. (F Aries, Cancer, Libra and Capricorn in the
Tropical Zodiac).

Here is the list of such harmonics with their phase-angles
measured from 0° Aries:

English Clergy

5th . .

. . 41

7th . .

. 102

22nd. .

275

26th . .

199

49th . .

182

58th . .

265

American Clergy

9th . .

. 340

Nonagenarians

9th . . . 262
18th ... 184
51st ... 178

Artists

5th .. . 253
47th ... 309

Physicians
12th ... 229
25th ... 82

31st ... 178
57th ... 112

Polio

24th ... 100
36th ... 168

We can show these phase-angles in diagramatic form as in
Fig. 86a. It can easily be seen that they do tend to have a
primary phasing at 0° Aries although, interestingly, there are
two or three good ones which have a phase mid-way between
the cardinal points, i.e. at the 45° intervals. These include the
powerful 12th among physicians which must be the best single
result we have.

? ? D

2?0

Fig. 86

Showing (left) phase angles of the stronger solar harmonics in the Astro¬
logical Association's collection of nativities and (right) the phase angles
of the 5th harmonic series in the charts of 7302 physicians, both re¬
vealing a tendency to a primary phasing measured from 0° Aries,
Tropical.

It is not certain that by simply taking the strongest har¬
monics from these sets we are necessarily adopting the best
policy. Striking evidence is to be had by taking some of the
“families” of harmonics which, as we have said earlier, show
up as being characteristic of these harmonic analyses of partic¬
ular groups of nativities.

The collection of 7302 physicians is easily the largest col¬
lection we have, and with the added accuracy which such
large totals give we can lean rather heavily on the harmonic
analysis of these doctors’ Sun positions. This particular har¬
monic analysis is given from the 1st to the 90th harmonic as
shown in the following table:

198

199

H: Harmonic

A: Amplitude

I*. Phase-

5.2

2.2

2.5

171

2.5

2.8

4.0

239

336

2.7

139

1.8

235

4.3

274

1.7

111)

6.2

229

1.1

262

1.9

1.2

100

2.2

356

2.2

162

1.0

133

158

2.3

277

2.8

349

1.2

340

1.9

2.4

240

4.7

3.6

284

2.2

201

125

3.0

1.5

4.5

178

285

2.1

102

4.2

3.1

265

2.0

108

2.3

332

1.8

223

2.8

249

1.4

284

3.1

186

3.3

340

2.8

318

235

184

2.2

107

1.1

184

1.2

266

1.4

1.5

347

1.9

317

1.2

207

288

2.1

163

1.1

311

1.8

190

5.8

112

2.5

1.5

273

1.6

1.8

124

3.7

251

2.5

194

2.6

217

3.5

3.0

156

1.2

338

1.4

295

3.4

354

4.6

1.9

289

1.1

317

3.6

340

3.0

327

1.2

2.1

3.9

2.1

337

2.2

115

1.3

287

1.0

235

1.5

249

4.0

2.3

3.3

211

3.1

175

2.6

4.5

342

3.7

264

1.4

260

One may draw attention to the phase-angles of the 5th har¬
monic and its sub-harmonics—i.e., all the multiples of five.

Omitting only four out
of the 5th we have:

of the first 18 of these

sub-harmonics

Harmonic

Phase

Harmonic

Phase

284

274

184

100

347

277

287

265

260

200

These phase-angles have again been set out in diagram
form (Fig. 86b) and there can be no doubt that it is the car¬
dinal points of the Tropical Zodiac which are providing the
marking points for our phasing.

Since it has a bearing on our last chapter in which we
discussed the principles- on which phasing is based, it must be
said that in some of these families of harmonics the same
‘bunching 5 of phase-angles is present but at other points be¬
sides the primary phase-angles. This is interesting and seems to
send us back to the idea that every phase-angle can have its
symbolic significance. However, it should be noticed that this
bunching would not take place unless the measuring points were
tropical in origin, for the variable position of the ayanamsa
(representing the distance by which the two Zodiacs are
out of phase) would be a variable fraction of the different
harmonics. This would have the effect of dispersing the ob¬
served bunching of phase-angles. For example, the mean
(Bradley-Fagan) ayanamsa of the physicians is about 23.07°,
corresponding to the year 1879-80. This would tend to disperse
the phase-angles not only from the primary phasing shown in
Fig. 86a, but from each other, so that the bunch effect would no
longer be present in Fig. 86b.

However, our study of these matters is still in its infancy
and one is reluctant to be dogmatic in a field where we clear¬
ly have much more to discover. It certainly would not be
surprising if some of the sidereal points we mentioned earlier,
such as the galactic centre or intersection of the ecliptic with
the plane of the galaxy, were capable of producing harmonics.
These may refer to such terrestrial phenomena as weather
cycles whilst the tropical reference points provide the basis for
the symbolism of nativities.

Perhaps the most fascinating lesson to be had from the
study of the solar harmonics in the collections of data we have
is the revelation of the remarkable mathematical structuring of
the solar rhythms at work in the different groups of nativities.

I summed up the position in relation to these in Astrology
Reborn : 9

“What it amounts to is this, that each one of these sets of birth
data — doctors, artists, nonagenarians, etc., are, when analysed in
this way, just like different crystalline substances, each one charac¬
terised by a different numerical structure.

201

“Over half a century ago, D’Arcy Thompson, in his
memorable book On Growth and Form, commented on
the reluctance of morphologists (in contrast to, say,
astronomers or chemists) to raise their study to a
science by the proper employment of mathematics.

It was as if they saw in the teeming forms of nature,
in the lineaments of the growing plant or the con¬
volutions of the snail’s shell, mysteries too deep and
too varied to lie within the scope of clear numerical
expression. Yet Thompson and others have since
shown how mathematical laws are at work in all the
forms of nature.

“Now science must learn that the lineaments of
human character and the convolutions of destiny too,
fall, no less, within the scope of number; for if it is
true that God made ‘every plant of the field before
it was in the earth, and every herb of the field be¬
fore it grew’, it is no less true that He measured the
ways of man before he was in the womb, and made
him an embodiment of ideal and divine numbers.”

NOTES

1. See for example Fagan, Cyril, Zodiacs Old and Few. London: Robert
Anscombc and Co., Ltd., 1951, or Los Angeles: Llewellyn Publica¬
tions, 1950.

2. For example, Bradley, Donald A., Profession and Birthdate, see Chapter
8, Note 4.

3. See Gleadow, Rupert, Your Character in the Zodiac, London: J.M. Dent
& Sons, 1908.

4. See Addey, John, “Tropical vs. sidereal,” Astrological Journal (Astro¬
logical Association, London), X (1968) no. 4. This is a book review of
Gleadow’s work cited in Note 3 above.

5. See Bradley, Donald A. and M. A. Woodbury, article in Science
(Journal of the American Association for the Advancement of Science),
Vol. 137 (1962), pp. 748-749. Abo see a similar article in Few Scien¬
tist, no. 306 (27 Sept. 1962).

6. See Landscheidt, Cosmic Cybernetics -- the Foundations of Modern Astrology ,
Aalen, Wuru.: Ebertin-Verlag, 1973.

7. See Chapter 4, Note 6.

8. That the British Clergy show so many more significant elements than
the American is interesting. I attribute this to the fact that British
clergy are much more homogeneous a religious group than their
American counterparts.

9. Addey, John, Astrology Reborn, See Chapter 1, Note 2 for details.

202

ASTROLOGY, HARMONICS
AND GENETICS

Of all the astrological problems which beckon to us from
the future there is one which must excite the thoughtful astrol¬
oger more than any other. It is also the problem the solution
of which may prove to be of greatest practical scientific value
to mankind. This is the question of how astrology and genetics
are to be related and, specifically perhaps, how the genetic
code is expressed astrologically.

To put the matter in a nutshell, we know that there are
laws of heredity by which natural characteristics are trans¬
mitted from generation to generation. We also know that the
natural characteristics of each person are described by the
horoscope calculated for his date, time and place of birth. It
therefore follows—and we must be clear about this, it does
inevitably follow—that the astrological code by which the
horoscope is interpretated must be in agreement with the ge¬
netic code by which natural traits are transmitted from one
generation to the next. The two things must be parallel ex¬
pressions of the same theme.

livery astrologer who has investigated this matter in even
a perfunctory manner suspects this to be true; every astrologer
who has investigated it more carefully and who also under¬
stands the reasons behind the issue knows beyond any doubt
that it is. and must be, true.

On the most basic scientific level Michel Gauquelin has
demonstrated the existence of an astrological relationship be¬
tween the nativities of parents and children in a massive scien¬
tific experiment involving the horoscopes (all calculated for the
lime of birth) of some 25.000 parents and children. All birth
data has been published. 1 The result of this experiment was to
show that if one parent had a certain planet rising or culmi¬
nating (sectors 36, 1. 2. 3 or 0, 10, 11, 12 in the division by
36 sectors — see f ig. 12) then there was a significant tendency
for his or her children to have the same planet in one of t hese
sectors. If both parents had the particular planetary position

203

then the tendency for the child to have it too was approxi¬
mately twice as strong. This is in conformity with genetic
principles and the probability of Gauquclin s result occurring
by chance was less than 1 in 500.000.

We may note in passing that this tendency was observed
to be stronger for the planets nearer to the earth—Venus,
Mars and Moon—than it was for Jupiter and Saturn. The
tendency was not observed to a significant degree for Mercury
or the outer planets. If the child was born on a day of high
geomagnetic activity the effect was more pronounced with all
bodies except the Moon.

We mention this work by Gauquclin because it does es¬
tablish beyond any shadow of scientific doubt that an astrolog¬
ical relationship does exist between the nativities of parents and
children. However, the relationship observed by Gauquelin
is rather general in character and is quite inadequate on its
own to meet the needs of providing a description of the
genetic transmission in all its complexity.

The larger question remains to be answered. Having
shown that an astrological relationship does exist, one must go
on from there to determine, step by step, the whole range ot
principles upon which the genetic transmission is expressed in
astrological terms. I believe that this is perhaps the greatest
and most exciting enterprise which now lies within the com¬
pass of coordinated scientific and astrological endeavour.

Let us consider what are the impediments to this enter¬
prise. There is one major obstacle and two minor ones. There
is no question about wViat the greatest impediment is; it is
DOUBT. A man who doubts the possibility of solving a prob¬
lem, or even the rationality of the subject matter, is certain to
fail. He must be wholly convinced of the reign of law through¬
out the universe, in small matters as well as in great. Noticing
a general similarity between the charts of parents and children
he must grasp the fact that this similarity rests upon clear and
definite principles that can be followed through to a more
complete understanding. lie must not think that because man
has free will (as he undoubtedly has. at all times ) the laws of
nature cease to operate in their own proper field. If he does
not proceed with conviction he will not address himself with
determination to a problem of this kind or if he does he will
abandon it as soon as the difficulties mount up.

Above all, we need to be confident in this matter that we
are not on a wild goose chase. And we are not. We need to
begin with a thorough-going conviction that we are embarking
upon a study which will yield up its secrets if we approach it
with intelligence and insight, with humility and patience. The
student who attempts to contribute to the solution of this
problem (and it is a problem fit for a prince of scientists)
must first be well assured in his own mind of the intelligibility
and accessibility of the solution. He must acquaint himself, as
far as he can, with the known laws of evolution and heredity,
whether Darwinian, Mendelian or biochemical, and he must
be prepared to seek out the analogies between these laws and
their astrological counterparts. If there are dominant and re¬
cessive traits in Mendelian genetics, then he should look for
some corresponding principle in astrological terms, and so with
every other aspect of genetic principles. It is true that there
may yet be important potential elements of the astrological
code which are still undiscovered, and there may be factors
for which the correct way of handling the material is not well
understood; indeed this is certain to be so and one can think
of many such uncertainties. But the lack of these need not
prevent a start being made in determining some general prin¬
ciples. Genetics was a very unsophisticated, even non-existent,
science when Mendel made his careful observations of plant
strains, and yet these were destined to yield one of the corner¬
stones of this study.

1 spoke of two minor obstacles to this study. The first of
these is the relative absence of recorded birth times and even
birth dates before the mid-nineteenth century. Parish registers,
which are an important source of information, normally give
the date of christening rather than the date of birth. I do not
know the position in the United States; there may be some
variation from state to state.

On this score we must do the best we can with the ma¬
terial available; scientific ingenuity can bridge many gaps and
in any case it may be that there are enough families with re¬
corded birth times over a good many generations to meet the
needs of the situation. One need only comment in passing that
ft is the duty of everyone who has the interest of astrology at heart to
do all in his power, for the sake of future generations, to ensure that
times of birth are accurately recorded (and preserved) in the society in
which he lives.

204

205

The other minor obstacle to the scientific investigation of
the astrological genetic code is uncertainty about the relative
significance of the times of birth and of conception . One would
suppose, prima facie , that since the moment at which the ge¬
netic transmission actually takes place is the moment of con¬
ception, then this time, which cannot at present be pinpointed,
must be of primary importance. This, strictly speaking, is not
so much an impediment to the investigation of astrological
genetics as one of the fundamental problems which such an
investigation must tackle. It is sufficient to say that there is
enough evidence to support the belief that the symbolism of
the actual moment of birth is comprehensive in its own terms
and that on this basis the time of conception may not be of
such crucial importance as one would suppose. It is even more
likely that with greater knowledge of what is involved, it may
become possible to deduce the time of conception from the
time of birth and other factors.

There is an astrological doctrine called the Trutine of
Hermes, supposed to be of considerable antiquity, which is
said to provide a rule whereby the time of conception can be
so deduced. My view is that no confidence can be placed in this
doctrine as it stands without further study, although, indeed,
it may provide us with clues and in due course may prove to
have truth in it.

One can view this problem philosophically in these terms:
All terrestrial life is a precipitation and a manifestation of an
inner order of ideas. Every individual is an idea, every family
is an idea, every nation, every race, every planetary family —
all are the living embodiments and expressions of spiritual
formative principles. This was. the teaching, in a pure form,
of the enlightened sages of antiquity. It is also a teaching
which reappears with greater or less clarit/ whenever men
seek to contemplate philosophically the underlying truths of
human life. Professor D. C. Darlington, one of the leading
geneticists of our day, in his work The Evolution of Man and
Society f sees the history of the genetic and evolutionary pro¬
gress of mankind as the history of the unfoldment and trans¬
mission of ideas. To quote from The Times (of London) review
of this book: “Ideas for him have always been, literally, em¬
bodied; ideas are people, ideas move as people move, settle

206

as people settle, propagate as people propagate.” Ideas, says
Darlington, “have marched on foot, ridden on horseback
and sailed on the sea” . . . and, he implies, have been trans¬
mitted genetically from generation to generation.

It is these ideas which are reflected in the astrological
themes of men’s origins. No science is adapted to see more
clearly than astrology the unfoldment in time of these ideas
insofar as they are genetically transmitted and woven anew in
each generation into the life of society with all its activities,
institutions and characteristics.

To return to the point at issue, the synthesis of genetic
material which takes place at conception and is symbolised by
that moment in time is obviously of radical importance as
providing the material basis of the genetic transmission. Yet it
may be that the formal cause or idea behind the incarnation
may be just as distinctly reflected in the moment of birth, i.e.,
the first moment of life as an individual, which I take to be
the first breath. I offer this thought without complete convic¬
tion as a possible justification for expecting that the nativity
may prove an adequate reflection of the genetic relationship.
This is a problem which we must take as we find it.

But why is it, one may ask, that the unravelling of this
problem should suddenly present itself as a possibility? The
principal reason, I believe, is the more distinct recognition of
the harmonic basis of all relationships in the horoscope and
the infinitely greater range of discriminatory symbolism which
this opens up. As long as we were limited to signs of the
Zodiac and conventional aspects and house divisions, no one
could believe that the complex requirements of the genetic
code could be adequately expressed in astrological terms. The
new harmonic viewpoint, when seen for what it is, does hold
out such a possibility.

In order to see how this process works, let us take an ex¬
ample, using a series of natal positions which are based on the
quintile division and which might therefore have escaped no¬
tice if only conventional aspects had been regarded. It so hap¬
pens that I have my father’s birth time exactly," my own and
those of my three children. My father was born with the Sun
on the midpoint of Saturn and Uranus and roughly 72“ from

207

each, a fifth part of the circle. These positions I inherited
with slight modification and in due course passed onto my
children, again in modified form. Fig. 87 gives the positions
for the three generations. (The aspects are to the nearest
whole degree).

fynention 1

Cpnaratwn 2

Gj&twntion 3

Fig. 87

In order to appreciate the connecting links here one must
remember the angles based on the 5th series: not only 72° and
144° but 36° and 108° (based on the half-quintile) and 18°
and its multiples (54°, 90 p , etc., based on the quarter-quin¬
tiles). There is also one aspect of 24° (a third of 72°), two of
45° (midway between 36° and 54" or 5/8ths of a quintile) and
one of 99 p (midway between 90° and 108°, or 1 3/8ths quin¬
tiles).

The point to notice in this example is that a very specific
group of positions has been taken and all other factors rigidly
excluded for the sake of keeping the example clear. We have
applied, as it w'ere, a magnifying glass to one particular plane¬
tary complex as it is manifested in three generations. One
could make the illustration more impressive in some ways by

208

introducing more factors and so multiplying the ‘coincidences’,
but then it would become too complicated to see the simple
force of the family resemblance in the three generations. The
resemblance between generations one and two is obvious
enough, but the continuation of the theme in generation three
is also clear when one looks at the positions carefully. The
basis of the continuity is the 5 th and its sub-harmonics.

If there is any doubt that this is a true pattern repeated
in three generations, the doubt must be dispelled by an exam¬
ination of the zodiacal degrees involved, for all these positions
are linked to points of the same zodiacal pentagon as shown
in Fig. 88. Still keeping strictly to the Sun, Saturn, Uranus
and M.C., we can list the positions shown in Fig. 87 as they
fall on these zodiacal degrees, Interestingly, in doing this we
can go back one more generation to my father’s parents,
whose Sun positions are also involved in the pentagonal
framework.

11*V*

lift

BQE2S

23° H-V

5° njr-H

17° W-m/

'■S5*

2 Grandmother

3 fallier

■HI

Saturn

23° x*

Uranus |

26*4*0

4 Thf Author

MC.

1 2° T

Sun

23 VH;

Saturn 6° fljj
Uranus 5*i’ ^

5 Daughter (1}

Uranus

25" if

6 Son

Saturn

\7 l A* ^

M.C

23*° XC

Sun

7 Daughter {2)

Sun

ji° T

209

In Table 1 the primary involvement in the ten points of
Fig. 88 is shown by the fact that the Sun is involved in every
case except one. The apparent exception (my elder daughter,
No. 5 above) confirms the principle rather than negates it,
for her Sun at 5° Gemini is thus 18° from the sensitive point
23° Gemini, one quarter of the 5th harmonic out of phase.
My own Moon is at Qh a Gemini, 18°02 ! from my Sun at
23 3 A° Gemini, so the inherited relationship is obvious.

No one who examines these positions carefully can doubt
that they are characterised by some kind of order. They are in
no wise exceptional for all families show such family patterns
in their horoscopes. But order by its very nature is distin¬
guished by law; one cannot have order appearing and main¬
taining itself by chance. It is to the discovery of these laws of ge¬
netic astrology that we suggest astrologers should now be addressing
themselves.

Before we leave the example just given there are two
points which are worthy of comment. The first is that where
some stable family pattern has been found such as our five or
ten pointed pattern shown in Fig. 88, one of the positions in
the pattern may be neglected for a generation or two, thus
column 4 (17 s Taurus-Scorpio) is empty in our list, and Col¬
umn 5 (29° Cancer-Capricorn) is rather thinly occupied. When
this happens, subsequent generations will revert to the neglec¬
ted degree area and, so to speak, ‘catch up’, perhaps by
marrying into these positions, and so restoring a neglected ele¬
ment in the ‘balance’ of the family idea. This law will often
explain the appearance of an apparently ‘new’ element in
family charts.

The second point is that there is some indication that the
five or ten pointed grouping we have used as an example may
have specific relevance in the tracing of a genetic line. There
is an undeniable connection between the number five and the
concept of the splitting up of a unity into parts, in this case
through the operation of genetic forces. This is reflected per¬
haps in the five/ten-fold structure of the D.N.A. molecule. It
stems from the truth that in the descent or katabasis of an
idea from potentiality into actuality through nine steps or

210

stages, 4 the fifth stage is the middle point, the point where
the unitive idea or whole is split up or differentiated into
parts in order that it can manifest through ‘body’ which con-

12 3
4 5 6
7 8 9

sists essentially of parts subordinated and superordinated to
each other as an objective or phenomenal whole which mirrors
the subjective and noumenal unity from which it springs.

This tendency for the fifth element in a series to be asso¬
ciated with fragmentation is often noticed, as in the fifth orbit
from the Sun being occupied by the asteroids. On a quite dif¬
ferent Level, it is found in such myths as that of Dionysius-
Zagreus being tom to pieces by the Titans, and other similar
representations of the splitting up of the World Soul into par¬
tial (human) Souls. Thus a fivefold/tenfold system is one which
might be looked for in astrological family themes.

For how' many generations do such family patterns main¬
tain themselves? The evidence suggests that they do in fact
survive for centuries, though I do not know of any full-scale
studies in these terms. On my sitting-room wall hangs a samp¬
ler stitched by my great-grandmother, the mother of number
2 above and the lady referred to in footnote 3 of this chapter.
The sampler indicates that she was born on 25 May 1819.
This is the same birthdate as daughter No. 5, so her Sun was
again at 4° Gemini, her Uranus being at 23" Sagittarius and
so on.

To the uninitiated this will seem incomprehensible. Is
there not a fresh infusion of new traits from other families as
each new generation marries? How can family patterns main¬
tain themselves in the face of such constant dilution? The ex¬
planation of this is simple, for the attraction of like to like is
constantly at work, not only through the obvious channels but
also through many unseen and cryptic ones, and it is far
stronger than is commonly supposed in this context. Anyone
who examines his family tree over a number of generations is
likely to be impressed by this tendency for family likenesses to
be maintained through marriage.

21L

If the reader will forgive another example from the writ¬
er’s own family, there is a very simple instance, this time from
the distaff side, which makes the point. It concerns the stabil¬
ity of Moon positions among the womenfolk in the family.
Fig. 89 shows the positions, including all the female birthdates
I have in the direct line on this side of the family.

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u ft. 19 May 1S*>)^l7v3

v (p. lAu^tsi 0) \ (MM f186»fy8)t

E-Wifc^) 19'03 V$

Fig. 89

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The point about the positions shown is that A is not re¬
lated to B, nor C to E, but in each case a son has married
someone with the same Moon position as his mother. Tenden¬
cies of this kind constantly operate to preserve family themes,
not merely in planetary positions as such but throughout the
whole range of the astrological ‘code’.

If these things are viewed from the outside instead of from
the inside, the question of whom one marries may seem like a
magnificent lottery. ‘X’ misses his train and whilst kicking his
heels in the station waiting room, whom should he meet but
this marvellous girl who seems so nice and friendly, and in
due course .... This seems like pure chance, but the out¬
ward chain of events which produces such situations is decep¬
tive; behind the apparently chance circumstances are a body
of formal causes in accordance with which events unfold. The

212

outworking of this body of causes is called Fate, which is the
outward aspect of the Wisdom of Providence. It is in no sense
arbitrary, but takes place in conformity with the essential na¬
ture of the human substances involved, modified by their past
free volitional acts.

Taking a wider perspective, we can see that each family
embodies, at any particular time, a number of different themes
or ideas. Perhaps for generations one might find a medical tra¬
dition in which successive generations of sons tend to become
doctors. In the same family there may be a more or less la¬
tent interest in say, art or the stage, expressed as a hobby or
enthusiasm by some members of the family. Eventually a gen¬
eration is bom in which all the medical interest or talent is
concentrated in one child while the interest in art or the stage
comes to the surface at last and other children follow' those
lines.

In these circumstances it will often be possible to trace
how a particular idea, tradition, characteristic or aptitude fol¬
lows certain geneological channels, one branch of the family
preserving one theme while another preserves a different one.
Obviously, in looking for such successions in terms of aptitudes
characteristics, etc., one must be prepared to look at principles
rather than particular forms of activity. What was an interest
in property ownership in one generation might become a town
planner or an architect or a building society employee in
another. I know of no other astrologers in my family but my
father was very interested in horology.

It is perhaps very important to emphasise for the sake of the
reader that sometimes family resemblances such as we have been speak¬
ing of are obvious. At other times they will only reveal themselves as a
result of careful and systematic analysis.

There is one problem which will no doubt have occurred
to some students w r hile reading this chapter: the effect upon
the time of birth of the artificial induction of labour. Michel
Gauquelin has demonstrated 5 that this effect is a real one in
the sense that the sympathetic relationship between the horo¬
scopes of parents and children is infringed where the induction
of labour becomes common practice.

213

The philosophical view of medical practices designed to
bring on, speed up or retard childbirth is not necessarily con¬
demnatory. The order of art is superior to the order of nature
and what is done wisely and for a good and sufficient reason
will tend to harmonize with the larger scheme of things. 1 he
criticism of much present-day practice in this field, however, is
that it is done unwisely, for insufficient reasons and, in partic¬
ular, without regard for the best interests of mother and child.
This is becoming recognised.

The objections which arc raised against the validity of
some horoscopes in these circumstances are not necessarily true.
There are always factors at work permitting or preventing con¬
ception at certain times, allowing or not allowing pregnancy to
run its full term, hastening or retarding childbirth. It must be
the standpoint of the astrologer that all these apparently
chance factors tend to combine, in loio, to lead up to the birth
at the appropriate symbolic moment. For example, Churchill’s
mother had a riding accident and Churchill was born two
months prematurely. Not every mother goes riding but small
incidents which may hasten or retard labour by a few days or
hours are common enough.

There is no good reason why the induction of labour
should be regarded as in a different category from all the
other evidently fortuitous circumstances affecting the time of
birth or conception. The fact that in some populous centres in
the West births are induced on a large scale does not in itself
affect the matter one way or another any more than does the
wholesale use of contraception or, for that matter, the large-
scale absence from their wives of soldiers or sailors in time of
war.

The relevant issue, perhaps, is that what is done well
tends to produce ordinate results and what is done ill, the
opposite. It should not surprise us unduly if the spirit of an
age which sanctions the folly of inducing labour for the con¬
venience of the attendants is also reflected in disharmonies in
the births which take place under such conditions—disorienta¬
ted births for a disorientated age. Looked at from another
point of view, we live at a time when the rate of change in
an unstable society is such as to accentuate the difference in
outlook, or to elongate the ‘gap’, between one generation and
the next. Where this effect is at its worst, which is also in the

places where the custom of inducing labour is commonest, one
can regard the shift observed by Gauquelin in the usual agree¬
ment between the nativities of parents and children as no
more than the astrological reflection of an existing phenome¬
non.

To sum up, we believe that there is now a case for mak¬
ing a definite attempt to clarify the whole relationship between
the description of hereditary forces and effects provided by
conventional genetics and the description provided by astrol¬
ogy. Some astrologers have already been thinking along these
lines. There is an article by Pam Bennett of the British Astro¬
logical Association 6 which certainly tackles the subject in the
right spirit and contains some interesting suggestions. Charles
Harvey, President of the Astrological Association, is unusually
fortunate in having several generations of birth times in his
family. He also has made some valuable suggestions, one of
which particularly appears to have the ring of truth. He has
noticed that alternate generations tend to reveal in their
charts various kinds of inversions and reflected positions, rather
like alternating positive and negative photographic images—
black on white, then white on black, then black on white
again. This suggestion agrees with the observation that chil¬
dren often seem more like their grandparents, in many respects
than their parents. There is also a brilliant study by Charles
Harvey of haemophilia in the descendants of Queen Victoria. 7

I believe that the crucial factor which can now contribute
to the elucidation of this problem is the more distinct recogni¬
tion of the symbolism of the whole range of harmonic intervals
in relating horoscopic features. In this context—in case the
position has not been made sufficiently clear—it would seem
that the major aspects refer to broad general similarities or
categories of traits, and that the more particular and idiosyn¬
cratic hereditary features arc shown by smaller harmonic inter¬
vals or unusual harmonic numbers.

Note, however, that an exact major aspect will include all
the sub-harmonics of that interval. Thus an exact aspect of,
say, 40° will not only show what is symbolised by the 9th,
but also will include the symbolism of the 18th, 27th, 36th,
etc. Physical traits in particular may be shown by the shortest
intervals, perhaps very short indeed, and this is one reason
why accurate birth times are likely to become increasingly
important.

214

215

Similarly, a particular kind of planetary contact can be
maintained ‘in the background’, as it were, for several gener¬
ations only to come to the foreground in a later generation
in the form of major harmonic contacts. For example 9° or
4 V 2 ° interval contacts (40th and 80th harmonics) might be
reintegrated into 18°, 36° or 72° aspects (20th, 10th, 5th har¬
monics) in a later generation, perhaps under the stimulus of
marriage with a partner showing the same class of contacts.
For this reason it is important to recognise the need for very
detailed analysis of the chart for minor harmonic intervals
when studying these things. The same applies in looking for
unusual harmonics.

To give a simple example, here is a family of five, father,
mother, and three children, who generally tend to have strong
! Neptune contacts. Is there any common contact which links

Neptune to the Sun and M.C., for example? Yes, there is,
but evidently only through a rather unusual harmonic, the
. . 46th of 7°50’, as shown in the following table. In order to

» ji follow up this line of inquiry, the Astrologer's Guide to the Har-

. monies 8 is an essential tool, listing as it does all fractions of the

f i' circle and their multiples.

Natal

Aspect

Near

Orb

Husband

Sun - Neptune
M.C. - Neptune

45*45’

117*35’

6/46

15/46

- 46*57’

= 117*23’

1*12’

0*12*

Wife

Sun : Neptune
M.C. - Neptune

172*27’

0*30’

22/46

0/46

= 172*10’

0*17’

0*30’

Daughter

Sun - Neptune
M.C. - Neptune

125*50’

23*37’

16/46

3/46

= 125*13'

= 23*28’

0*37’

0*09’

Son

Sun ■ Neptune
M.C. - Neptune

47*44’

116*30’

6/46

15/46

= 46*57’

= 117*23’

(T47’

0*53’

Daughter

Sun - Neptune
M.C. - Neptune

165*50’

47*48’

21/46

6/46

= 164*20’

= 46*57’

1*30’

0*51’

Obviously, one does

not attach much

significance

to such

a short list of positions considered in isolation. They may or
may not be significant. The example is intended only to illus¬
trate a point: in researching this subject, one must be pre¬
pared to examine unusual harmonics and to make detailed
comparisons.

216

It may be objected that we have no idea what signifi¬
cance should be attached to the 46th harmonic. True, but in
this respect, wc are in the same boat as the other geneticists.
Then progress has consisted not so much in deciphering the ge¬
netic code as in discovering what are its ingredients. We have
a good start on them for we already have at least some idea
how to read our code.

It is too soon to envisage how this branch of knowledge
will eventually be applied to man, although it will probably
not be in any way we might now expect. The development
and application of such things must be allowed to take its
own time and its own course in the context of the develop¬
ment of society as a whole. In the eighth book of Plato’s
Republic Socrates admits that although the ideal society he has
described in that book will not easily be changed, sooner or
later it is likely to fall away from its perfection. The reason he
gives for this is that children will be generated at unseasonable
times and will grow up to disrupt the established harmony.

Similarly, perhaps the recovery of the understanding of
proper times and seasons will ultimately have an important
role to play in the regeneration of society. However, it is like¬
ly to call for a greater measure of wisdom than prevails in
our present councils. 9

NOTES

1. Gauquelin, Michel and Francoise, Birth and Planetary Data Gathered
Since 1949, Series B, Vo Is 1-6 gives birth data of parents and children:
Series C. Vol. 1 summarizes results. See Chapter 4, Note 2 for de¬
tails. Gauquelin, Michel, Cosmic Influences on Human Behavior is also
relevant; see Chapter 4, Note 1.

2. Darlington, 13.(1., The Evolution of Man and Society, New York: Simon
& Schuster, 1970.

3. This was a stroke of lurk. It became a legal requirement that the
times of birth oi twins should be registered in England and Wales in
1870. My father was a twin born on 3 Ort. 1870 and my grandfather
registered their times of birth as 3:15 a.rn. and 4:05 a.m. (my father).
4:05 looks like an attempt at accuracy, and he had good reason to be
on his toes for the event. His wife's mother had died in giving birth to
twins on the same date, October 3rd. a generation earlier. Such ‘coin¬
cidences' are not uncommon where family histories are remembered.

4. See Chapter 11 on the Navamsa symbolism.

217

NOTES

5. For discussion of the relevance of the induction of labour to birth
times see Gauquelin, Michel, Cosmic Influences on Human Behavior, es
pecially Chapters 15 and 16 (see Chapter 4, Note 1 for details).
Gauquelin gives additional material in Series C, Vol. 1; See Chapter
4, Note 2 for details.

6. Bennett, Pam, “Astrology and Heredity,” The Astrological Review, Fall,
1972.

7. Harvey, Charles, “Astrology and Genetics: Haemophilia,” in Correla¬
tion 3 (a research publication of the Astrological Association, London),
XI (1969) no. 2.

8. Williamsen, James S. and Ruth E Astrologer’s Guide to Ike Harmonics,
see Chapter 12, Note 2.

9. There is an interesting side-light to be found on this subject in the
Guinness Book of Records where wc arc told that the highest IQ. ever
recorded is that of a Korean boy, Kim Ung Yong (b. 7 March 1963).
The unusual thing about this boy is that both his father and mother
were born at 11;00 a.m. on 23 May 1934. This is analogous to the mar¬
riage of close kindred where any family weakness (or strength, as in
this case) is likely to appear In an exaggerated form in the offspring.

i i T

218

THE RELEVANCE OF
OTHER CYCLE STUDIES

The picture which has unfolded in this book is one which
is built upon the idea of the harmonics of cosmic periods. In this
context astrology can now be seen to be of one piece with a
far larger field of studies which are now engaging men’s minds
and which depend upon the same principles.

The study of biological rhythms in man and nature has
expanded rapidly in the past twenty years — about the same
length of time that parallel ideas have been developing in
astrology — and now progresses by leaps and bounds. All over
the world science has become interested in biological, physio¬
logical and other rhythms. All these studies are, in very truth, as¬
pects of the larger astrology. It is true of course that there are
plenty of scientists who resist the idea that these rhythms are
in any way related to planetary and other cosmic movements.
However, they have their backs to the wall and the eclipse of
their viewpoint is approaching with visible inevitability.

On the other side of the fence there are plenty of astrolo¬
gers who insist that scientific studies of biological rhythms have
nothing to do with astrology. On both sides of the fence the
isolationism is due very largely to ignorance of what is hap¬
pening in astrology as well as of the results of other scientific
inquiries. Most astrologers are ignorant of how far biological
studies overlap their own ideas, as well as of the new depth of
research in astrology.

It is true that there are many differences of opinion about
the nature of the relationship between cosmic ‘influences’ and
the phenomena related to them. It is some indication of the
changing climate of thought that there are pioneers of astro¬
logical research who appear to think in traditional scientific
cause-and-effect terms and philosophical scientists who are
beginning to take a more mystical view of things.

At present most perceptive astrologers are nearer the truth
than most orthodox scientists. This is because they have a
more vivid realisation that efficient causes represent the imple¬
mentation of formal causes and therefore that the order of
existence is a reflection of the order of ideas. In this sense
phenomena are, in the last resort, symbolic expressions of nou-
menal realities. Such ideas, such noumena, arc symbolised by

219

ideal numbers and, objectively, by cosmic existences; this is
the basis of astrological interpretations. On these terms there is
no reason why astrologers should not be able to assimilate into
their thinking the biological rhythms discovered by science and
with them whatever chain of efficient and material causes
scientists discover or conceive of as producing these rhythms.

On the subject of biological rhythms, there can be few
people nowadays who have not heard of ‘circadian’ rhythms,
that is, rhythms (whether in man, animals or plants) which
are ‘about one day’ in length. Many of these are directly
based upon an exact mean solar day of 24 hours; others are
a little longer or a little shorter. In this context we must un¬
derstand that a sidereal day (the time taken for the earth to
turn on its axis once in relation to the Fixed Stars) is about
23 hours 56 minutes 5 seconds. The mean solar day is a little
longer because the Sun appears to move forward a little each
day in relation to the stars. The Moon moves forward even
more, so the length of the mean lunar day is just over 24.8
hours. All the planets move forward in one day, each by a
different amount, so there is also a mean Saturn day, a mean
Jupiter day and so on. It is possible that some of the circadi¬
an rhythms observed in nature are based on some of these
varying periods. This is certainly true of some creatures in re¬
lation to the lunar day. The crab, for example, follows a
lunar day, suggesting, incidentally, that whoever gave the
name of ‘the crab’ to the Moon’s sign, Cancer, knew some¬
thing!

One would suppose that it would be a relatively simple
matter, by careful investigation, to find examples of plants and
animals which responded to different planetary days. Unfortu¬
nately the issue is more complicated than this. We have seen
throughout this book that we are dealing, again and again,
not simply with planetary periods but with the harmonics of
planetary periods. For example there are three principal lunar
months; the synodic of 29.53059 days (the period from one
conjunction of Sun and Moon to the next), the sidereal of
27.32166 days (the period from one conjunction of the Moon
with a given Fixed Star to the next) and the Draconic of
27.2122 days (the period of the Moon between successive con¬
junctions with its North Node). There are harmonics of each

220

of these which fall in the circadian period (say 23 to 25 hours)
as there are hosts of other harmonics of about this duration
derived from other cosmic periods. This will make the alloca¬
tion of particular cosmic rhythms to particular phenomena a
difficult task.

This brings us, conveniently, to the work of the Founda¬
tion for the Study of Cycles of Pittsburgh, Pennsylvania. This
organization is and has been for years easily the most out¬
standing of any devoted to the subject of cycle study. The
Foundation has been fortunate in commanding the support of
those who are interested in economic and business cycles, and
it has consequently been the recipient of grants. But the Foun¬
dation has never allowed its interest in the commercial appli¬
cations of cycle study to cloud its zeal for the wider truths of
the subject and its researches have been conducted with true
scientific impartiality and thoroughness. The inspiration for its
work has evidently come, in very large measure, from one
man, Edward R. Dewey. The fact that Dewey saw the need
for such an organization and found time to initiate and de¬
velop it concurrently with his researches is some measure of
his far-sightedness and vigour of mind. The work of the Foun¬
dation is so important and has so many points of contact with
the subject of this book that it deserves a fairly full descrip¬
tion.

The Foundation for the Study of Cycles, then, was found¬
ed in 1941 in Pittsburgh by Dewey who has been its President
since its inception. He already had many years of cycle study
behind him and had written a book on the subject. The
Foundation describes itself as the oldest organisation devoted
to interdisciplinary research in rhythmic fluctuations. ‘Rhyth¬
mic fluctuations’ are identified as cycles of phenomena, in any
field, which recur with reasonable regularity and over a suffi¬
ciently long period of time to be isolated as unlikely to be
produced by chance.

In its thirty-odd years the Foundation has collected and
classified some thousands of such cycles, although many and
perhaps most of these are regarded as tentative. They are
drawn from the fields of astronomy and astro-physics, biology,
climatology', geology, geophysics, hydrology and hydrography,
medicine, physics, economics and sociology. Each of these
categories is divided into numerous subordinate groups of
phenomena each with a long list of entries.

Besides collecting and co-ordinating these cycle studies the
Foundation set out to verify and measure the cycles, to re¬
cord their latitudes and longitudes, periods, wave-shapes, tim¬
ings and strength with the greatest possible accuracy. It coop¬
erates with other organisations, acts as a clearing house for
scientific work in this field (w'hich now grows rapidly each
year) and generally tries to bring the greatest possible defini¬
tion to the problems and results of work in which periodicity
makes its appearance.

As testimony to the probability that the cycles they study
are of non-chance origin, the Foundation adduces the following
items of evidence:*

1. They persist over hundreds and, where records are
available, even thousands of years.

2. In economic and social phenomena they persist un¬
changed in spite of major environmental modifications,

[ such as the Industrial Revolution.

' 3. After distortion, rhythms revert to the pre-distortion

* timing and period.

v 4. They continue to operate after discovery.

! 5. Rhythms of identical period are found in diverse and

s seemingly unrelated phenomena as if they were the re-

• suit of some common cause.

' M 6. Rhythms of identical period in different phenomena

synchronise so that their crests come at about the same
[ calendar time, thus emphasising the presumption of

'!; interrelationship.

; ) 7. Rhythmic cycles of the same period show definite geo-

! graphical configurations with distortions similiar to the

distortions of magnetic declinations.

8. Many cycle periods bear simple numerical relationships
to each other, thus creating “families” of cycles such as
%ve have noticed in our own studies.

Needless to say, one of the central problems, if not the
central problem, which has preoccupied the Foundation through¬
out its work is the question of what is the regulating or causa¬
tive factor behind these manifold expressions of the principle of
periodicity which, again and again, show the clearest possible
internal evidence of a common cause.

222

Before commenting upon the Foundation’s own conclus¬
ions it would be as well to take a look at one of their cycle
studies. The issue of the Foundation’s magazine, Cycles, for
August 1970 was devoted entirely to a summary of some of
the evidence referred to in items 5 and 6 of the above list, in
accordance with which it was found that there are numerous
cycle periods embracing a widely diverse assortment of phe¬
nomena not only as to the precise length of the cycle but also
as to the timing of the peak incidence of activity in the cycle.
In other words, the cycles shared a common length and phase. 2

In this issue of Cycles it was stated that some 19 cycle
periods of this kind had been closely studied by the Founda¬
tion. The)' range in lengths from four years at the shortest to
164 years at the other end of the scale. Of these 19, 17 were
of 22 years or less.

The 8.0 year cycle which we take as an illustration is not
by any means the most dramatic of those given, but it illus¬
trates well the variety of material used. Dewey records that
65 different phenomena have been alleged to have a cycle of
between 7.95 and 8.01 years, but of these only 37 have been
accurately timed. All known cycles of this period which have
been timed are included in this study,

The way in which the ideal crests (the period of peak in¬
tensity as mathematically obtained) of the various cycles cluster
is shown in the diagram below. Each dot represents the time
of peak activity in one phenomenon and is numbered with
reference to the table given. All the dots relate to the time
scale marked along the bottom of the diagram; the vertical
position is for convenience of spacing and has no significance.

The table which follows the diagram gives the numbered
list of phenomena, the span of years for which records exist
and which has been used for the determination of the cycle
length, the ascertained length of the period and the date of
the ideal crest in years and decimals of a year. The original
article gives full references for each item in the list
of phenomena. '

223

•8.0 YEARS-

8.0 YEARS-

i?; e h

I? 35 § i 21

16 2 . 3 %

3 56

• • • 25

5 20 #

• 26

15 • «

• 19 27

4 28

• 30

26 •
• 32

• ® •

13 • 22

> • M •

i h * 35 * 3 * 2*9

• 23 ♦

H 0 16 • 35

#34* 24 #

t 3 • 36

• • ♦ • 25 •

6 1 2 5 20 # 30

# # • 26 •

9 2 15 | # 32

• • [9 27 #

JO 0 14 • • 33

^ 4 28

IT • 22

• 17

• 35# 21 «
12 ^°8 a 29

• • 23 •

U • J6 « 3

• 34 • 24 *

6 12 5 20j

• f « 26

9 2 15 # •

10 #
7

♦ 19 27

14 # •

4 28

AVERAGE
TURNING TIME

1961.3

AVERAGE
TURNING TIME

1969.3

AVERAGE
TURNING TIME

1977.3

Numbers Phenomena

1 Lynx Abundance, Canada, 1735-36—1950-51

(Secondary Cycle Visible After Adjustment for the 9.6-Year Cycle)

2 Pig Iron Prices, U S.A,, 1764-1961

3 Rail Stock Prices, U S.A., 1831-1955

4 Crude Petroleum Production, U.8.A., 1861-1964

5 Cotton Acreage Harvested, U.S.A., 1866-1964

6 Sweet Potato Production, U S.A., 1868-1964

7 Anthracite Coal Production, U S.A.. 1824-1964

8 Precipitation, Philadelphia, 1820-1964

9 Wheat Prices, England, 1760-1875, 1844-1914

10 Whiting Abundance, Mersey Estuary, 1893-1927

11 Red Squirrel Abundance. N. E., U.S.A., 1926-1938

12 Steel Ingot Production, U.S.A., 1867-1955

13 Era*. Purchasing Power, U.S.A., 1873-1936

14 Cigarette Production, U.S.A., 1880-1961

15 Goodyear Tire and Rubber Company Sales, 1926-1957

16 Barometric Pressure, Alps, 1865-1916

17 Stock Prices, U.S.A., 1631-1964

18 Company G Sales, U.S.A,, 1913-1955

19 YielttPer Acre of the Leading Crops, U.S.A., 1882-1918

20 Raw Materials of Manufacturing Production, U.S.A.. 1882-1913

21 Coal Production, U.S.A., 1881 (also given as 1882) -1913

22 Iron Production, U.S.A., 1881 (also given as 1882) -1913

23 Rainfall, Ohio Valley, 1839-1910

24 Ratnfcll, Dakotas, May and June. 1882-1918

25 Rainfall and Growth of Pines. Prtacott, An«ma, c.l867-c.l90?

26 Yield Per Acre of the Leading Crops, France

27 Rainfall, Ohio Valley, c l800 c 1900

28 Yield Per Acre of the Leading Crops, United Kingdom, 1760-1914

29 Sauerbeck’s Index of Wholesale Prices, England, 1818-1913

30 Barometric Pressure, U.S.A,

31 Rainfall, Illinois, 1870-1910

32 Rainfall, U.S.A , 1881-1921

33 Lead Production, U.S.A., 1821-1964

34 Butter, Price Per Pound, New York, 1830-1966

35 Sugar Prices, U.S.A,, 1700-1964

36 Cotton Production, U.S.A., 1790-1964

37 Barley for Grain, Acreage Harvested, U.S-A-, 1866-1964

I '

It will be seen that the average date of the crest for these
phenomena, in the period shown, falls at 1961.3 (April 1961)
and succeeding eight-year intervals. The majority of the cycles
fall within one year of this mean. Notice also that the phe¬
nomena listed include weather cycles, cycles in animal abun¬
dance and various commercial, industrial, agricultural and
economic cycles.

The degree of clustering of the ideal crests is pronounced
but it is by no means as dramatic as in some of the studies
given. This clustering has not been calculated in terms of
probability. However, in some of the more striking cycles the
degree of clustering has been measured. In the 6.0 year cycle,
where the ideal crests of 38 different phenomena are concen¬
trated in a very narrow time-span, the odds against a chance
result are given as less than two in 10 trillion. In the case of
the 54-year cycle covering 35 different phenomena the result
would not occur by chance more often than five times in 100
trillion. These two cycles are mentioned because they are re¬
ferred to in the summary of this chapter.

There is very little need for comment upon the illustration
given. It will be seen that the real impact of these studies
arises not so much because of the similarity of cycle length
but because of the degree of synchronkity shown. It is the way
the rhythms of similar periods coincide in their phasing which
implies a common causal agent behind these cycles. It should
be remarked that all 19 of the cycles examined do show this
synchronicity.

The question we must now ask ourselves, as the Founda¬
tion itself has repeatedly done, is what is this regulating fac¬
tor? I cannot give an authoritative history of the Foundation’s
thinking on this subject, yet simply because the Foundation
has always sought to cultivate a thoroughly scientific approach
to its problems, within the context of the scientific ideas of the
day, I believe it is true to say that there was certainly no
strong predisposition, and there may even have been some re¬
luctance, to look to celestial revolutions for an explanation. On
the other hand, because the Foundation has sometimes found
itself, in the past, like Gauquelin and others, more or less on
the wrong side of the pale of scientific orthodoxy, it has in the
long run kept itself free from the usual prejudices of current
‘scientific’ thinking.

226

I have no doubt that a good deal of thought and scrutiny
must have been given to climatological factors as possible reg¬
ulative agencies in these cycles. But this view merely begs the
question. The rigid weather cycles (reflected in, for example,
studies of Arizona tree rings over 1,040 years, Nile floods over
1,341 years or Lake Saki varves over 4,189 years) are neither
more remarkable nor less than the rigid cycles found in inter¬
national and civil strife (as reflected in Professor Raymond H.
Wheller’s Index of International and Civil Battles 600 B.C.—
1957 A.D., extending over 2,557 years and providing a history
of human conflict drawn from all available sources).

In short, if our planet and its inhabitants lived in splen¬
did isolation in the universe it might very well be expected to
follow its own chequered career. But since it does not, but
rather exists in a cosmic environment to which it is linked by
countless invisible bonds, it is natural that sooner or later ter¬
restrial rhythms should be seen to accord with cosmic rhythms,
and this is the conclusion towards which the Foundation has
been moving, slowly, perhaps reluctantly at first, but always
with a certain inevitability and, in the past few years, with
growing excitement.

In Cycles for April, 1969, Dewey reviews, in a lengthy
‘Letter to Members’, some of the projects which were waiting
to be tackled. 4 Included were matters which had aroused his
interest, clues begging to be followed up and results which
were probable signposts to new discoveries. Let us have some
extracts from this letter so that we may see the lines along
which his thought was moving. These are only scattered ex¬
tracts and they do not do full justice to the care and vigilance
with which Dewey approaches his work:

“A 17-week cycle is dearly visible in the last wave of
the sunspot cycle. A 17-week cycle in stock prices i3 also
present over the same span of time. The last 17-week
cycle in stock prices (in Dow-Jones Industrials) continues
backward as far as these figures are available (1897). Its
exact length turns out to be 17-1/6 weeks.

227

“Does the 17-week cycle in sunspot numbers also
continue backward? And with more data, and hence more
refinement of measurement, will it also prove to have an
ideal length of 17-1/6 weeks? If so, do the two cycles syn¬
chronise, either at the actual stock price latitude or at
polar timing as suggested by what is known of latitude
passage?” (This relates to magnetic declination.)

“If the sunspot and stock price cycles are found to
have identical period and phase, can we assume a solar
cause for the earthly behavior? Or is there a more funda¬
mental causation factor that affects both sun and earth?

“Suppose, as we would expect from previous experi¬
ence, the two cycles are identical in period, but with
crests of the cycle on the sun coming after the crests of
the cycle of the same period on earth, is the lag by the
amount one would expect from what is known as latitude
passage, or is it of some other amount?

“Is the concentration of variable-star periods in the
17-week range a mere coincidence, or is it in some way
connected with this cycle on the sun and on the earth?

And again, on another important issue:

“A short time ago, in analysing a comprehensive re¬
connaissance of sunspot numbers with alternate cycles re¬
versed (i.e. flipped, so that they were above and below
the base line, considered as an axis) I noticed five peaks
on the periodogram at periods that conformed almost ex¬
actly to the heliocentric synodic periods of the five outer
planets. 3 I wish to study this interesting behavior in depth
to see if there is further evidence of planetary-solar rela¬
tionships.

“1 would like to know, for each of these five cycles,
if this correspondence is consistently present throughout
the 266 years for which data are available, and if there
are variations in length of the various waves that corre¬
spond to the variations in the length of corresponding
heliocentric synodic periods. Then, too, we need to know
the shapes of the various sunspot cycles and whether or
not they crest at the actual time of conjunction, or at
some other time. . . .

228

“It has also been observed that minor peaks on the
periodogram of sunspot numbers with alternate cycles re¬
versed have periods that correspond to fractions and mul¬
tiples of these same synodic periods. Are all these corre¬
spondences mere coincidences or are they meaningful?

“If there are planetary-solar relationships . . . are
the planetary-terrestrial relationships 1) direct or 2) by
way of the sun?”

And again:

“One of our members, who wishes to remain anony¬
mous, has observed that when there are planetary con¬
junctions in certain celestial longitudes*’ there are advances
in stock prices; when the same conjunctions occur in other
celestial longitudes there are declines in stock prices.

“This is a very curious observation and some years
ago I took the trouble to plot all these conjunctions from
1897 (the earliest daily stock prices) to date by longitude
and to compare stock price movements with planetary
movements . . . There was indeed a rather marked
correspondence. I employed a statistician from Cam¬
bridge University to evaluate the significance of the
correspondence. He said that it could not be the result
of chance more often than once in a million times!”

And again:

“The next project which comes to mind for investi¬
gation in depth has to do with the 6.41 month cycle that
I found in Standard and Poor’s Index of Industrial Com¬
mon Stock Prices 1871-1952. I reported to you on this
cycle in Cycles in September 1953 (p. 228).

“The reason that 1 am so interested in this cycle is
that its length of 6.41 months is almost exactly one fourth
of the length of time it takes Mars and Earth to line up
with each other (as seen from the Sun). The synodic per¬
iod of these two planets is 25.63 months. One quarter of
this interval is 6.405 months. This length is only .005
months or about 4 hours away from the stock market
length . . (Actually, one quarter of the heliocentric
synodic period is 6.4075, which is even nearer the stock
market length).

229

Dewey then goes on to say how he would verify this re¬
lationship, which he is careful not to assume simply on the
coincidence of length of period.

He ends his thoughts on these and many similiar matters
with these observations:

“Of course, this whole enquiry’' might prove to be a
flop. All we have to go on, so far, is an apparent coinci¬
dence of period. . .

“On the other hand, if these do prove to be corre¬
spondences of period, phase and regularity, the problem
is no more than posed. The question arises: How could
the movements of the planets conceivably have anything
to do with mass psychology as reflected in stock market
activity? Here cycle study comes to a dead end. The
problem must be turned over to the physicist, the physiol¬
ogist and psychologist. Cycle study has done its work in
showing that a problem exists.”

Our only observation is that if he does turn the problem
over to the physicist, the physiologist and the (modern) psy¬
chologist, he will get answers which will beg just as many
questions and will leave him not one jot the wiser.

It will be seen that a good deal of Dewey’s thinking cen¬
tres round his discovery that sunspot cycles are related to the
synodic periods of the planets. Dewey was the first person to
make this discovery: see Cycles for October 1968* Since then
this correspondence has been much more fully explained by
Dr. R. A. Bureau and Dr. L. B. Craine of Washington State
University. Their work was reported in Nature magazine* and
summarised in lay terms in The Astrological Journal of Spring,.
1971. 4

There are numerous terrestrial phenomena which are more
or less well-recognised as coinciding with the sunspot cycle.
This inspired The Times of London, when reporting on the dis¬
coveries of Bureau and Craine, to observe in their “Science
Report” of 5 December 1970:

“Six of the seven strongest harmonic frequencies
found in the sunspot cycle are definitely matched by
Bureau and Craine with periodic alignments of the giant
planets. This sort of alignment, with one or more of

the other giants either lined up with Jupiter on the same
side of the Sun or in opposition on the other side of the
Sun is just the relationship studied by astrologers.

“Since it is also clear that variations in the sunspot
cycle can affect the earth’s environment through their
influence on the solar wind, it may be that there is a
sound scientific basis for some astrological predictions.

“The radiation from the Sun is one of the prime
hazards to manned space flight, so we find the curious
anomaly that the dates of future space flights might be
chosen using the text book astrological techniques of
Kepler to predict low sunspot activity.”

It only remains to say that the work of the Foundation
for the Study of Cycles is now advancing in scope and speed.
They now have a European division: The International Insti¬
tute for Interdisciplinary Cycle Research at Leiden, and they
are collaborating with similar bodies which are springing up
all over Europe. They report that as a result of this collabora¬
tion there are now 87 scientists engaged in digging up refer¬
ences in 39 branches of science and in 17 languages. This is
the first step to a projected ten-volume Catalogue of Cycles.

For ourselves, there are two things we have found admir¬
able about the work of the Foundation. Both may be due to
the beneficient example and lucid mind of Edward Dewey
through which the Foundation’s work is so often expressed.
The first is that in a world in which specialised scientific stud¬
ies are usually described in a rigamarole of obscure jargon
which effectively prevents one from discovering what light
there is to be gleaned therefrom, the publications of the Foun¬
dation are generally written in the most clear and informative
prose. The second is that, judging again by its publications,
the Foundation still seems to live in a world in which wisdom
takes precedence over knowledge. Some sense of the mystery
and profundity of common things still remains, and this de¬
spite their earthy interest in business cycles! Let us hope that
their association with the larger world of present-day science
with its often teeming irrelevances does not destroy their in¬
telligibility or their sense of values.

231

We have seen in this chapter that a well-organised body
specialising in cycle studies has found that countless aspects of
human and natural activity show cyclic or wave patterns.
This has been done through the use of highly sophisticated
mathematical techniques developed in over thirty years of
intensive work.

Of greatest importance and interest to us is not only the
fact that these cycles often show an extraordinary degree of
persistence and stability over long periods of time, nor that
the same cycle frequencies evidently apply to a wide variety of
phenomena showing a high degree of synchronicity of timing
throughout, but rather it is that the cycles are often found in
‘families’, so that the cycle lengths are fractions or multiples
of one another. This is simply another way of saying that such
cycles are sub-harmonics of one major wave-length. This is
fully in accord with our own findings in collections of birth
data of different groups of people; for example, in the nativi¬
ties of clergy, the 7th, 49th and 98th harmonics of the solar
distribution. Many similar examples have been found.

The harmonics which we have met in individual nativities
are mostly (but not all) of a relatively short frequency, say
fractions of the solar year. The cycles studied by the Founda¬
tion are mostly longer ones and relate as a rule to activities
of large groups of humanity (as reflected for example in eco¬
nomic cycles) or in the movements of nature.

Now we have said before that astrology is full of circles
or cycles. One of the longest cycles we are accustomed to
think of is the precessional period of approximately 25,920
years, commonly divided into what are called Great Ages of
of 2,160 year each, such as the Piscean Age and the Aquarian
Age. These ‘ages’ are thought of as relating to just such mass
movements in the life of mankind as are studied by the Foun¬
dation on a smaller scale. It may not be surprising therefore
that out of the group of 19 cycles referred to earlier and sing¬
led out by the Foundation as being of wide application, one
of them, the 54 year cycle, is an obvious sub-harmonic — the
40th (40 x 54 = 2160) — of a Great Age. Others, such as the
6.0 year and 9.0 year cycles, are in turn sub-harmonics of
the 54 year cycle. This may or may not be relevant but it
would be entirely in accord with our findings if it were to be
so.

There are students of astrology who assert that such things
as we have described in this chapter have nothing to do with
astrology. The proper field of astrology, they say, is with the
inner nature of man, with his inner qualities, impulses and
characteristics. These they regard as being ‘higher’ than out¬
ward events and conditions.

This is a misunderstanding of the nature of astrology.
Astrology always and everywhere deals directly with nature —
nature and its operations, through the cryptic order, or upon
matter, nature in mankind, nature in individual man, nature
in the cosmos; but whether it is inner or outer it remains
nature. That which is truly rational and spiritual is above
nature and above astrology' except insofar as it may take for
itself a natural and corporeal vehicle, when it remains free,
rational and spiritual in itself and therefore above fate and
the cycles of time, but is accessible to the astrologer who
views it in the manner of the speculative philosopher, that is,
using the word speculative in its correct sense (and not its col¬
loquial one. which implies doubt) as derived from the Latin
speculum, a mirror — seeing the spiritual partially reflected in
its outward activity.

NOTES

1. Dewey, Edward R , Cycles — Selected Writings, Pittsburgh, Pa.: Foun¬
dation for the Study of Cycles. Inc., 1970, pp. 40-51.

2. Cycles (Official Bulletin ol the Foundation for the Study of Cycles),
XXI (1970), no. 7.

3. The graph on page 224 and information on the 8.0 year cycle are re¬
constructed from Dewey, E.R , “The 8-year Cycle,” Cycles, IV (1953)
no. 5; “The 1956 Postscript to Cycles: The Science of Prediction, Part IX
The 8-year Cycle," VII (195f>), No. 10; and “The 8-year Cycle,"
Vol. XX (1969), No. 2

4. Dewey. E.R.. “Letter to Members," Cycles t XX (1969), No. 4.

5. The ‘heliocentric synodic periods are the average time intervals be¬
tween conjunctions, as seen from the Sun.

6. Actually, in the sign Capricorn though Dewey is perhaps a little
reluctant to say this!

7. Dewey, E.R. “A Key to Sunspot-Planet ary Relationship,” Cycles,
XIX (1968). no. 10.

8. Bureau, R.A. and Craine, L.B., article in JSature. Vol 228, 5 Dec,
1970. p. 984.

9. Mather. Arthur. “Planets and the Sunspot Cycle," The Astrological
journal , (Astrological Association, London), XIII (1971). no. 2.

232

233

(

SUMMING UP

In Chapter 1 of this book we began by saying that there
had been in the twentieth century a great revival of interest in
Astrology and, with this revival, a determined effort to re¬
examine, reformulate and extend the practical knowledge of
the subject. More specifically, all sorts of new techniques and
systems have been devised and attempts have been made to
introduce new factors and to clarify some of the major prob¬
lems of the subject.

Nevertheless there has been one overriding obstacle to the
complete success of these efforts, namely the lack of any clear
understanding, not only of the great system of First Causes up¬
on which the fundamental truth of Astrology rests, but also of
the most basic laws and principles which determine the real
nature of traditional astrological concepts such as signs, houses
and aspects. In other words we still lack the precise means of
interpreting the symbolic relationships of the heavenly bodies
to one another and to the great circles in which they move in
relation to all those many fields in which Astrology is applied
and especially in the field of human character and destiny.

The great system of First Causes by which the foundations
of astrological truth are established is a topic the illumination
of which has not, to my knowledge, been adequately at¬
tempted in modern times, although without it our knowledge
must remain imperfect and shadowy like all knowledge which
is not securely rooted in the vision of spiritual realities.
Why should there be any relationship between the heavens
and terrestrial life? What exactly is the nature of the ‘in¬
fluences’ which Astrology studies and by what energy are
they communicated? If the effect is viewed as purely synchro¬
nistic, what is the basis of this synchronistic correspondence or
bond? What is the precise relationship of the heavenly bodies
to the human soul and to its corporeal vehicles? Where does
their dominion over terrestrial life start and where does it end?

These and many similar questions remain largely un¬
answered and have not been touched upon in this book. Their
elucidation depends, I believe, upon an understanding of the
profound Doctrine of Substance whereby every effect in the en¬

tire universe is the result of the act of some kind of substance
whether spiritual or corporeal, natural, human or Divine.

But even if these primary issues remain uncertain, at least
we can now' have a much clearer idea of the right conceptual
framework for the study of the secondary effects which follow
from First Causes and which are normally regarded as the
main subject matter of Astrology.

These secondary effects tell us, so to speak, how Astrology
works as opposed to why it works. In order to elucidate these
the author has, over the past 20 years, studied collections of
astrological birth data compiled both by himself and by fellow
researchers. By treating the planetary positions so obtained as
if they were iron filings scattered over different astrological
‘force fields’ it has been possible to form a clear conception,
for the first time, of just how (that is to say, upon what
model) the astrological forces at work in the nativity actually
operate.

The picture so revealed and which we have tried to ex¬
pound in this book is one of the harmonics, that is the rhy¬
thms and sub-rhythms of cosmic circles. These cosmic circles
or cycles are potentially of great variety, including, as they do
all celestial phenomena which are characterised by periodicity.
But the ones we have particularly studied relate to those fac¬
tors which form the basis of the recognised elements of horo-
scopic symbolism: the diurnal circles of the planets, their geo¬
centric synodic periods (relating to their motion from conjunc¬
tion to conjunction), and their geocentric zodiacal positions.
All these are geocentric in character; what value heliocentric
and other periodic factors have one cannot say, but one can
assume the principle involved to be of universal validity once
the right application of each factor is known.

The central principle which is seen to be involved in the
symbolism of all astrological positions is the one illustrated in
Fig. 19 of this book. Every circle in Astrology, as represented
by the motion or apparent motion of any body or point from
a significant starting-point, through 360°, to the same relative
position, represents some whole or unity with symbolic corre¬
spondences in all those fields to which Astrology is applied.
Furthermore the division of these circles by different numbers

234

235

can be understood as applying to the subordinate parts of each
of the wholes or unities so symbolised. These symbolic divis¬
ions of circles can then be viewed as producing a number of
positive and negative poles at equally spaced intervals round
the circle (Fig. 19) according to the number by which the cir¬
cle is divided. The astrological effects follow from the positions
of the planets in relation to these points.

There are two great benefits which accrue from this more
distinct understanding of how Astrology works. The first is the
realisation of the fact that all the traditional basic tools of
horoscope interpretation are based on wave formations derived
from the harmonics of cosmic circles. 1 This knowledge enables
one to clarify many areas of doubt; such as the way in which
astrological ‘forces’ build up in the various circles, throwing
light on the nature, distribution and orbs of aspects, the char¬
acter and limits of zodiacal and diurnal divisions and sensitive
, ‘areas’ in these circles.

The second important benefit is the demonstration of the
significance and value in Astrology of a far greater range of
number symbolism than has hitherto been recognised, and
w'ith this the means for testing and exploring the content of
such number symbolism.

We have tried to show, notably in Chapter 21, that this
f vision of the basic principles of Astrology' is thoroughly in

harmony with the findings in other disciplines which address
l . themselves to the study of the occurrence of periodic phenome-

I na in biology and in human life generally.

’ Finally we have indicated the significance of this enlarged

view of astrological symbolism in relation to the study of ge¬
netics. Because the genetic code and the astrological code both
provide a blueprint of the incarnating type they must be par¬
allel expressions of the same theme. This correspondence can
now be explored in far greater detail and should be productive
of valuable results.

We should emphasise in passing that the new insight into
the true elements of astrological symbolism gives us a more
credible view of how the nativity can coincide so precisely
with the appropriate symbolic cosmic conditions. The major

236

harmonic patterns, being relatively slow forming, determine
the approximate time of birth. The higher frequency har¬
monics indicate possible appropriate moments of birth of
shorter duration but which occur more often. Thus in the
case of, say, the 100th harmonic of the Ascendant, there will
be one hundred moments in the day of equivalent value, so
that, one after another, the wards of a complex combination
lock can engage, as it were, to yield a moment of birth
which corresponds symbolically with the ‘pattern of the life’
to be born.

To some, this kind of picture appears to introduce an ele¬
ment of rigid determinism into human life which is repugnant
to one’s sense of the truth about the human condition. It is
in matters of this kind that those who are unaccustomed to
the problems of mystical philosophy habitually fail to see the
point. Mystical truths necessarily involve the element of para¬
dox since they are concerned with the relationship of two totally oppos¬
ing things, spirit and matter. Fate and free will must always exist
and operate side by side. The total description of the former
in the horoscope in terms of principle does not in any way
inhibit the latter. The human will cannot be otherwise than
perpetually free because it is the elective faculty of a free
spiritual being (though he may not always make positive use
of it!). The principles of fate must equally operate at all times
to provide the field of action in which free choices are to be
made.

Books on occultism and the like are frequently the worst
offenders in spreading misconceptions about these matters.
They foolishly talk about certain events being ‘fated’ and
others being the result of free choice. This is nonsense! These
misconceptions also provide the clearest evidence that occult¬
ism and mystical philosophy are two totally different things.
Occultism, being concerned with the cryptic forces operating
in nature and matter, retains an essentially materialistic way
of looking at things. Mystical philosophy, being concerned
with the relationship between spiritual and material aspects of
truth, must embrace both and adopt paradoxical mystical
modes of thought and expression.

All fate is freely chosen because it is the result of past
volitional acts; in the present it provides the field of action in
which free will can operate (could one make free choices in a

237

vacuum?). All fate is beneficent in the sense that it provides
ideal scope for willing the good. It is beneficent, too, in the
sense that without the laws of fate there would be no certain¬
ty that any volition, good or bad, would ultimately be con¬
nected with its appropriate consequences and life would be¬
come a chaos. What was done with good intent might never
bear good fruit. What was done with evil intent would not
(as it inevitably does) produce those remedial and even puni¬
tive conditions in our lives which tend to redirect our efforts
to return to the universal harmony.

The destiny with which we are born and which is fully
described in principle in the nativity, is merely a special appli¬
cation of these general truths. All manifested life is a limitation
in the sense that it introduces us to definite circumstantial
conditions. The good man, however, is never a prisoner of
fortune since what is a limitation from one point of view is an
opportunity from another. From this larger viewpoint, all that
he meets with affords him opportunities for exercising the mar¬
vellous and varied powers of the soul, heroic and gentle, grave
and gay:

He who kisses the joy as it flies
Lives in Eternity’s sunrise.

Let it not be thought—heaven forbid—that we would
seek to diminish the wonder of the soul’s incarnation or try
to express in a few neat rules and graphs the mysterious
workings of Divine Providence in its all-wise and all-just ap¬
portionment of human destiny, although, under the law of the
attraction of similars, these are, in truth, simplicity itself:

.Fresh

Issues upon the universe that sum
Which is the lattermost of lives. It makes
Its habitation as the worm spins silk
And dwells therein. It takes

Function and substance as the snake’s egg hatched
Takes scale and fang; as feathered reed-seeds fly
O’er rock and loam and sand until they find
Their marsh and multiply. (From the Lord Buddha’s
sermon in The Light of Asia, Book Eight)

One of the noblest uses of Astrology is, as it has always
been, its value as an aid to the contemplation of the great
verities of man’s estate and his relationships to the Cosmos
and to God. If this book has contributed a few insights into
this great science and so enabled anyone to glimpse more
clearly the mysteries and beauties of the Divine Order and
Harmony, the author will be more than satisfied.

NOTES

1 . Interestingly, the revelation that astrological forces’ manifest as tem¬
poral rhythms which ebb and flow, rather than as simple divisions of
duration of time, links up with the very oldest teachings. There can
be little doubt that Egypt was the cradle or fountainhead of the eso¬
teric teachings of at least the Western tradition. In this connection
Isha Swaller de Lubicz (wife of R.A. Swaller de Lubicz, both serious
students of Ancient Egyptian thought) provides a number of lengthy
commentaries at the end of her book, HerBak, Disciple. These are
based on her insights into Egyptian esoteric teaching. The commen¬
taries w'crc not translated by Sir Ronald Eraser along with the books
themselves. They have only recently been rendered into English by a
friend of the writer, Dorothy Smith oi Prestatyn. In Commentary Six,
on Astronomy-Astrology, the last, section is headed ‘Tate, Grace and
Determinism.” In this Swaller de Lubicz says, speaking of the Egyp¬
tian view of epochs of time: “That which can be foreseen is the date
of change in the pattern of the times. But the times are, above all,
rhythms and not (periods of) duration. And to these rhythms numbers
can be assigned, which are functional values.”

238

239

APPENDICES

APPENDIX I

A SIMPLE WORKING PLAN FOR THE INDIVIDUAL
OR SMALL GROUP OF RESEARCHERS

Having studied this book, the student may feel that he
would like to try his hand at some original research in the
field of harmonics, and he may wonder how he should set
about it. There is certainly plenty of scope for individuals or
small groups of students to tackle projects which will help to
build up our picture of how harmonics work. At present we
are at the stage of groping our way towards an understanding
of the numerical basis of structures in the psyche, in human
society and in the body. The relationship of these to each oth¬
er and to numerical structures in nature is similarly unfolding.
In this process of exploration there is a great need for an
abundance of quite small-scale (as well as larger scale) studies
of different sets of data drawn from different fields. Studies of
nativities showing psychological traits, disease conditions, vo¬
cational allegiances and so on are all badly needed in order
that we can begin to distinguish the significance of different
harmonics in various contexts and to arrive at a better under¬
standing of the principles by which they are to be interpreted.

Some of the larger groups and organizations in the astro¬
logical field are at present organising computer facilities to
cover every stage and aspect of this kind of work so that larg¬
er projects can be tackled more easily. But individual students
with a taste for this kind of investigation need not feel that
they have no part to play. Indeed it is worth emphasising that
all the pioneering work in this field has been done, and in
many cases continues to be done, without computers. The stu¬
dent who is prepared to work patiently through the various
processes of collecting and analysing data “by hand” enjoys
many advantages over those who are fully mechanised for the
job. As he works slowly and steadily at his task, he contin¬
ually notices small things which escape the attention of the
man with the computer. He is in touch w r ith his material from
start to finish, and has time for reflection. He can adapt him¬
self to clues which he notices, turning aside to follow up small
points which often lead to new discoveries.

243

Above all, it is the fact that his mind is close to his ma¬
terial which gives him the advantage. 1 believe it is true that
when he has done as much as he can with pen and paper,
there is often much benefit from having a full harmonic analy¬
sis done by mechanical means. This is really impossibly time
consuming by hand. Yet even then he will look at the com¬
puter printout with a sharper eye and a deeper understanding
for having done much of the preliminary work himself.

Even those who do not wish to engage in systematic re¬
search, however, may care to tackle a project such as is il¬
lustrated in this appendix. When it comes to understanding
harmonics there is nothing which teaches one more effectively
than working with them.

First of all, what is the minimum size for a collection of
nativities to be examined for harmonics? There is no simple
answer except that the more unusual or specific the condition
studied the smaller will be the collection needed. The more
unusual any factor is, the more sharply one may expect it to
be distinguished astrologically. A few hundred cases—even
less—of those who follow some very unusual occupation may
be enough to tell one a great deal; for a more general cate¬
gory such as scientists or writers, a much larger collection will
be needed. But a glance at the graph shown in Fig. 80 sug¬
gests that the added benefit to be gained in accuracy beyond
say 2000 or 3000 cases is small unless one is looking for great
detail.

As an example of a fairly small-scale study and the meth¬
ods one can adopt to carry it through, I am indebted to
Charles Harvey for permission to make use of a collection he
made of the birth dates of hydraulic engineers. This collection
includes the birth data of all those in Who’s Who in Engi¬
neering (1968) who are listed as being hydraulic engineers
or specialists in hydrology or water supply. This is a rather
specific class of occupation and carries the particular interest
for the astrologer that it is especially concerned with one of
the four elements. In all, we find that there arc 334 specialists
of this kind listed.

The first step of course is to extract the names and dates
of birth and to list them in due order. In a case of this sort

244

the names will probably be given in alphabetical order so
there is no need to give a page reference to one’s source book.
Having listed the dates of birth, one may decide that one will
simply make a study of say the Sun and Moon positions. If
one proposes later to examine aspects, one must first remem¬
ber the difficulties and problems of such a study arising from
planetary stations, as described in Chapter 9. Then one would
rule columns for all the planetary positions and duly set about
entering the noon positions for each date.

Let us suppose that we have entered the position of the
Sun for each day at noon and wish to examine what forces
are at work regulating its distribution in these nativities. Our
list may start off as follows (I do not have the original list of
names and birthdays, so these are merely illustrative):

Name Date Sun

1. Smith, J.

2. Williams, M. F.

3. Brown, W r .

4. Jones, A. C.

5. Robertson, A. J.

.etc.

27 Dec. 1920
14 Nov. 1917
12 Aug. 1925
22 Mar. 1919

28 Apr. 1931

5.28 Capricorn
21.33 Scorpio
19.13 Leo
0.49 Aries
7.15 Taurus

We now want to know how many Sun positions fall in
each degree of the Zodiac. For this we use a 360 degree grid
as shown opposite. It is best to number the columns across the
top from 0 degrees to 29 degrees; then number the degree
boxes at 10 degree intervals up to 360 degrees for use in deal¬
ing with aspects. One can put the sign symbols down the left
hand side when one is dealing with zodiacal positions. This is
an all-purpose grid and a little experience will soon make its
use familiar. Note the details which should be entered at the
head of the page.

Working through our list of hydraulic specialists, then, we
can put a stroke in the appropriate box for each Sun position.
In our example we have put the total number of Sun positions
for each degree for the sake of legibility. Case 1 goes in at
5° Capricorn, Case 2 at 21° Scorpio, and so on. Because we
have started our numbering across the top at 0 degrees, Case

245

4 goes in at 0 degrees Aries. In this way one need only take
note of the whole degree number, although we list the posi¬
tions in degrees and minutes so as to get as much accuracy as
possible when we come to calculate solar aspects.

There is no virtue in treating 0° Aries as covering all po¬
sitions from 29°31’ Pisces to O'30’ Aries. U is just as accurate
to put the the positions in with regard to the whole degree
number; cither way we have 360 totals and the phase angle
can be measured from the point 0° Aries just as easily one
way as another, provided the computer is so adapted.

Having obtained our total number of Sun positions for
each degree, there are several things we can do straight away.
By adding across wc can give a total for each sign, by adding
down we can give the total for each degree of the 12th har¬
monic (30 degrees in length).

We have totalled the positions for each sign down the
right of the grid and these are as follows:

A ries

Taurus

Gemini

Cancer

Leo

Virgo

Libra

Scorpio

Sagittarius

Capricorn

Aquarius

I’isces

The

striking

feature of

these positions which

we notice

straight away is that the negative signs tend to be high, posi¬
tive signs low'. Insofar as those who deal with water supply
and hydrology must have a great deal to do w r ith earth as
w r ell as water, this is a satisfactory start. If w r e actually draw
out this distribution pattern (Fig. I) wc shall think of two
things. First, we shall feel sure that there is a strong 6th har¬
monic (60 degrees in length) giving alternate signs high and
low 1 . Secondly w'e notice a “beat” effect with a powerful oscil¬
lation bctvvcen positive and negative signs at one point in the
distribution tailing off to only a very slight contrast at another
point. We shall therefore conclude that as well as the 6th,
there is a strong adjacent harmonic, either the 5th or 7th,
(so that the two harmonics coincide at one point and cancel
each other out at another, see Fig. 74),

247

Let us tackle the 6th harmonic first. This is 60 degrees in
length. For these longer waves it is quite sufficient to take the
total for each sector of 5 degrees-, this will give us six totals in
each sign and twelve in each 60 degrees. Reading from our
grid then, here are the totals in runs of 60 degrees. These
have been added up to give the whole 60 degree distribution
pattern (Table 1). Ignore the further addition sum in sets of
lours for the moment.

Table 1: 60° runs by 5° sectors.

227365 769944

435235 773758

475511 727436

444560 3624 10 5

422653 459137

603549 576532

24 18 26 26 25 23 33 33 36 30 28 32

25 23 33 33

36 30 28 32

85 71 87 91 = 20° by 5° sectors
(Total: 334)

It is a good idea after performing an operation of this kind to
check that one’s total agrees with the number of cases one
started with — 334 — so as to make sure one has not lost
any positions during the process of transcribing or counting.

We can now draw out our 60 degree distribution pattern
in graph form — see Fig. 11a. Looking at this graph we can
see our 60 degree wave (the 6th harmonic) and we can also

248

see what appear to be three waves super-imposed upon it, as
shown in Fig. Ilb. This must be a wave of 20 degrees (the
18th = 6x3). We can easily check this by going back to our
totals in Table 1 and putting them down in runs of 4 as
shown. This yields four totals for each 20 degrees which we
can again draw in graph form (Fig. Ill) to enable us to see
the size and phasing of our 18th.

In both Fig. I la and Fig. Ill we have drawn our phase
angle scale along the bottom of the graph. Wc can see that
the 6th harmonic has a phase of about 260 and an amplitude
of about 18% (a rise and fall of 5 on a mean of 28). Similar¬
ly the 18th harmonic has a phase of about 290 and an ampli¬
tude of roughly 10% or just over. Be careful when drawing
the graph to remember that the first total, in this case 24,
falls in the middle of the first 5 degrees. This affects where the
phase will fall when one is using graphic methods to deter¬
mine it.

We can now go back to our thirty degree-by-degree distri¬
bution totals which we have arrived at by adding downwards
along our grid. It is sensible to draw this out to help us to
see what harmonics, if any, are present. When we do so,
(Fig. IV) w'e have to look rather carefully to see what the
chief elements are. It is only by experience that one can learn
to spot the significant factors in these graphs, although some¬
times they are quite obvious. Of course when we are dealing
with a relatively small collection of data spread, as in this

graph, through 30 separate totals, the numbers are low and so
the element of randomness obtrudes and makes it harder to
see what is what. After some study we may conclude that
there appear to be two interesting features.

Fig. IV

First we notice that there tends to be a peak roughly
every six degrees which have been marked with crosses. We
can test this 6 degree wave by setting down our degree totals
from across Lhc bottom of the grid in runs of six:

Table 2: (?

runs

single

degrees

,53

,48

_34j

190 144

In all these cases we can tell very roughly whether there
is a significant harmonic present by asking if one half of the
run of totals is widely different from the other. They should
differ from the mean by at (east the square root of the mean
distribution. In this case the mean is 167 (334 -4- 2), the
square root of which is about 13. Thus, we are looking for
one half of the distribution to be over 180 and the other less
than 154. As can be seen, we have totals of 190 and 144 and

250

this gives a very elementary indication of significance. This
will be disputed by statisticians but it is a rough sort of guide.

Drawing out our graph from Table 2 (Fig. V) we can
immediately sec the second factor of interest in this distribution,
namely that alternate degrees are high and low. Thus the to¬
tals for the alternate degrees of the Zodiac can be arrived at
conveniently from Table 2;

Table 3: Odd Even

53 60

77 48

62 34

192 142

These high and low scores for alternate degrees of the
Zodiac are just as strong a feature as for alternate signs of the
Zodiac, in fact the contrasting totals are the same in each
case: 192 and 142. The difference is that whereas there is sel¬
dom much doubt about which sign of the Zodiac the Sun is
in, the fact that wc arc dependent upon noon positions on the
day of birth for the degree position means that there is rela¬
tively quite a large element of approximation at work here.
Therefore the true contrast between odd and even degrees is
probably even greater than is indicated by the totals 192 and
142.

This emphasis on odd or even degrees is a feature which
tends to appear in many such results. What it relates to I

251

cannot say, and it would be worth while for some student to
try to discover what it indicates. In the 7302 physicians the
emphasis falls strongly in the same way as in the present case.
Anyone who investigated this would have to ascertain that this
effect was not produced by some unnoticed recurring tendency
in the Sun’s noon position, although there is reason to think
that it is not due to this.

Looking back to Fig. V and our 6 degree wave (the 60th
harmonic, one fifth of a sign) we can see that this is a very
vigorous presence with a rise and fall of about 12 on a mean
of 56, or just over 21% amplitude. The phase is about 150
degrees.

Before leaving the 30 degree distribution pattern, w r e may
remark that there is evidently no 30 degree wave as such nor
one of 15 degrees. The 5th sub'harmonic of this scries is easily
the strongest and the only significant presence apart from the
odd and even degree rhythm.

What next? The 4th harmonic is often a significant fea¬
ture, though not as often in the Zodiac as in Gauquelin’s
diurnal positions. We ought to test for this, even though the
sign totals (Fig. 1) do not suggest its presence. For this we
shall set down our 5 degree totals from Table 1 in runs of 18
totals (5° x 18 — 90°). (We could make them into 10 degree
totals in runs of 9 if we wished).

Table 4: 9CP runs by 5° sectors

Column: 12 3 4 5 6 7 8 9

2 2 7 3 6 5 7 6 9

7 7 3 7 5 8 4 7 5

44456 (13 62

4 5 9 1 3 7 6 0 3

*-r

{

()

1718 23 16 20 20 20 1919

19 ,

170 155

If we draw this series (Fig. VI) we can see that there is
only a very slight 4th harmonic. The best contrast we can get
from our totals is a split of 179 vs. 155 (columns 3-11 vs.
12-18, 1-2) between the highest run of nine totals and the

252

lowest. There is probably a modest 4th harmonic with a phase
of about 180 degrees and a small amplitude which would be
confirmed by a similar set of data from another country.

Coming now to the 5th harmonic, wc have a slight prob¬
lem. We cannot keep to our 5 degree block totals because 5
degrees will not divide into 72 degrees. However we can over¬
come this by taking our totals from the grid in blocks of 6
degrees. This is rather a nuisance but at least it has the ad¬
vantage that it entirely eliminates the 6 degree wave which we
have already noticed. Going back to our grid and taking the
totals for each 6 degree sector through the Zodiac, we have:

Table 5: 72° runs by 6° sectors

256667 7 14 6546

255796 695853

284566 448523

71 13 643 57 3 676
28616 5 968752

15 27 34 25 31 27 31 40 30 31 23 20

31 40 30 31 23 20

46 67 64 56 54 47 = 36° run
(Total: 334)

We can split these totals into two halves so that one half
has 188 and the other 146, a fairly good result. When we
draw the graph it seems probable that the principal ingredient
besides the 5th (72°) is the 10th (two halves of 36°). This we
have confirmed In Table 5 in the usual way, and the resultant
graphs are shown in Figs. VII and VIII.

253

We can see here that both these harmonics are strong, the
5th having an amplitude of over 20% (phase about 180°) and
the 10th of about 25% (phase about 150°). We can also see an
18 degree wave (20th) crossing and recrossing the 36 degree
wave, but this is not so strong — about 10% or less.

We said when we looked at Fig. I, showing the distribu¬
tion through the signs of the Zodiac, that it looked, because
of the “beat” effect, as though we should find a 5th harmon¬
ic or a 7th. As a matter of fact there is one thing about that
'‘beat” effect which suggests that we might find both, a 5th
and a 7th. This is that the strong oscillation and the flat part
of the graph do not fall exactly opposite each other in the
Zodiac as they should if it were a simple combination of 5th
and 6th or 6th and 7th.

So lei us look at the 7th harmonic — a number, incident¬
ally, which has more than a touch of association with Neptune
and might well appear in these watery nativities. Here we
have difficulties again because, since the 7th part of the circle
is 51°25.7’ approximately, there is nothing we can do to divide
up our distribution into exact 7ths. However, a close approxi¬
mation is really all we need. Thus we are dealing with a
wave 51W long.

What we do is to put down our 5 degree totals in runs
of ten totals (= 50 deg. instead of 51 Va deg.). At two points
in the Zodiac we drop one of our totals so as to keep the
harmonics in step as far as possible, thus:

laoie o;

Stf instead of 5T26’

iocr

”

” 102“ 52’

155“

”

” 154“ 17’

205“

”205“ 43’

255“

”

”257“ 09’

31(T

”

”308" 34’

360“

Total 327 ( + 7)

It will be seen from the successive degree-steps of the true
7th series shown on the right that we are never out of step
by more than two or three degrees. This is a small shift in a
wave of SIVa degrees. Of course we could if we wished get
greater accuracy still by going back to our grid and using
separate degree totals but the above method is usually quite
accurate enough.

Drawing now our graph (Fig. IX), we see how we have
obtained a perfectly clear and convincing result with a vigor¬
ous 7th harmonic and its third sub-harmonic winding its way
to and fro across the line. The 7th has an amplitude in the
order of 18% (phase about 180°) and the 21st (= 3x7) is not
much weaker (say 12 - 15%) and phased at about 270°.

Looking back now over our results, we find that we have
been able to extract from this quite modest collection of data
the following convincing harmonics:

Amplitude %

Phase

5th (72°)

180

6th (60°)

260

7th (51W)

180

10th (36°)

150

18th (20°)

10+

290

21st (17°)

12+

270

60th ( 6°)

150

It is worth noting that if we had used our raw degree
totals from the grid instead of 5 degree totals, we might well
have found some more short waves besides the 60th.

In addition to these, we have noticed a strong tendency
for a 180th of 2 degrees. We have not checked the 9th al¬
though we easily could use our 5 degree totals in runs of eight
totals (5° x 8 = 40°). But as a matter of fact, if the student
cares to try this, he will chiefly notice the two waves of the
18th harmonic (20 degrees in length) which we have already
spotted.

The above harmonics are well and clearly shown. I would
expect most of them to appear in any parallel collection of
nativities of hydraulic engineers and hydrologists from another
country, provided that their work and background approach
was not too different from those given in Who's Who in
Engineering. This is a small collection of nativities but the
harmonics we have obtained evidently show up so well because
the character of the work they are involved with is distinctive.

If one were attempting to analyse the harmonic distri¬
bution of aspects in a collection of data such as this, one
would begin by listing the angle from the slower moving
planet to the faster one, always measuring round the circle
in the direction of its motion. Thus, suppose our original list
of names and birthdates gave the positions of the planets,
one would tackle say the Sun-Mars aspects as follows:

256

1. Smith, J.

2. Williams, M.P-

3. Brown, W.

4. Jones, A.C,

5. Robertson. A.J.

Dotr

27th Dec. 1920
14th Nov. 1917
12th Aug. 1925
22nd March 1919
18th April, 1931

Suit

5.28 Capricorn
21,33 Scorpio
19 13 Leo
0,49 Aries
7.15 Taurus

Afarj

23.10 Aquarius
6.25 Virgo
29-46 Leo
12.06 Aries
9.29 Leo

Angtis Sun-Mars
312
75
349
349
268

In these few cases, we have been unlucky in having to go
the long way round the circle to measure the aspect in several
cases because the Sun was approaching the conjtmetion. Notice
that we measure the angle to the nearest whole degree, having
regard to the minutes of longitude, thus in case 3 the Sun is nearer
to 11 degrees from the conjunction than it is to 10 degrees.
One always measures from the slower-moving planet to the
faster one.

This process of calculating the angle seems very labourious
at first but becomes easier after a time. It certainly teaches
one why computers were invented and also why, so far,
relatively few aspect-studies have been made.

Having obtained our list of angular relationships, we
simply go through our list putting a stroke in each appropriate
box of our grid, which is numbered for this purpose. Having
thus obtained our degree-by-degree distribution of Sun in re¬
lationship to Mars, we can proceed with our harmonic analysis
exactly as before.

In doing this for the first time, the student will often
have to stop and think exactly what he is doing, relating the
process and its results to the aspect circle and its relationships.
All the time he is doing this he will be learning to think har¬
monically and this is what we want.

When he has obtained his results, they can be listed and
if possible published. In the coming decades, more and more
such harmonic analyses of different sets of data will be pub¬
lished and at the same time, studies will be published of
number symbolism in its different applications to the nativity.
From the interaction of these two—experiment and hypothesis,
hypothesis and experiment—a picture will be built up of the
interpretative basis of relationships in the horoscope. It will be
a basis far more integral and comprehensive than anything we
now possess in astrology.

257

Footnote:

Students may be interested to know that in the Moon’s
position in the nativities of hydraulic engineers, the emphasis
on the water signs was even more marked over the other
three elements:

A ries

Taurus

Gemini

Cancer

Leo

Virgo

Libra

Scorpio

Sagittarius

Capricorn

Aquarius

Pisces

However, one must be very cautious about making assump¬
tions on the basis of a literal understanding of the four
elements. A collection of charts of specialists in aerodynamics
showed Air signs to be easily the weakest! A strong third
harmonic placed all the emphasis in Fire.

Acknowledgements to Charles Harvey who made both
studies.

258

APPENDIX II

SOME POINTS BEARING ON HARMONIC ANALYSIS

Harmonic analysis is a procedure by which a wide range
of mathematical expressions or observational data relating to
periodic phenomena can be broken down into a number of
components each of which is a simple wave motion. Anyone
who has read this book or examined Appendix I will have
gathered the general idea of what is involved without any
reference to the standard mathematical procedures which char¬
acterise harmonic analysis proper.

From the point of view of the material dealt with in this
book we may note that any observed distribution of planetary
positions can be broken down into wave forms and fully de¬
scribed in such terms. The standard method of harmonic anal¬
ysis is often known as Fourier analysis after the French math¬
ematician, Fourier, who first satisfactorily tackled this type of
problem.

It is not our purpose in this appendix to describe the
procedure of Fourier analysis for this can be obtained from an
appropriate textbook. In any case the process is extremely te¬
dious if carried beyond the first few' terms and is normally
best done by computer. In this connection one may mention
that standard computer programs for harmonic analysis are
generally available.

There is however one issue which is not often dealt with
specifically in works which describe harmonic analysis and
which is therefore worth commenting upon here. In all har¬
monic analysis of observational data the aim is to determine
what regular harmonic wave patterns are present in the dis¬
tribution of a given number of totals. The number of totals
which describes the distribution will vary. For example Michel
Gauquelin, the French researcher, in studying planetary dis¬
tributions in the diurnal circle, divides the circle by 12 (cor¬
responding roughly to the twelve houses of the horoscope) or
by 18 or 36, giving the total number of planetary positions in
each sector. These divisions by L2, 18 and 36 show a success¬
ively more detailed picture of the distribution. Having regard

259

lo the acknowledged element of approximation in registered
birthlimes, any division beyond 36 sectors would seem to have
little value, although a more detailed analysis based on accur¬
ate birthtimes would no doubt prove of great interest.

In all analyses of planetary distributions in the circle of
the ecliptic a much higher degree of accuracy is possible be¬
cause planetary motions in this circle are much slower and
therefore a total for each degree of the Zodiac has always been
used In this book. In other words all distributions of Sun,
Moon and planets in the Zodiac have been analysed by 360
totals.

The questions to be considered are: What is the effect of
greater accuracy upon the results of harmonic analysis when
we use a larger number of sector totals? What, in general, are
the limitations imposed upon the scope of harmonic analysis
by the number of totals available?

To take a simple example, suppose we are examining the
distribution of the Sun through the signs of the Zodiac and so
have a total for each of the twelve zodiacal sectors. The total
for Aries may be, say, 42. This lumps together all the Sun
positions which fall in Aries. But suppose we then go on to
count up the number of Sun positions in each dccanatc (each
10° sector) of the Zodiac. We may then find that within the
sign Aries there is a very unequal spread of cases. Perhaps the
first decanate has 26 cases, the second 10, and the third 7.
Although the total is 42, the 12 sector analysis treats this
total as if it were centered on the middle of the sign, whereas
wc know that in fact the majority of cases falls near the be¬
ginning of the sign. This is bound to affect the accuracy of
the amplitude and phase yielded by harmonic analysis.

The more numerous the divisions made in studying the
distribution and the greater the number of sector totals we
have, the more accurate will be the result of the analysis.
This might seem obvious but even those who were very well
acquainted with harmonic analysis found it difficult to estimate
just how- much the results would be affected for any harmonic
by increasing the number of totals in the data used for the
analysis.

In order to obtain some idea of how much the results

260

would be affected, Colin Bishop of the Astrological Association
Research Section and others ran one set of actual data through
the computer dividing the distribution into different numbers
of sectors. For this purpose the Sun positions of 1024 children
with poliomyelitis were chosen (see Chapter 8). These positions
were originally given as 360 degree totals. It was therefore
possible to group this solar distribution into two sectors of 180
degrees, or into four, six, eight and so on up to 360 sectors,
and to consider how the amplitude and phase yielded by
harmonic analysis was affected as the divisions became more
numerous.

First as to amplitude , some typical specimen results arc
shown in Fig. I. Along the bottom of the graph is shown the
number of divisions of the zodiacal circle by which the distri¬
bution was successively analysed. The vertical scale shows the
amplitude for the 2nd, 6th, 7th, 11th, 24th and 36th harmon¬
ics as given by computer analysis when the same original data
was divided up by various sector totals.

It will be seen that as the number of sector totals increas¬
es (that is to the right of the graph) the amplitude yielded
tends to become progressively more stable. When there are
few sector totals relative to the number of the harmonic the
amplitude oscillates, sometimes wildly. Despite these oscilla¬
tions of value we can say, in a general way, that the ampli¬
tude will seldom be seriously distorted (more than by 2% or
3% of absolute amplitude ) provided the number of sectors is in
the order of between four and six times the number of the
harmonic. To obtain a reliable result as to amplitude, one
should have a number of totals in the data which is four
times, and preferably six times, the number of the highest
harmonic analysed. This will usually yield an amplitude within
2% or 3% of the true amplitude. 360 degree totals will usual¬
ly be fairly reliable up to the 60th or even the 90th harmonic,
although there may be occasional exceptions.

The same sort of rule can be shown to apply in relation
to phase. Fig. II shows the phase angle yielded by computer
analysis of the same polio data for the 3rd, 4th and 5th har¬
monics. In this case, instead of saying the margin of error will
not usually be more than 2% or 3% provided the number of
totals is six times the number of the harmonic, we must say

261

that the error will not usually be more than 20° or 30^ of

phase.

This modest experiment does at least throw some light on
an obscure topic and it is hoped that it will be of help as a
very general guide to other researchers.

262

GENERAL INDEX

Amplitude.

13-14. 20, 2«

calculation of ... .

. 45-46

expected mean . . .

. . Ml-182

mean.

.13

percent.

. . , 13, 28-29

Apollo ..

.9.5

Artemis.

.95

Arts, the.

104-105, 127

Ascendant.

.2.5-26

in harmonic chart .

.102

Ascending node ....

.14 15

Aspcctarian, harmonic

. 135-136

Aspects . . . 4-3. 34,

Ch. 9, Ch. 14

and retrogradation .

.72-73

considered

harmonically . . .

Ch. 9. Ch. 14

inadequacies.

. . . 67. 74-75

major.

. 69, 129, 131

minor.

.129

orbs of (see Orbs) 67, (19-70, 12911

traditional concept of . . . 67, 75

true nature of ... .

. 78. Ch 14

Astrologer r x Gu idt. to tke.

Harmonics .

100, 1380, 216

Astrological Association Research

Section.

. . . 28, 198

Ataturk.

.96

Avanamsa.

1.94-195, 198

Barnden, John.

.139

Beautiful, the.

.85

Bennett, Pam.

.215

Biological rhythms research . 220-221

Birtht imos, registration

of.24, 188-189, 205-206

Body, analogy of . . . .

.85

~BciX'(ypc' Zodiac T>]

L 56, 171. 193

Bradlev,

Donald 65. 192, 194 195, 196-197

Brief Biot’rufihit'i .

... 117, 127

Catalog r if Harmonics (see Astrologer's

Guide to the Harmonics)

Circadian rhythms.220

Circles.83ff

Completion.95, 116, 121

Conception, lime of.200

Criichlow, Keith.134

Culmination, upper and lower . . 25

Cusps

of houses.30, 32

of signs.51-52

Cycles, Study- of

and sunspots.226-229, 230

causes.

. 222

cosmic implications of . .

. . 227

criteria of.

. . . 222

8 year ... . . . .

. . 223ff

families

(sec Harmonics, /amities) . .

... 232

planetary correspondences

. ,228ff

Darlington, D.C.

206-207

Deductive method.

146,168

Degree areas

. . 107-108. 117, 124, Ch 15

at harmonic intervals . .

145, 147

in aspect and diurnal circles 1481T

harmonic nature of ....

145-146

positive and negative . . .

146. 148

symbolism of.

. . . 144

Delphi.

... 95

Descending node.

. 14-15

Dewey, Edward R.

(sec Cycles, Study of) ....

. , 221 IT

Directions (see Progressions)

Diurnal circle

(set; Harmonics, in diurnal cu

rle)

Diurnal motion.

. 23. 34

Doctrine of Substance ....

. . . 234

Ebertin School of Asirologv

. 114

Ecliptic circle .... 34-35.

51H. 60fl

harmonic division of

(sec Harmonics, in ecliptic circle) . 68

Entclcchv.

.... 95

Extroversion.. .

.... 58

Fagan. Cyril.80.

192. 195

Families (see Harmonics, families

and Cycles. Study of)

Firebrace, Brig. R. 51. 192,

. 194-195

First causes.

. . 23411

First principles (sec General I.

MIL'S)

Five, symbolism of 103-105. 210-211

Fixed Stars {see Sidereal Zodiac)

Formal cause;.

... 213

Foundation for the Nludv of Cycles

(set; Cycles, Study of) . . . .

6.5. 221 IT

Four elements.

. . . 103

Four, symbolism of . . . 103.

. 114 1 15

Fourier Analysis.

. 28. 259

Free will.

. . . 237

Fundamental (see Harmonics, 1st)

Galactic: center.1!)7

Galactic equator.197

Gauquelin, Francoise 23, 24, 189
Gauquelin, Michd.

(see harmonics, and Gauquelin studies)
and signs and aspects ... 57, 75

genetic research.204

methods.23

research 23 -20, 172, 179. 180ff. 259
Getieral Laws or first principles
(sec Deductive method. Inductive.

method) . 107,174

Genetics.Ch. 20

and disease . 215

and 5th harmonic. 20711

astrological study of , . . . 204-205
evolution of ideas ...... 200-207

Gauquelin research.204

laws of.205

Genetic transmission.200

Glcadow. Rupert.51. 192-193

Gnostic faculties (sec Mind)

Good, the.85-86

Graham, Charles M. 178 (n)

Hamblin, David.U7

Harmonics.5-6, 11-12

and Gauquelin studies .... Ch. 4

and hierarchies.8511"

and prime numbers
(see Numbers, prime)

and rctrogradation.72-73

calculations.Ch. 0 , 91-93,

10th. 253-254

11 lb.. . 134

12 th.18-19, 53

13th.134-135

15th.19, 126-127

17th.19

18 th.249

21 sl.255

24th.OOff, 77

25th.65. 136

27th.134

36th. 77

40th. 216

48l1i .01

49th .. . . . 62-63

60th.251

98th. 62-63

108th. . . ,79

120 th . 01

125th .65

Harmonics analysis

(see Fourier Analysis) .. 28

of Gauquelin results.29

problem of significance . . . 18111

use of graph paper in. 43 ff

Harvey Charles. 215, 244, 258

Harvey, Ronald F.137

Heart. 83

Helens, Michael..139

Heredity (see Genetics)

Hierarchies.84-85

Hindu Astrology . . . 79, 91-95, 100

Houses (see Harmonics.

in diurnal circle) .4, 22, 65

as harmonic divisions. 68

in Gauquelin studies .... Oh. 4

100-102, 24311"

charts . 93. 100, Ch. 13

families. 05, 232

in aspect circle

Ch. 9. Ch. 11-13, Ch. 14
in diurnal circle Ch. 4, Ch. 0, 124
in ecliptic circle

. . Ch. 7, Ch. 8 . 68 , 124

micro-. 134. 137-138

phasing (sec Phase)
practical

application of . . . 83, Ch. 11-13
research (See Research plan)

sub-. 18 20,55.61,70

symbolism.Ch. 5

Unifying effect of Theory 124-125

unusual. 210

1 st or fundamental

11 - 12 . 18. 121 . 122

2 nd. 11 . 18-19

3rd. 18-19.30-31

4ih. 18-19. 20-28. 253

3th .05. Ch 12. 125-120,

20711, 247. 253-254
Olh . , II 55. 110. 247. 248-249
7th . . 6211', 1| Off, 247,254-25.5

«'b.114

9th (sec Navamsa) , . 4711. Ch. II

l Cbiinp .178

Ideas. 84-85, 206-207

Indian Astrology (see Hindu astrology )
Induction of labor

(see Labor, induction of)

Inductive meihod . .

.174

Inferior planets.

.73

Inspiration.

, . 1!>4. 116

Introversion ..

..58

journal of Interdisciplinary.

Cycle Research .

. . 24, 189

Judas.

. , 135(n)

Jung. C.G.

.151

Jupiter (see Venus-Jupiter)

75, 80-81

Labor, induction of , .
Landscbeidt, Theodore

Lao Tse.

Lasso ns, Leon.

I«asl. Supper.

London University . .

213-214
, . . 137
. . . 153
. , 23-24
.135
... 58

Macrocosm/microcosm .85

Magnetism.36

Marriage . . 93-95, 104, 109, 154ff

Mars. 39, 41-42, 75, 80-81

Material cause .. 114

Mathematics.6-7

Mayo, Jeff. 58

Mean planetary days.220

Measuring points

in diurnal circle.179-180

in ecliptic circle.197ff

Midheaven.102

Mind.84

Moving total.52

Munkasey, Michael.139

Quadrupliclty. 54

Quintile aspect

(see harmonics, 5th ) Ch. 12, 125-126

Relationship of

astrological factors . . - 68-69, 83ff

Republic of Plato ..217

Research attitudes.76

Research plan. 243ff

Rctrogradation.72-73

Rhythms research
(see Cycles, Study of)

Nature magazine.58

Nature, philosophy of.. . 233

Navamsa . 37, 79-80, Ch. 11

calculation of.91-93, 101

Neptune. 75, 80-81

Nine, symbolism of ..... . 95-96

90* dial.114

Novtle aspect

(see Harmonics, 9th, Navamsa) 125

Number.35, 86

prime.37, 121, 134

symbolism of .... 38-40, 87, 99,
103, 121-122, 236
Numerical potency.36

One-degree progressions
(see. Progressions, symbol ic)

Orbs. 4, 62, 69, 129fl‘

Panchanisa (see Harmonics, 5th) 100
Part/whole relationship
(see Whole/part relationship)

Peak (sec Waves ) .15-16

Peak distribution.179

Peak phase or peak direction ... 16

Period.11-12

Phase.14-17, 29-31

determination of .30, 31,

176, 1861T

hypotheses concerning ... 177ff
of harmonics .... 176, 183, 186ff
Phase angle (see Phase)

Plato.217

Pluto. 75, 80-81

Polarity ..55-56

Power.109, Ill-112, 125

Precession of equinoxes . . . 192, 232
Prime numbers (see Numbers , prime)

Prime vertical.179

Progressions

secondary. 154ff

Sun-Venus at marriage , . 154-155
symbolic.155, 16 Iff

Venus-Saturn at marriage . . 155fl

Saturn (see Vemts-Saturn) . . 25fT, 75fl,
1051T, 135, 155

Secondary progressions

(see Progressions, secondary)

Sept lie aspect

(see Harmonics, 7lh ).125

Seven, symbolism of 104, 111, 116ff

Shodasvargas. 79, 94, 114

Sidereal astrology.192ff

Sidereal Zodiac .... 56, 69, Ch. 19
Signs of Zodiac (see Ecliptic,

Harmonics, in ecliptic circle) - . 34, 68 ,
247

Six, symbolism of . . 104, 111, 116

Social Structure.85

Socrates.217

Solar Apex. 197

Somerford, W.H. .159-160

Soul.84ff

Square aspect

(see Harmonics, 4th) .114-115

Subharmonies (see Harmonics, sub-)

Sun-Venus progressions.154

Symbolism

(see Number symbolism, Four, Five ,

etc.) .Ch. 5

Synodic periods .34

Thompson, D’Arcy. 201-202

360 degree grid. 245ff

Three, symbolism of.103, 115

Transits.151, 15911

to harmonic positions .... 98-99
Tropical vs. Sidereal dispute

.... 69, Ch 19
Tropical Zodiac . . . 192, 195, 198ff

Trough (see Waves) .14-15

True, the ..85-86

Trutine of Hermes.206

Twelve

Importance of , - . . - 51, 93, 115
limitation of.37

266

267

Unfbldment of life.151ff

Unity . 84-8(1

Unusual harmonics

(see Harmonics, Mint)-, Harmonics,
Unusual)

Uranus.75, 80-81, 10 .off

User's Manual (see Astrologer's Guide
to the Harmonics)

Venus (see Sun- Venus /impressions)

Venus -J up iter.127

Venus-Saturn.135, 15511

Verniers of aspects.80

Vertex/Anti-vertex.179-180

Vibration.36

Walter, Dr. Hans-Jorg.126

Watt, James .96

Waves.Ch. 2, Ch. 3

combinations ol . . . 19-20, Ch. 17

complexes.Ch.17

heal.168ff, 247

box . .t 171

kirk. . . 168

sawtooth .. 171

**g*ag. 171

in astrological

circles ... .34, 41, 51. 60, 68

length . 11-12

sine. 11

whole numbers of.18-19

Whole/parl

relationship , . . 84-8.5, 121, 23511

Will.85-86

Williamsen, Dr James S-

and Ruth E. .'.139ff

Windsor, Donald A.58

Yin and Yang . 153, 178

Zodiac (set- Ecliptic-, Harmonics,
in ecliptic circle)

268

INDEX OF ASTROLOGICAL STUDIES

Addcy, John .... 105flf, 207ff, 212

Armstrong, Neil.128

Artists.65, 127

Astrologers

105ff

Baudelaire.

Beethoven.

Berlioz.

Betrayal.

Blake.

Blindness.

Bolshevik Revolution
Bronte, E-

Brook, Rupert.

Browning R. and E B

.127

118, 119, 127

.118

.135

. .. 127, 135
. . . 137-138

.97

.135

.96

Joyce, James.127

Marriage . 94-96, 154ff

Mozart.109, 135

Nonagenarians.198

Carter. Charles.105fT

Cezanne. 119

Churchill, W. 97-99, 116-117,

121, 125, 128, 214

Clark. Jim.119, 128

Clergymen

American.65

British.62ff

Composers.Il7ff

Creativity.110 111,116

Da Vinci.119

Davison, Ronald .105ff

Debussy.118

Delinquents, Juvenile .... 169-170

Delius.118, 127

Doctors (see Physicians)

Edward VIII.109-110

Einstein.128, 136

Fdgar, Edward.135

Fire-brace, Brig. R.U>5ff

Fermi, Enrico.97

Ford, Gerald R.I 12, 125, 163

Graham, Billy.128

Haemophelia ..215

Hardy, Thomas.135

Harvey, Charles.105JT

Health.115-116

Hereditary principles . 2()7ff, 216

Hitler . 109

Hydraulic engineers. 244ff

Physicians .... 25ff, 5Iff, 194, 198fl

Piggolt, Lester.108

Poliomyelitis.60-61

Professional attainment

(see Gauque.lin, M.) .. . 23ff

Rave! .118

Rainfall.196-197

Romantic composers (see Composers)

Rudhyar, Dane .I05ff, 128

Ruskin... . 120

Russell, Bertrand.128

Schubert.118, 119

Schumann.118, 127

Scientists.25ff, 172-173

Sex. Ill, 120

impotence. 120

Shelley.127, 133

Soldiers. 41ff

Soviet Union..97

Sportsmen . 39-40

Stewart, Jackie.1L9, 126

Van Gogh

Zola, Emile

269

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