Gift of The People of the United States Throughthe Victory … · 2017. 2. 26. · 4 DIRECTIONAL ASTROLOGY Significators, in this scheme, are the Midheaven, Ascendant, Sun, and Moon

Gift of The People of the United States

Through the Victory Book Casnpaign

/ (A. L A. — A. R. C — U.S. 0.)

To the Armed Forces and Merchant Marine

Th» Old Corner Book

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DIRECTIONAL ASTROLOGY

DIRECTIONAL ASTROLOGY

TO WHICH IS ADDED A DISCUSSION OF

PROBLEMATIC POINTS AND A COM

PLETE SET OF TABLES NECESSARY

FOR THE CALCULATION OF

ARCS OF DIRECTION

BY

SEPHARIAL

AUTHOR OF

"COSMtC SYMBOLtSM," " A MANUAL OF ASTROLOGY,"

"A MANUAL OF OCCULTtSM," " THE KABALA OF NUMBERS,"

"KABALtSTtC ASTROLOGY," ETC-

PHILADELPHIA

DAVID McKAY

604-608 SOUTH WASHINGTON SQUARE

1 92 1

rharvarpN

UNlVERSiT A

^J_IBRAR> J

PRtNTED tN GREAT BRtTAtN BY

NEtLL AND CO., LTD.,

EDtNBURGH.

PREFACE

A word by way of introduction to this work may

be necessary, inasmuch as it deals with a technical

subject, and the scope and purport of it cannot

very readily be apprehended by the casual reader.

It is essentially a book for the astrological student.

To the astronomer it is particularly informing

in that it brings out the more scientific part of

the subject and shows the mathematical basis

underlying the " lucky hits " to which many

of our astrological exponents have undisputed

claim.

The general scope of this work embraces all

that is essential to the art of " directing " as

practised by Claudius Ptolemy and Titus de

Placidus, and more recently by Sir John Wharton,

Mr John Gadbury, Commander Morrison, R.N.,

and Mr A. J. Pearce, all of whom pursued the

same general principles of astronomical directing,

and differed considerably in their application of

the celestial arcs to the measure of time. These

points are reviewed and critically examined in

the following pages.

v

vi DIRECTIONAL ASTROLOGY

An attempt having been made to bring the

Arabian system of a day for a year into accord

with the astronomical system of a degree for a

year, some suggestions have here been made as

to their rapprochement, the feeling being that,

where credit is claimed for one system over another

by exponents of either, the probability is that

there is truth in both and hence there must be a

co-ordinating factor. In the attempt to scientific

ally extend our horizon to include a prescience of

coming events, we have primarily to remember

that there are many ways up a mountain, but

there is only one top. A study of these various

methods may lead to the conclusion that they are

all leading in the same direction. It is as if one

should say there are three hundred and sixty paces

from end to end of the path, and another should say

that there are three hundred and sixty-five. Both

may be right according to their count and the

measure of their tread, but the actual length of

the path will remain the same whatever they make

of it. This pathway is that which a man has

to travel from his cradle to his grave ; and there

is nothing that concerns a man so vitally as that

he should know its trend and gradient, its pitfalls

and rocky eminences, in advance of his going, so

that experience may be laid by the heels and made

to serve instead of to subjugate. And in the

direst extreme of human experience we have to

remember that " the wise man foreseeth the evil

PREFACE vii

and obscureth himself, while the ignorant pass on

and are hurt."

I have used a well-known and thoroughly

authenticated horoscope for purposes of illustra

tion, and anybody following the rules here given

in relation to that horoscope will have no difficulty

in following them out in respect to any other

horoscope. Particular care has been taken to

define the principle underlying each operation,

and to give a clean-cut rule of procedure. Unlike

most authors, who proceed by befogging the mind

of the student with technicalities and afterwards

explaining them by means of an appendix, I have

devoted the first chapters of my work to technical

definitions which are essential to the proper under

standing of the subject ; and until these are clearly

apprehended and understood, the student need go

no further.

To save further expense and trouble, my pub

lishers have completed my work by the insertion

of a complete set of tables, which include tables

of Right Ascension and Declination for every degree

of the zodiac, together with the ascensional differ

ence due to the latitudes of London, Birmingham,

and Liverpool under the present obliquity of the

Ecliptic ; also tables of Sines and Tangents, and

tables of Proportional Logarithms. These are all

that are essential to the present treatise, and in

themselves constitute a very valuable addition to

the volume. It is, of course, presumed that the

viii DIRECTIONAL ASTROLOGY

student of " Directional Astrology " will have

mastered the preliminary task of setting a horo

scope for any given time and place with adequate

precision, and hence that he is familiar with the

use of an ephemeris. The present work is intended

to replace and supersede Prognostic Astronomy,

which is now out of print.

Beyond this I have nothing to say, save that I

trust to have done my work efficiently and to have

left no point on which a reader need question me.

In such case the work may be regarded as complete,

and so I hope it will be found.

SEPHARIAL.

CONTENTS

CHAP. PAOE

1. Astronomical Definitions 1

2. Example Horoscope 11

3. Directions in Mundo 18

4. Directions in the Zodiac .... 25

5. Zodiacal and Mundane Parallels . . 32

6. Order op Directing 37

7. Effects of Directions 40

8. Planetary Indicators and the Measure of

Time 49

9. Illustration 57

10. Ptolemy and Placidus 62

11. Directions under Poles . . . .71

12. The Part of Fortune 81

13. Lunar Parallax and Semi-diameter . . 86

14. Lunar Equations 94

15. Cuspal Distances 99

16. Suggested Method of True Directing . 107

17. Conclusion 117

Appendix—Tables of Sines, Tangents, etc. . 125

Tables of Right Ascension and

Ascensional Difference . . 173

Tables of Proportional Logarithms . 181

iz

Directional Astrology

CHAPTER I

ASTRONOMICAL DEFINITIONS

The following definitions must be fully understood

by the student before the more intricate part of the

system of directing is undertaken.

Longitude is of two kinds : longitude in the Orbit,

and longitude in the Ecliptic. The latter is the only

one recognised and used in this system. It is de

fined as distance from the vernal equinox, Aries 0,

measured on the plane of the Ecliptic or Sun's path.

Latitude.—Celestial latitude is distance north or

south of the Ecliptic.

Declination is distance north or south of the

Equator. The Ecliptic lies in declination 23° 27'

north and south.

Right Ascension is distance from the vernal equinox

measured on the plane of the Equator. Right

ascension thus answers to geographical longitude

in the same way as declination answers to geo

graphical latitude.

Meridian Distance is the distance of a celestial

1

2 DIRECTIONAL ASTROLOGY

body from the midheeven of a place ; that is to say,

from its meridian, measured in right ascension.

Semiarc of a planet is half the time it remains

above or below the horizon of a place, measured

in degrees of right ascension. The diurnal semi-

arc is half the arc in right ascension of a planet

above the horizon, and nocturnal semiarc is half

the time it is (measured in right ascension) below the

horizon. The diurnal semiarc taken from 180° will

give the nocturnal semiarc, and the nocturnal semi-

arc taken from 180° will give the diurnal semiarc.

Horizontal Arc is the distance in right ascension

from a body to the point of its rising or setting.

The semiarc less the meridian distance is always the

horizontal arc.

Oblique Ascension is the right ascension of a body

increased or diminished by its ascensional difference,

according as its declination may be south or north.

In northern latitudes the right ascension is in

creased for a body having south declination and

decreased for a body having north declination, but

the reverse of this is the case in southern latitudes.

Ascensional Difference is the time (measured in

right ascension) that a body is above or below the

horizon more or less than six hours. If, therefore,

its semiarc is more than 90° the excess of 90° is

its ascensional difference. All bodies that are not

exactly on the equinox (Aries 0 or Libra 0) have

ascensional difference. For a planet in south

declination the ascensional difference is added to

ASTRONOMICAL DEFINITIONS 3

its right ascension to get its oblique ascension, and

for bodies having north declination the ascensional

difference is subtracted. The reverse of this gives

the oblique descension. The O.A. plus or minus 180°

gives the obi. descension of the opposite point.

Pole of Latitude.—The pole of a place is the same

as its latitude. The pole of a planet is measured

by a circle of position or small circle parallel to

the meridian of a place. The pole of the ascendant

is the same as the latitude of the place, and this

diminishes as we reach the meridian, where it is 0.

Direction is the process by which we bring the

body of a planet to the longitude or body of another

in a different part of the heavens either by its

rising or setting, and this direction of one body to

another, or to the place of another, is measured

in right ascension ; that is to say, by the number

of degrees which pass under the meridian of a

place in the interval. All directions are taken in

the prime vertical, or circle of observation—that

in which a person stands upright facing south.

Having the proportional distance of a planet

between the meridian and horizon, we may bring

another body to the same proportional distance

along its own arc until it appears to be in the same

relative position as the first body. This supposes

that the position and influence of a planet is

indelibly located in that part of the heavens in

which it was found at the moment of birth. All

arcs of direction are measured in right ascension.


Significators, in this scheme, are the Midheaven,

Ascendant, Sun, and Moon. These are the bodies

or positions that are directed or moved in the

prime vertical in order to form conjunctions,

oppositions, and various aspects with other posi

tions and bodies. They are called " significators,"

from the fact that they are found to signify certain

things in the life of an individual ; as, the Sun

signifies male relationships, the Moon female relation

ships, the Midheaven honour and position, credit,

etc., and the Ascendant the health and general

play of events in the individual sphere of life. For

further elaboration of this point refer to the Text

book of Astrology or The New Manual of Astrology.

Promittors.—These are the planets Neptune, Ura

nus, Saturn, Jupiter, Mars, Venus, and Mercury.

The Sun and Moon may also be classed as promittors

when the Midheaven or Ascendant is directed to

them.

Logarithms, invented by Baron Napier of Mer-

chiston, first-class mathematician and astrologer,

were designed for the purpose of simplifying calcu

lations in spherical trigonometry. In this scheme

the arc of 90° of a right sphere is made to equal

10-00000, which is called the radix. Then, having

the logarithm of any arc, it may be multiplied into

any other arc by simple addition of their logarithms ;

and, similarly, arcs may be divided by one another

by subtracting one logarithm from another. Napier

thus emphasises the fact that multiplication is


merely the addition of a number to itself a given

number of times, while division is merely subtrac

tion a number of times. Then by means of a

proportional circle we can multiply and divide any

arc by simple addition and subtraction. The com

plement of an arc is what it lacks of 90°, and as

this is equal to the radix 10, the complement of a

logarithm is what it lacks of 10. Thus the loga

rithm of the sine of 32° is log. sine 9-72421, which

is also the log. cosine of 58°, because 58 is the

complement of 32, both together making 90. The

arithmetical complement of the logarithm is 0-27579,

since this, added to the log. sine of 32°, makes

10-00000. Familiarity with the use of logarithms

will readily establish their great value in all mathe

matical calculations connected with the sphere.

I may now ask the reader to take in hand an

ephemeris for the current year, 1916, and turn

to the 1st January, and the above definitions may

then be illustrated.

Let us suppose that a birth took place at noon,

Greenwich mean time, on that date in London.

The ephemeris being calculated for mean noon at

Greenwich, there will be no equation of time

necessary. The Sun, Moon, and planets will be

in the positions indicated in the ephemeris. The

Sun's longitude is seen to be Capricornus 9° 45' 14".

The Sun never has latitude, inasmuch as it defines

the Ecliptic, distance above or below which con

stitutes celestial latitude. All other bodies have


latitude except when they are on that point where

their orbits cross the Ecliptic, that is, their nodes.

The course of the Sun being across the plane of the

Equator at an angle of 23° 27' it will attain that

declination at the solstices ; that is to say, on the

21st June and the 22nd December. On the 1st

January it is found to have declination 23° 6'

south of the Equator, and, therefore, would be im

mediately overhead at noon at a place which had

geographical latitude 23° 6' south, and the Sun's

diurnal course around the Earth would follow this

parallel of latitude. The Sun's right ascension

(R.A.) can be found in the tables (see Appendix)

from its longitude.

Rule 1.—To find the R.A. of any body without

latitude.

From the log. cosine of its distance from the

nearest equinox subtract the log. cosine of its

declination. Remainder is the log. cosine of its

R.A. from the same equinox.

Example : The Sun is here 80° 15'

from Aries 0 . . cos. 9-22878

Its declination is 23° 6' cos. 9-96370

Distance in R.A. from

Aries 0 = 79° 23' . cos. 9-26508

Therefore from 360° take 79° 23', and the R.A.

of the Sun is thus found to be 280° 37'. Note that

it is sufficient for our purpose to take the various

quantities to the nearest minute of space.


Now take the Moon's place in the ephemeris,

which is seen to be Scorpio 17° 54'. This is 47° 54'

from Libra 0. The declination of the Moon is

22° 7'. Reference to the tables will show that the

declination of Scorpio 17° 54' is 17° 10' only, and

we therefore know that the Moon has latitude

and is not on the Ecliptic at this time. The ephe

meris shows it to have 5° 9' of south latitude. In

finding its R.A., therefore, we have to take this

latitude into account.

Rule 2.—To find the R.A. of a body having

latitude.

Add the log. cos. of its distance from the equinox

to the log. cos. of its latitude, and from the sum

subtract the log. cos. of its declination. The

remainder is log. cos. of its R.A. from the same

equinox.

Example : Moon's distance from

Libra 0 = 47° 54' . cos. 9-82635

Its latitude is 5° 9' . cos. 9-99824

Sum . . cos. 9-82459

Moon's declination,

22° 7' . cos. 9-96681

Its R.A. from Libra 0= 43° 53' cos. 9-85778

R.A. Libra 0 =180° 0'

Moon's R.A. = 223° 53'


Note.—If we take the arithmetical complement

of the log. cos. of the declination and add it to the

log. cos. of both the latitude and the longitudinal

distance, we shall have the same result.

The R.A. of the other bodies is taken in the same

manner, as they all happen to have some measure

of latitude. Only when a body is in its node, and

therefore coincident with the Ecliptic, does it have

no latitude. In such case its R.A. is the same as

that of the degree of the Ecliptic it holds.

We have next to find the meridian distances of

the several bodies. To do this we have to find

the R.A. of the Midheaven and Nadir, and take

the nearest distance in R.A. of each body. Thus

at noon on the 1st January 1916 the sidereal time

is 18h. 39m. 16 sees. Convert this into degrees

and minutes of the circle, thus : multiply the hours

by 15 and call them degrees ; divide the minutes

of time by 4 and call them degrees and minutes

of space ; also divide the seconds of time by 4

and call them minutes and seconds of space.

Thus 18h. =270° 0' 0"

39m. = 9° 45' 0"

16s. = 0° 4' 0"

R.A. of M.C.=279° 49' 0"

180° 0' 0'

R.A. of I.C. = 99° 49' 0"

The upper meridian is called the Midheaven


(medium cceli) and the lower meridian is called the

Nadir (imaum cceli).

Having the R.A. of the M.C. and I.C., we

are able to find the quantity of R.A. which

separates the various planets from them, and this

is the meridian distance of each of such planets.

Thus the Sun's R.A. was found to be 280° 37',

and that of the M.C. (to which it is nearest) is

279° 49'. The difference is 0° 48', which is therefore

the meridian distance of the Sun.

The Moon is found to be in the South-west

quarter of the heavens, and therefore nearer to the

upper than the lower meridian. Its meridian dis

tance must therefore be taken from this point.

Meridian distance of Moon= 55° 56'

The other bodies are taken in the same way

according to which meridian (upper or lower) they

are nearest in R.A.

The semiarcs of the planets and luminaries have

next to be found.

Rule 3.—To the log. tangent of the latitude of

place for which the figure is set, or the horoscope

cast, add the log. tangent of the planet's declina

tion. The sum is the log. sine of the ascen

sional difference of that planet under the latitude

of birth.

Thus :

R.A. of M.C.

R.A., Moon

= 279° 49'

= 223° 53'


Uniformly, add this ascensional difference to

90° when the planet's R.A. is less than 180°,

and subtract it from 90° if the planet's R.A. is

more than 180°. The result is the diurnal semiarc

of that planet. By subtracting this from 180°

you will have the nocturnal semiarc.

Finally, by taking the meridian distance of the

planet from its semiarc (diurnal if above the

horizon, and nocturnal if below), you will have the

horizontal arc, or distance in R.A. from the horizon.

Next find the proportional logarithm of the

semiarc of each body, and take its arithmetical

complement. Add to this A.C. the proportional

logarithm of the planet's meridian distance. This

is the constant log. of the planet for purposes of

directing.

Enter all these elements into a single table,

which is called the Speculum, an example of which

will be found in the following pages. The scheme

will now be ready for the practice of directing.

CHAPTER II

EXAMPLE HOROSCOPE

Fob the purpose of illustrating the method of

directing by proportional semiarcs, I have selected

the horoscope of John Ruskin, whose Fors Glavi-

gera, Mornings in Florence, and other world-

renowned works have stamped him indelibly as

artist and man of letters as well as an independent

thinker of considerable virility.

He was born at 7.30 in the morning of 8th

February 1819, in London.

It is an invariable rule in practice to use that

semiarc and meridian distance which are related

to one another. Thus the Sun in the speculum

is just below the east horizon at the moment of

birth, as may be seen by comparing its nocturnal

semiarc with its distance from the lower meridian,

which are 110° 1' and 108° 44' respectively. This

shows the Sun to be 1° 17' below the horizon. But

as by the diurnal rotation of the earth on its axis

from west to east the Sun will be carried above

the east horizon upwards towards the Midheaven,

during the course of which it will pass the places

n


Speculum.

Planets. Lat. Deolin. E.A.Merid.

Dist.

Semi-

are.

Hor.

Aro.

O O 0 O / o / o /

Sun — 16 13 S. 321 12 108 44 110 1 1 17

IN. 17 21 52 51Moon 5 25 39 N. 120 50 2 30

23 S. 21 34 S. 47 46 51 60 11 13 20Mercury . 0 296

10 N. 18 10 S. 6 26 10 65 37 39 27Venus 5 276

55 S. 45 S. 6 49 10 59 53 10 43Mars 0 21 299

21 S. 26 S. 37 52 41 62 3 9 22Jupiter . 0 20 302

Saturn 56 S. 6 54 S. 348 81 2 98 45 17 431 54

Uranus . 6S. 23 24 S 12 53 57 1 44 80 262 49

13 N. US. 47 17 59 5 41 14Neptune . 1 22 267 51

EXAMPLE HOROSCOPE 13

of Mars, Mercury, Venus, Neptune, and Uranus, it

will be convenient also to have the semidiurnal arc

and the meridian distance from the Midheaven.

For whenever we use the nocturnal arc we always

use the corresponding meridian distance from the

lower meridian, and whenever we use the diurnal

arc we also use the corresponding meridian distance

from the Midheaven or upper meridian. This point

should not be forgotten. It cannot be overlooked

if the constant log. of the planet is inserted in the

speculum, because this embodies the proportion

of the semiarc to the corresponding meridian

distance.

Ruskin was agreeably disposed towards the idea

of planetary influence in human life, for, although

he confessed entire ignorance of the subject himself,

he was always willing that others should have the

full benefit of his experience and views, and he

readily gave his birth data to those who sought

it for the purpose of astrological calculations.

His assertion that " there is more in it than is

generally supposed " was doubtless the opinion he

formed of the science from experience ; and if it

does not carry the weight of scientific criticism, it

stamps Ruskin, at all events, as a man of fearless

integrity of thought.

In this horoscope we have a remarkable illustra

tion of the principles of astrology. The Sun and

Jupiter are rising in the humane sign Aquarius,

while most of the planets are rising and above the


horizon. These are indications of success and dis

tinction in the world. The conjunction of Mars

and Mercury in opposition to the Moon indicated

that asperity and outspokenness which characterised

this man of genius and rendered him fearless in the

expression of his views. His eccentricities may

well be attributed to the meridian position of

Uranus and Neptune, while Venus, in closest aspect

to Jupiter, and well elevated, disposed to success

in the pursuit of art, of which he became a foremost

exponent. But, of course, these positions do not

make character. They only afford the opportunity

for its full expression. Character and environment

together constitute destiny, and it is undoubtedly

often the case that one or the other of them is a

misfit. It is only when we get a strong innate

character with appropriate celestial environment

that we look for the expression of genius.

We may now proceed to use this horoscope to

illustrate the principles of directing.

Take first the Midheaven. This is directed by

right ascension, and the planets coming to the

meridian will form arcs of direction to it. The

aspects to Midheaven should be noted. Thus the

semisquare aspect falls in Capricorn 26° 28', and

the sextile aspect is Aquarius 11° 28', and planets

coming to these points will form aspects in the

zodiac to the Midheaven. The square aspect falls

in Pisces 11° 28'; and as Saturn is lower in the

heavens than that point, it must come up to the

EXAMPLE HOEOSCOPE 15

place of this aspect and form the zodiacal square

to the Midheaven. And the times in which these

aspects are formed by the several planets will be

in the proportion of their semiarcs. These direc

tions are in zodiac.

The other kind of direction is in mundo—that is,

in the circle of observation or prime vertical. Thus

a body that is on the cusp of the twelfth house is

in mundane sextile to the Midheaven or upper

meridian, and one that is on the cusp of the eleventh

house is in mundane sextile to the horizon or Ascen

dant. A planet that is in the middle of the eleventh

house will be half way between the Midheaven and

Ascendant, and, therefore, in semisquare aspect in

mundo, because the meridian and horizon are

always at right angles to one another. If a planet

is not thus situated at the moment of birth it will

afterwards attain that position, and the number

of equatorial degrees which pass under the meridian

from birth to the time when the aspect is formed

will be the measure of the arc of direction. The

original position of a body, either in the zodiac or

in mundo, is always that to which direction is made.

Mundane Directions are those that are made to

the apparent place of a celestial body, or to its

aspects, in the circle of observation.

Zodiacal Directions are those which are made to

the geocentric longitude of a body, or to aspects

of that longitude, in the circle of observation or

prime vertical.


All directions are formed by the rotation of the

Earth upon its axis from west to east, by which

the planets appear to rise, culminate, and set,

pursuing a course that is from east to west. The

lines or arcs traversed by the planets in this ap

parent motion are parallels of latitude of the same

quantity and denomination as geographical parallels

of latitude—that is, lines parallel to the Equator.

The planets follow the parallel of declination in

which they are found at the time of birth.

It is understood that the radical imprint of a

planet is localised in that part of the heavens it

occupied at the moment of birth ; and although the

actual planets do thereafter change their declina

tions and semiarcs, as well as their meridian dis

tances, the radical imprint of the planet remains

ever the same, and is to be regarded as entirely

distinct from the planet itself, which, of course,

moves along its arc in the heavens.

In the process of directing we are, therefore, only

concerned with the radix or root horoscope and

the changes which thereafter take place in the

heavens, not among the bodies themselves, but

in their relations to the radix. All directions of

this nature are formed within a few hours of the

moment of birth.

Directions (whether in the zodiac or mundo)

are of two orders. These are " direct " and

" converse."

Direct directions are such as are formed by one

EXAMPLE HOROSCOPE 17

body being carried by the motion of the Earth

towards another body or aspect in the heavens

that precedes it. Converse directions, however,

are such as are formed in the opposite direction.

Thus in the foregoing horoscope of Ruskin, if we

bring the Sun to the place of Jupiter, or Mars,

or Mercury, or Venus, these would be direct direc

tions, because that is the direct motion of the bodies

in the heavens. But if we brought the Sun to

the place of Saturn it would appear that we are

carrying it backwards to a position that it held

previous to the moment of birth. This, however,

is not the case. The Sun is joined to the Earth

by a direct ray which is called its earth-line, and

it is this line which, by the rotation of the Earth

on its axis, is carried down (bearing the solar im

print) to the place held by Saturn at the birth.

This is a converse direction. But if we bring

Saturn up to the place of the Sun it would be a

direct direction.

Therefore all directions are formed by the one

natural fact of the Earth's rotation on its axis, and

aspects that cannot thus be formed are not within

the category of primary directions.

We may now pass on to illustrate the method of

forming every kind of direction, direct and converse,

in zodiac and mundo.

2

CHAPTER III

DIRECTIONS IN MTTNDO

The principle involved in this process is that which

enters into the construction of the horoscope,

wherein we take one-third of the Sun's tropical

semiarc as the extent of the house or division of

the prime vertical. This principle enters into the

construction of the tables of houses for various

latitudes, the Sun's extreme declination remaining

a constant quantity.

But in every horoscope we have the various

planets with different declinations, and therefore

with different semiarcs ; and consequently we are

dealing with arcs which, although parallel to the

Equator and to one another, are not parallel to the

circle of observation. Hence an equal division of

the prime vertical into twelve parts or houses

will not effect an equal division of the various

planetary semiarcs, which cut the meridian and

horizon at varying angles depending on their

declinations. Nevertheless, it has been found in

practice' that one-third of the semiarc, great or small,

is equal to a house-space under the pole of that planet.

18

DIRECTIONS IN MUNDO 19

Suppose a planet to be exactly rising at the time

of birth. Let its semidiurnal arc be 66° 21'. This

is an arc of right ascension. Therefore when it

has traversed one-third of its arc from the horizon

to the meridian, 22° 7' will have passed under the

meridian, and that will be the arc of the planet's

direction to the cusp of the twelfth house. Another

22° 7' will bring it to the cusp of the eleventh house,

and yet another arc of the same value will bring it

to the meridian. When on the cusp of the twelfth

house it will be in sextile aspect to the Midheaven,

and when on the cusp of the eleventh it will be in

sextile to the Ascendant, both directions being in

mundo, as distinguished from similar aspects in

the zodiac.

If the Sun or Moon happen to be exactly on the

cusp of a house, then the planet coming to the cusp

by one-third divisions of its semiarc will simul

taneously form aspects in mundo to the Sun or

Moon. But if they are not so placed, then we have

to find their proportional distances from the nearest

cusp or limit of a house, and bring the planet to

the same proportional distance in order to form

the aspect.

Rule.—To find the cuspal distance of a planet.

Note the cusp to which it is nearest at the time of

birth. The distance of that cusp from the horizon

compared with the planet's horizontal arc will give

the planet's cuspal distance.

Example.—In the specimen figure the Sun is


nearest to the cusp of the first house or ascendant,

and therefore its horizontal arc, 1° 17', will be

its cuspal distance. The Moon has a semiarc of

52° 51', and its horizontal arc is 2° 30', and as

this is nearest to the cusp of the seventh house,

that will also be its cuspal distance.

Now, as in all directions, the body to which

direction is made is considered to remain stationary

while the body directed is moved towards it by its

natural motion in the heavens, we here direct the

Moon to the sesquiquadrate aspect of the Sun,

which it attains in the middle of the fifth house,

that point being four and a half houses, or 135°,

from the ascendant. The Sun, however, is not on

the ascendant, and therefore we have to bring

the Moon to a proportional distance from the middle

of the fifth house. Thus :

As the semiarc of the Sun, 110° 1',

prop, log 0-21381

arith. comp 9-78619

Is to its cuspal distance, 1° 17', . 2-14693

So is the semiarc of Moon, 52° 51', . 0-53223

To its proportional distance, 0° 37',

prop, log 2-46535

Now, as one-third of the Moon's semiarc is 17° 37',

that will be its house-space, and one-half will be

8° 48£', making for one and a half houses 26° 25£',

and from this we subtract the above proportional


distance, namely 0° 37', and there remains the arc

of direction : Moon, 135°, Sun in mundo, 25° 48£'.

Another example : Bring the Sun in the ex

ample horoscope to the mundane conjunction with

Jupiter.

In order to effect this the Sun has to cross the

horizon, its distance from which has been found

to be 1° 17'. Thereafter we employ its diurnal arc

and bring it to an equivalent distance from the

horizon southwards as Jupiter is in the horoscope,

by proportion of their semidiurnal arcs.

Jupiter's semiarc is 62° 3', and its meridian dis

tance 52° 41', their difference 9° 22', which is the

horizontal arc of Jupiter and therefore its distance

from the cusp of the first house. Then we say :—

As the semiarc Jupiter (arith. comp.) is to its

cuspal distance, so is the semiarc of the Sun (diurnal

=69° 59') to its proportional distance from the same

cusp southwards. This works out as follows :—

S.A. Jupiter, 62° 3' . log. 0-46253

S.A. Sun, 69° 59' 0-41028

Sun's prop, distance =10° 34' log. 1-23144

Arith. comp. 9-53747

1-28369Cusp, distance, 9° 22'

Sun to horizon = 1° 17'

Arc of direction = 11° 51'

Sun conj. Jupiter to.


It should be observed that the arc of direction

to the horizon must always be added when the

planet or body has to cross the horizon in forming

the direction. Here the proportion of the Sun's

arc to that of Jupiter gives a cuspal distance of

10° 34', and to this has to be added the distance

of the Sun from below the horizon, making the arc

altogether 11° 51'. When crossing the meridian

to form a direction, no change of arc is necessary,

but the arc to the meridian, which is the meridian

distance of the planet, must be added to the arc

formed on the other side of it.

It should be observed also that the body to

which direction is made, and which is supposed

to be stationary, supplies the first and second terms

of the proportion, while that body which moves

to form the direction supplies the third term and

the resulting fourth term. In practice it will be

found expedient to arrange all the mundane

aspects in the order in which they are formed by

each of the planets. The Midheaven and Ascendant

remain stationary, and the Sun, Moon, and planets

are the promittors that are moved to form direc

tions upon them. Take one of these bodies at a

time and make a list of the mundane directions

it forms to the Midheaven, Ascendant, Sun, and

Moon, calculate them, and arrange them afterwards

in the order of their values. Always remember

that the diurnal motion of the Earth upon its axis

from west to east is the underlying cause of all


directions, and that the planet to which direction is

made, remains still, while the other moves towards

it. You cannot then go wrong in your application

of the method.

Direction to the conjunction in mundo is effected

by bringing the body of a planet to the body of

another, and not to its zodiacal longitude merely,

as is done in the case of the zodiacal conjunction.

Thus in the case of Uranus to conjunction M.C.

in mundo, we take its meridian distance as the arc

of direction, whereas in the zodiac we take the

meridian distance of its longitude, Sagittarius

23° 25', and this will be the arc of direction.

In all cases we bring the body of the planet

directed to the conjunction or aspect of another

body in mundo, to form mundane directions, all

such directions being formed in the prime vertical,

and expressed in terms of right ascension.

It will be found convenient to have the constant

log. of the cuspal distance of each planet in the

speculum. Subtract the proportional log. of the

semiarc from the proportional log. of the cuspal

distance. This will give the constant log., to which

we have merely to add the proportional log. of the

semiarc of any other planet to find the proportional

cuspal distance of that planet.

It has been customary to regard the semiarc of

a planet as equal to the quadrant, and therefore

one-third as equal to a house or 30°. This is true

in regard to a prime vertical whose pole is the


same as the declination of the planet, but it is not

true in regard to any other pole or geographical

latitude. That is why we take the proportion of

the semiarcs in finding the cuspal distances of

planets. The test is this : If we take the oblique

ascension of a planet, that is, exactly one-third of its

semiarc from the horizon, it should have the same

oblique ascension as the cusp of the twelfth house,

but by adding 60 to the right ascension of the Mid-

heaven to get the oblique ascension of that house,

we shall find that if the planet has any other declina

tion than 23° 27' there is a difference between the

two results. It cannot, therefore, be truly said that

a planet is in mundane sextile aspect to the Mid-

heaven when it is one-third of its semiarc above

the horizon, inasmuch as its position in the prime

vertical does not then coincide with the cusp of

the twelfth house ; but it may be said to correspond

with that cusp on the general proposition that all

circles are equal to one another and therefore that

all quadrants are equal, and in practice it is found

that one-third of a semiarc corresponds with one-

third of the prime vertical, and this was allowed

by Placidus, who was the first exponent of this

system of mundane directions.

CHAPTER IV

DIRECTIONS IN THE ZODIAC

These are calculated on the same principle as

mundane directions, that is to say, by proportion

of the semiarcs ; but instead of taking the actual

body of the planet, or its position in the prime

vertical, we take the longitude only and direct to

that, and also to its aspects in the zodiac.

Thus in the horoscope of Ruskin the planet

Neptune holds the longitude Sagittarius 28° 22',

and therefore its zodiacal sextiles will fall in

Aquarius 28° 22' and Libra 28° 22', its squares

in Pisces 28° 22' and Virgo 28° 22', and so on.

The longitude of the planet, or its aspect if we are

directing to it, remains stationary, and the actual

body of the planet or luminary which is directed

to it is moved along its own semiarc until it reaches

the longitude or aspect to which direction is made.

Therefore we take the meridian distance and semi-

arc of the ecliptic degree held by a planet and use

these as the first and second terms of a proportion,

in which the semiarc of the body directed forms the

third term.

26


Example.—Direct the Sun to a conjunction with

Jupiter in the zodiac.

Jupiter's longitude is Aquarius 0° 20', and from

the tables we find this longitude to have R.A.

302° 31', from which take the R.A. of Midheaven,

249° 56', and we get its meridian distance, 52° 35'.

The same tables give the ascensional difference

under London as 30° 51', which, taken from 90°

as the declination is south, gives the diurnal semi-

arc = 59° 9'.

Prop. log. meridian dist.

„ semiarc

Constant log. Aquarius

Prop. log. Sun's semiarc

. 52° 35' = -53442

. 59° 9' = -48332

. 0° 20' = -051 10

. 69° 59' = -41028

Sun's prop. dist. 62° 13' = -46138

Take from Sun's merid. dist. 71° 16'

Arc of direction . . 9° 3'

The constant logarithm of a longitude, once ob

tained, should be reserved, as it will serve for all

zodiacal directions made to the same point of the

ecliptic by simply adding the log. semiarc of the

body directed to it. We then have the proportional

meridian distance, which, compared with its original

distance, gives the arc of direction.

Uniformly, find the R.A. of the longitude to

which direction is made ; from this derive the

meridian distance. Find its declination, and from

DIRECTIONS IN THE ZODIAC 27

this derive the semiarc. Subtract the propor

tional logarithm of the semiarc from that of the

meridian distance, and derive the constant log. of

the given longitude. To this constant log. add

the log. semiarc of the body directed to it, and

thus obtain the proportional distance of that body

from the meridian at the point of direction. The

difference between this and its radical meridian

distance is the arc of direction.

Examples :—

1. Direct the Sun to aspects of the Midheaven

in the zodiac. The aspects to which the Sun

applies are the sextile in Aquarius 11° 28', the

semisquare in Capricorn 26° 28', and the con

junction in Sagittarius 11° 28'.

Aquarius 11° 28' has R.A. 313° 55'

The Midheaven has R.A. 249° 56'

Merid. dist. of aspect = 63° 59' prop. log. -44921

Asc. diff. 23° 9'

90° 0'

Semiarc 66° 51' prop. log. -43017

Constant log. of aspect in Aquarius 11° 28' = -01904

Add prop. log. Sun's semiarc diurnal -41028

Sun's prop. dist. from M.C. 66° 59' -42932

Radical dist. of Sun from M.C. 71° 16'

Arc of direction, Sun sextile M.C. = 4° 17'


2. The next aspect of the Sun to the Midheaven

in zodiac falls in Capricorn 26° 28', which is the

semisquare aspect of 45°.

The R.A. of this longitude is 298° 29', and its

meridian distance is therefore 298° 29' -249° 56' =

48° 33'. Its ascensional difference is 28° 40', which

gives its diurnal semiarc=61° 20'.

Proportional log. 48° 33' -prop. log. 61° 20' con

stant log. of aspect, -10150

To this we add the

prop. log. of Sun

as before, namely, -41028

•51178 = 55° 23' Sun's propor.

meridian dis

tance ;

which take from 71° 16' Sun's radical

distance,

remains 15° 53' the arc of di

rection Sun

semisq. Mid-

heaven.

3. The next aspect of the Sun to Midheaven in

zodiac is the conjunction. For this the calculation

is simply the difference of their right ascensions.

That of the Sun is 321° 12'

That of the M.C. 249° 56'

Difference 71° 16'=arcof direction.


These examples will doubtless serve for all cases

that may arise in the course of directing a planet to

the longitude and aspects of another in the zodiac.

We may now consider converse directions in the

zodiac. These are calculated in exactly the same

manner as the direct directions ; but instead of

moving the directed body forward in the heavens,

that is, from the Nadir to the Ascendant, from the

Ascendant to the Midheaven, from the Midheaven

to the Occident, and so on, we move it conversely

against the natural diurnal motion of the celestial

bodies in the heavens. Thus, in the example

horoscope the Moon is in Cancer 27° 8'. There

fore, to bring Saturn to the square aspect of the

Moon in the zodiac, we have to bring it to Aries

27° 8' by converse motion. We therefore find the

meridian distance and semiarc of that point in

the ecliptic, the meridian distance being taken from

the lower meridian, to which it is nearest, and the

semiarc being the nocturnal arc. Find the con

stant log. due to this point of the zodiac, and add

to it the log. of the nocturnal semiarc of Saturn.

From this we derive the proportional distance of

Saturn from the lower meridian, and the difference

between this and its radical distance is the arc of

direction.

Similarly, we bring the Sun down the eastern

heavens to form the converse zodiacal conjunction

with Saturn. Here we take the meridian distance of

Pisces 17° 5', and also its semiarc. Find the con


stant log. due to these and add to it the log. of the

nocturnal semiarc of the Sun. The sum will be the

prop. log. of the Sun's meridian distance at the

conjunction, and the difference between this and the

radical distance of the Sun from the same meridian

will be the arc of direction.

The bodies of Jupiter, Mars, Mercury, Venus,

Neptune, and Uranus are brought to the zodiacal

conjunction with the ascendant conversely by the

measure of their horizontal arcs, which are derived

by subtracting the meridian distance from the

semiarc.

Thus Jupiter comes to the conjunction with the

ascendant in zodiac conversely in an arc of 9° 21',

Mars in an arc of 10° 43', Mercury in an arc of

13° 20', Venus in an arc of 39° 27', Neptune in an

arc of 41° 14', 1 and Uranus in an arc of 44° 8'.

Similarly, the Moon is brought to an opposition of

the ascendant in zodiac by an arc of 2° 30', which

is the difference between its semiarc and meridian

distance. This arc is much smaller than appears

from its longitudinal position, and is due to the

fact that the Moon has 5° of north latitude. A body

with much north latitude sets much later and rises

much sooner than does the degree of the ecliptic

it holds. This is the radical difference between the

mundane and zodiacal positions of a celestial body.

1 An ephemeris of the approximate longitude and latitude of

the planet Neptune from 1800 to 1900 a.d. is published by

Messrs Foulsham & Co. Price Is.


The Midheaven is directed to the conjunction

with these planets in the zodiac by an arc equal

to the difference of the R.A. of the Midheaven and

that of the longitude of the planet.

Thus Venus comes to the Midheaven with the

R.A. of Capricorn 5° 49', which is 276° 25', and

the difference between this and the R.A. of the

Midheaven 249° 56' =26° 29' arc of direction of

Midheaven conjunction Venus in zodiac.

Uranus comes to the Midheaven in the zodiac by

an arc of 12° 53', Neptune by an arc of 18° 17',

Venus by an arc of 26° 29' (as above), Mercury by

an arc of 46° 44', Mars by an arc of 48° 41', Jupiter

by an arc of 52° 36', and the Sun by an arc of

71° 16'. These arcs, it will be observed, differ from

the meridian distances of the several bodies as

given in the speculum by an increment which is

due to the latitudes of the various bodies. The

meridian distances in the speculum will be the

same as the measure of their directions to con

junction with the Midheaven in mundo.

We may now pass to another series of directions.

CHAPTER V

ZODIACAL AND MUNDANE PARALLELS

In astrology the parallel of declination is deemed

of the same significance and value as the conjunc

tion, but its effects are more lasting, and if formed

near the tropics, Cancer 0 or Capricorn 0, they will

last for years together and characterise a whole

period of the life.

A zodiacal parallel is formed by directing a body

to the place held by a zodiacal degree which has

the same declination as that held by a planet to

which direction is made.

Example.—The Sun at birth has 15° 13' of

declination. On the principle that all parallels

of declination, being at the same distance from

the Equator, act magnetically in unison, any

body coming to an ecliptic degree which holds the

same declination as the Sun, namely, 15° 13',

whether north or south of the Equator, will act as if

in conjunction with the Sun. Reference to the tables

will show that there are four points which have this

same declination, namely, Aquarius 18° 46', Taurus

11° 15', and Scorpio 11° 15'. Therefore, if we

.•32

ZODIACAL AND MUNDANE PAEALLELS 33

direct any body to any of these four longitudes in

the zodiac by the rules given for directions in the

zodiac, we shall bring them to parallels of the Sun

in zodiac. The process is exactly the same as if we

were directing to an aspect in the zodiac.

A mundane parallel is formed by the direction

of a body to the same distance on one side of the

meridian or horizon as that radically held by

another body on the other side of the same meridian

or horizon. These can be readily computed by

reference to their horizontal arcs.

Example.—Bring Saturn to the mundane parallel

of the Sun. The Sun's radical distance from the

horizon northwards is determined by the difference

of its meridian distance and semiarc, namely,

110° l'-108° 44' = 1° 17', and we therefore have

to bring Saturn to the same distance above the

horizon. The semiarc of Saturn is 98° 45', and its

meridian distance 81° 2' ; its horizontal arc therefore

is 17° 43'. Then say : As the semiarc Sun is to its

horizontal distance, so is the semiarc Saturn to its

proportional distance, which, being added to the

first or radical distance of Saturn from the horizon,

will give the arc of direction.

Some writers on this subject have repudiated

the parallel in mundo formed upon the horizon, but

without adequate reason being adduced in support

of their objection. Yet the same writers have not

denied the efficacy of parallels formed on the same

side of the meridian, one south and the other

3


north, as in the 4th and 9th houses, or the 11th

and 2nd, 10th and 3rd, etc., forgetting that bodies

so placed are at equivalent distances from the

horizon !

The rule for parallels is the same as for aspects.

As the semiarc of the stationary body is to its

meridian distance, so is the semiarc of the moving

body to its proportional distance, which, taken

from its primary distance, or added if it passes into

another quadrant in forming the aspect, will give

the arc of direction.

Thus we may bring Saturn to a parallel with the

Moon in mundo. The Moon here is 2° 30' from the

west horizon, and below it. If we bring Saturn

along its own arc until it reaches a proportionate

distance below the east horizon, we shall have a

mundane parallel formed on the same side of the

horizon, but on opposite sides of the meridian.

We could work this problem by reference to the

meridian distances of the two bodies from the

Nadir, and the result would be the same.

It should be observed that the Sun and Moon

are regarded as significators in the formation of

mundane parallels by the other bodies, and the

meridian and horizon therefore become sectors,

upon which the parallels are formed.

Another form of the parallel in mundo is what

is known as the rapt parallel. This is formed by

the motion of the Earth on its axis, whereby the

various bodies are carried from east to west at

ZODIACAL AND MUNDANE PARALLELS 35

their several relative distances from one another

until they come to the same distance on either side

of the meridian or horizon. In this case both

bodies move in the prime vertical at a rate pro

portionate to their relative semiarcs.

Rule.—As half the sum of their semiarcs is to

half the sum of their meridian or horizontal dis

tances, so is the semiarc of the body applying to

the angle, to its distance from that angle at the

formation of the parallel. This distance taken

from its radical distance from the same meridian

or horizon will give the arc of direction.

What we are actually doing is to bring the

meridian or horizon to the mid-distance between

the Sun and a planet, or between the Moon and

a planet. And these mid-distances are of the

greatest significance, whether in the zodiac or in

mundo. Here we are considering them only in

mundo.

Example.—Bring the Moon and Saturn to a rapt

parallel. This is formed on the lower meridian.

Semiarc, Moon (nocturnal) 52° 51'

Saturn „ 98° 45'

2)151° 36'

Half sum of semiarcs . 75° 48' prop. log. 37560




Merid. dist. of Moon . 50° 21'

„ Saturn . 81° 2'

2)131° 23'

65° 41' prop. log. 43782

Semiarc, Moon . . .52° 51' „ 53223

Proportional dist., Moon . 45° 48' „ -59444

Radical distance . 50° 21'

Moon rapt, par., Saturn = 4° 33' arc of direction.

Note.—In all cases where the Midheaven (meri

dian) and Ascendant (horizon) are employed as

sectors, the Sun and Moon are employed as signi-

ficators. They form aspects by their own apparent

motions in the prime vertical, and the planets form

aspects to the radical of the Sun and Moon by

the same motion. This is the underlying principle

of all parallels in mundo, and all rapt parallels.

Remember that in mundane directions you are

always dealing with the bodies themselves and not

their longitudes.

CHAPTER VI

ORDER OF DIRECTING

The student will do well to employ some definite

method of noting the various directions, and of

collating and tabulating his results, otherwise he

is sure to overlook some that are important when

considered in association with others that attend

them, whether they be of the same or a contrary

nature. Thus, if in a train or sequence of evil

directions there should occur a good aspect of

Jupiter to the Sun or Moon, the health and fortunes

will be greatly sustained thereby, so that what

would otherwise appear a fatal set of arcs, in the

presence of this benefic arc of direction would lose

that extreme significance, and, although sickness

might supervene, the good direction would indicate

a favourable crisis.

The following method is therefore suggested as

inclusive of all legitimate directions.

1. Mundane Directions

(a) Direct all the bodies to aspects and con

junctions with the Ascendant from east to west

and from west to east.

37


(b) Direct each of the bodies to all the aspects

and the conjunction with the Midheaven, both

ways.

(c) Direct the Sun to other bodies and their

aspects in mundo, both ways.

(d) Direct the Moon to other bodies and their

aspects in mundo, both ways.

(e) Direct each of the planets separately to

mundane aspects and conjunctions with the Sun.

(/) Do the same in regard to the Moon.

(g) Direct the Sun to mundane parallels with the

Moon and planets.

(h) Direct the Moon to mundane parallels with

the Sun and planets.

(i) Direct the Sun to rapt parallels with the

Moon and planets.

(j) Direct the Moon to rapt parallels with the

Sun and planets.

2. Zodiacal Directions

Follow the same order as for mundane directions,

omitting classes (g), (h), (i), and {j) (mundane

and rapt parallels), which are not formed in the

zodiac.

Note that in zodiacal directions a body is always

moved to a longitude to form a conjunction or

aspect, never the reverse of this. Also that the

meridian and horizon are fixed circles which do not

move in regard to any particular locality. The

Midheaven and Ascendant are those points where

OEDEE OF DIRECTING 39

the ecliptic cuts through the meridian and horizon

respectively.

All this long process of directing may appear

to be very tedious. It certainly requires patience

and method. But once done it lasts for a lifetime,

which is a point to be considered. In possession

of such a chart one may direct one's course with

wisdom and success, avoiding those dangerous

shoals, sandbanks, and breakers which occur in

the course of every life—or, if it be beyond the

power of a man so to do, he can at all events divest

evils of much of their power over him by adjusting

himself to them, making provision against times of

evil fortune and doubling his efforts when times of

prosperity are shown. Thus may a man order his

going and bring his life to a peaceful end. Sudden

death cannot overtake the man who has know

ledge of the time of that event years in advance ;

and the keen edge of many afflictions, to which an

all-wise Providence may dispose us for the greater

ends of life, are dulled by a philosophic anticipation,

so that, cutting less deeply, they leave the vital

soul of man unhurt. Therefore, rather than pray

that what is foreordained by the laws of life to

the inscrutable ends thereof may be averted, let

us rather pray with the Psalmist : " Teach me the

number of my days, that I may apply my heart

to wisdom."

CHAPTER VII

EFFECTS OF DIRECTIONS

In order to complete this section of the work, which

deals with that system of direction by semiarcs

currently practised and approved, it will be neces

sary here to indicate the general effects of directions,

so that the nature and import of events may be

known as certainly as the time at which they are

likely to transpire. I am here speaking of " effects "

of directions as if these latter had a direct dynamic

result upon the character and actions of an indivi

dual. I am disposed to classify astrologers in three

main groups—fatalists, casuists, and idealists—

according to the various views they take of the

nature and purport of astrology. The Fatalists

believe, or profess to believe, that there is a planet

ary configuration and an event which attends it.

They admit no possible intervention, amelioration,

or extenuation. Che sard sard, and that is the end

of the matter. They argue a certain necessity of

connection between character and environment as

we find it and planetary positions at the moment

of birth. As regards " directions," all of which

40

EFFECTS OF DIRECTIONS 41

are formed within a few hours of the birth, they

speak of them as " seeds sown " in the plastic

soil of the human soul which spring up and bear

fruit at the appointed time, as measured by the arc

of direction. They are born when they are born

by necessity of universal law, and they die when

they die because fatal arcs of direction are then

in force.

They speak of laws of Nature as if they were

dynamic forces against which mankind cannot

possibly contend. They forget that laws are only

mental concepts induced upon our minds by an

apprehension of the correlated successiveness of

events, and that what we know about natural laws

is an infinitesimal part of the possibly knowable.

They speak of the bodies of this microscopic solar

system of ours as if they were the be-all and end-all

of existence. They forget that the continuity of

matter is a fact only on the material plane, and

that there are forces of an immaterial nature which

transcend both matter and what we call the laws

of material existence. The moral law is an illustra

tion of this. It is spiritual in its origin and spiritual

in its effects. If astrology teaches fatalism, its

use is at an end and it becomes a suicidal science,

since there is no object in knowing that which

must inevitably take place. It would reduce man

to an automaton and divest him of all moral

responsibility.

The Casuists are those astrologers who accommo


date their facts and figures to popular concepts

by a discreet use of a melange of spurious philo

sophy. They forever quote the effete adage : " The

wise man rules his stars, the fool obeys them " ;

and that other which says : " The stars incline

but do not compel." They put a premium upon

the wisdom of experience and the will-power of a

purposeful character, and promptly consign a man

to destruction by telling him that his horoscope

indicates he has neither one nor the other. They do

not suggest to him that astrology, properly conceived

and applied, is in itself the very concrete of experi

ence, nor that the will-to-be and the will-to-do are

functions of the human soul which rise superior

to all circumstance, outlasting life itself.

The Idealists are those among astrologers who

regard the intelligible universe as the expression

of a Supreme Intelligence, who regard the planetary

combinations merely as symbols, knowing that

the causes of all effects are within man himself, the

cogniser of all experience. They regard the " signs

of the times " as the driver of a locomotive regards

the signals, not as " causes " of disaster, but as

warnings against it, an open book to those who can

read the signals, but of no value to those who

cannot. They look upon the science of astrology

as a wireless operator looks upon his code-book,

merely as a means of interpreting the signals—a

science evolved by man for the service of man.

My own view of the matter is that there is some


thing to say for the materialist side of the question,

and a great deal more for the idealistic. There is

not the shadow of doubt in my own mind as to

the material fact of the interaction of the planetary

bodies, nor as to the fact that this interaction is

registered by an intervening body of the system

only at certain angles. The Platonic dictum that

" God geometrises " is nowhere better illustrated

than in the law governing the interaction of bodies

belonging to the same system. The physical

effects of the syzygies, and especially of ecliptic

conjunctions of the luminaries, are immediately

appreciable. The law of the tides is a concrete

example of the fact of interplanetary action. We

cannot deny the dynamic effects of planetary

action on the material plane, and we have every

reason for including in this category the human

organism, compounded as it is of cosmic elements

and in direct physical relations with a material

environment. But that does not warrant us in

extending our views to include the action of physical

bodies upon the immaterial part of us, the only

part of us that is essential and distinctively human.

The only thing that can directly affect the soul of

man is the soul of another human being. There is

continuity of action upon all planes of existence

because there is a continuity of matter upon all

planes, but we have no grounds for extending the

range of action from one plane to another plane,

except it be by mediation or agency. Else we


could say that a good soul must be possessed of a

sound body, a beautiful soul of a comely body, and

that our moral principles are derived from what we

eat and drink—instead of which, what we eat and

drink depends on our moral principles. There is

sound philosophy in the words of Tennyson when

he says that " Soul to soul strikes through a finer

element of its own." It is capable of acting

mediately through the physical body or immediately

through its own essential being. These views will

doubtless alter our viewpoint in regard to much

that hitherto has been regarded as fundamental

to a belief in astrology. The effort to accommo

date the facts of astrology to the materialistic

science of a generation agone has tended to this

issue. Without in any way disposing of astrology

as a physical science, it is high time that we learned

to interpret the facts of that science in the light of

the higher spiritual teaching to which we have

access. Otherwise we shall debase the science and

enslave our own souls. In such case it were better

that our astrology had never been written. As a

physical science, astrology has an immense future

before it in this utilitarian age upon which we have

embarked ; but as a fatalistic creed it is not worth

an hour's study.

These remarks will enable the reader to under

stand why, in the following statement of the

" Effects of Directions," I have pursued the

common practice of attributing certain results or


sets of conditions as accompanying the formation

of " directions " or planetary combinations in the

horoscope subsequent to the birth. They should

not be regarded as inevitable " effects " of such

directions, but rather as things signalled, as if we

should hoist the red light to indicate " danger

ahead," the green light for " caution," and the white

light for " road clear." These signals do not

cause disasters, but our ignorance of them, our

inability to see them, or our wilful disregard of

them may very well result in a catastrophe. Human

science has harnessed many of the subtle and

intangible forces of Nature and deployed them to

the service of man. It may do the same with cosmic

forces that are as universal as etheric action

The Midheaven

This point of the horoscope stands for dignity,

influence, authority, and position, the worldly

honour and credit of the subject, and for all that

is associated with his social and communal status.

Good directions, such as the sextile and trine

of all planets, and the conjunction and parallel of

Jupiter, Venus (and Mercury when well aspected

at birth), are indications of an enhanced posi

tion, higher honours, social distinctions, increase

of prestige, etc.

Evil directions, such as the semisquare, square,

and opposition of all planets (including the Sun

and Moon in this category), and the conjunctions


and parallels of Uranus, Neptune, Saturn, and

Mars, indicate assaults upon the good name and

credit of the subject, hurt to the business affairs,

loss of position, rivalries, and unprofitable associa

tions.

The Ascendant

This point of the horoscope indicates things

personal to the subject, as health, general welfare,

comfort, environment, changes, and the common

relationships of life, that which affects him through

collective influence, the public state of affairs,

etc.

Good aspects (as above enumerated) tend to

benefit the subject by a variety of means differing

as the nature of the planet which is in aspect by

direction.

Evil aspects signal bad health, obstacles, hin

drances, incommodities, troubles and annoyances

of various kinds, according to the nature and

position of the planet directed.

The Sun,

when in a hylegliacal place (as defined by

Ptolemy), has significance of the vital constitution

and life of the subject. Generally it stands for

the father and male representatives of a family,

and for the honour, credit, and position of the sub

ject himself. It is thus associated more particularly

with the Midheaven.


The Moon

denotes the health, changes of fortune, the

mother and female representatives of the family,

the functional powers of the body, and, in its

association with the Ascendant, public bodies, the

populace, and public concerns generally.

If in a hylegliacal position, it indicates the vital

organs and life of the subject.

Note.—Ptolemy defines certain parts of the horo

scope as being vested with a vital prerogative,

wherein the Sun has precedence by day and the

Moon by night. It is a moot point whether other

bodies, being in such positions (in the absence of

the luminaries), may not be vested with the same

prerogative, and again, whether the Sun or Moon,

not radically in such a position, may become

invested with such significance by coming to a

hylegliacal place by direction after birth. Failing

either the Sun or Moon, Ptolemy invests the

Ascendant with the properties of hyleg or life-

giver. But, whatever may be concluded in this

debatable matter, it is certain that the Ascendant

is most generally affected by evil directions at the

time of a physical crisis, the afflicting planet

generally indicating the nature of its cause.

The above points in the horoscope, the Mid-

heaven, Ascendant, Sun, and Moon, are the signi-

ficators, because they signify such persons and

things in the life of the subject as are capable


of being affected by the conflict of human circum

stance.

All directions are made either (a) by the natural

motion of the significators to the places and aspects

of the planets, or (6) by the natural motions of

the planets to the places and aspects of the signi

ficators.

The triangle (trine) and parts of it are good

aspects, and indicate some advantage according

to the position and nature of the planet directed.

The cross (square) and parts of the square are evil

aspects, and indicate similar disadvantages.

CHAPTER VIII

PLANETARY INDICATORS AND THE MEASURE

OF TIME

The following definitions of planetary indications

are necessarily only partial and incomplete, but

they will serve doubtless to convey a more or less

definite idea of the nature of events which may

be expected to attend directions formed by them

with the various significators.

It should be observed that the house which a

planet directed to holds in the horoscope of birth,

or that which a planet which is directed arrives at

when the aspect is complete, has chief significance

in regard to the department of life in which the

events will transpire, the nature of those events

depending primarily on (a) the nature of the aspect

and (6) the nature of the planet involved.

In this light, therefore, it may be said that

Neptune in good aspect indicates events of a bene

ficial nature connected with the use of the faculties

or some special faculty, and frequently in connec

tion with a form of art ; benefits from unexpected

sources coming mysteriously to the subject ; unseen

49 4


and intangible influences at work for the benefit

of the subject ; brilliant flashes and inspirations of

the mind ; spiritual aid ; intuitive activity.

In evil aspect by direction it denotes chaotic

and mysterious events adverse to the interests ;

scandal, secret enmity ; undermining of the credit

by misrepresentation and fraud ; treachery, am

bush ; an involved state of affairs ; nervous leak

age and depletion of energy ; wasting of tissue ;

physical ennui and decline of the vital powers

from inscrutable causes ; apprehension, fear, and

dread of consequence ; danger of espionage ; loss

by fraudulent concerns and false investments ;

mental unrest and loss of faculty.

Uranus in good aspect denotes civic and

governmental honours, preference, advancement ;

unexpected benefits arising out of public concerns

and affairs ; ingenuity, inventiveness ; originality ;

success in mechanical and engineering business ;

strokes of good fortune coming from unexpected

sources ; new associations and alliances.

In evil aspect this planet denotes the breaking

down of existing relationships, lesions and fractures,

partings and separations, loss of a sudden and

unlooked-for nature ; hurt by strikes and public

demonstrations ; nervous lesion, paralysis ; breaks

and dislocations.

Saturn in good aspect indicates favours from

aged persons and benefits from old associations,

long investments, time contracts, and a general

PLANETARY INDICATORS 51

state of stability and steadiness in the fortunes,

congenial retirement and sequestration.

In evil aspect Saturn depletes the vital powers,

causes physical hurts by falls and contusions, morbid

diseases, colds and chills, inhibition of bodily

functions ; loss of money and property ; mental

and nervous depression ; privations, obstructions,

hindrances, and general misfortunes. Saturn is

anciently known as the Greater Infortune.

Jupiter in good aspect denotes increase of fortune,

opening up of new and lucrative opportunities,

expansion of interests, advancement, progress,

honours, confidence, good judgment, a general

feeling of expansion and well-being, both physical

and mental.

In evil aspect Jupiter denotes losses, errors of

judgment, vanity or excessive confidence, disfavour

of legal men and clericals, physical disabilities

arising from congestion and surfeit, excess or

over-indulgence, " too much of a good thing," too

much confiance en soi, and consequent loss of esteem

with others. It indicates a period of low finance,

due to lavish expenditure, severe losses, or heavy

investments. Jupiter is anciently known as the

Greater Benefic, but it is certain that its evil aspects

denote anything but a beneficial state of affairs.

Mars in good aspect denotes activity, new

enterprises, great output of energy with commensu

rate good results, travelling, the executive powers

are stimulated, and much profitable work is done.


Benefits accrue from military men, business con

nected with iron, steel, and fire. The muscular

system is strengthened and there is a disposition to

increased activity. Honours due to deeds of daring

and chivalry. Women frequently marry under this

aspect.

In evil aspect Mars denotes hurts by burns,

scalds, fire, and steel, with loss of blood, abrasions

and cuts, and also fevers and inflammatory con

ditions of the body or that part of it indicated by

the position of Mars by direction. Loss by fire or

theft, sometimes attended by violence. Sudden

alarms and disasters of various sorts. Mars was

anciently known as the Lesser Infortune.

The Sun in good aspect indicates increase of

prestige, honours and emoluments, new friends

and associations of a creditable character, general

advancement and good fortune.

In evil aspect the Sun denotes losses, disfavour

of superiors, troubles through male members of the

family, the chief, overseer, or manager of a business ;

loss by governing bodies ; ill-health due to fevers.

Reverses of various sorts according to the house in

which the direction is completed.

Venus in good aspect signifies social and domes

tic success, pleasures and enjoyments, gifts and

presents, decorations ; the young court or marry,

and the mature have children born or daughters

engaged or given in marriage, and such events

happen as cause pleasure and satisfaction. The


affectional nature is stimulated and the health

is good.

In evil aspect Venus denotes sorrows, disappoint

ments, bereavements, grief, and losses, domestic

and social troubles, and hurts associated with young

women or children. Venus was anciently known

as the Lesser Benefic, and the less one has of it when

in evil aspect the better for all concerned.

Mercury acts in terms of the planet to which at

birth it is in closest aspect ; but if not within orbs

of an aspect with any planet, then in terms of the

ruler of the sign it occupies. In good aspect it

usually signifies activity, much occupation of a

profitable nature, connected with writings, science,

and business of a general nature. Travelling,

profitable journeys, good news, gain in connec

tion with the avocation or trade. An active time

generally.

In evil aspect Mercury produces annoyances and

disturbances, evil news, worry and anxiety, many

short journeys to and fro to no purpose or profit,

sleeplessness, irregular feeding, unrest.

The Moon in good aspect denotes pleasant and

profitable changes, a change for the better in the

general state of affairs, gain by public associations

and concerns, favours from women of mature age,

popularity.

In evil aspect it denotes loss by any of the above

means, and a state of unrest both physical and

mental which leads to neglect of duties and conse


quent loss. Hurts from women. Some public

affronts may be suffered. Changes are unfortun

ate, and best avoided.

The Measure of Time

In the foregoing system of primary directions

by proportion of the semiarcs, the measure of time

is 1° = 1 year, and every 5' = 1 month.

Considerable discussion has been devoted to the

question of time measurement in directions. Those

who advocate the Arabian system of a day for a year

have sought to bring primary directions into line

with that system by equating arcs of direction made

on the foregoing principle of semiarcs, by adding

the arc to the Sun's right ascension at birth, and

then finding the day after birth at which the Sun

attains this new right ascension. The count is

made at the rate of one day for a year of life, and

two hours for every month.

Others, again, have sought to apply a plus incre

ment at the ratio of 365 to 360, seeing that the Sun

moves through 360 degrees in 365 days, which is

the same as taking the Sun's mean motion 59' 8" as

the value for 1 day= 1 year.

But it is obvious that none of these methods has

any direct application to the system we are now

concerned with, inasmuch as all the directions

formed by the diurnal rotation of the Earth on its

axis are formed within a few hours of birth so far

as they apply to a life of ordinary length, and


they are measured in degrees of right ascension—

that is to say, by the passage of the Equator under

the local meridian in the prime vertical,—and

therefore degrees of right ascension are the only

uniform basis of measurement. It certainly does

not seem consistent to measure arcs by one method

and equate them in terms of another.

It should be observed, however, that primary

directions in right ascension do not always coincide

exactly with the events they are held to signify.

Sometimes they are too short, and sometimes too

long, but never more than a few minutes either way.

Commander Morrison, R.N., was of opinion that

the event signified was delayed or accelerated by

reason of current transits in the horoscope at the

time, and he further states that the chief effects

may be expected to transpire when the lunar or

secondary directions come into accord with them.

This gives rather a wide margin of operation to the

primary direction, and has led many to the con

clusion that the secondary direction is, after all,

the important one and deserving of primary con

sideration. A very little experience will show that

it is not so, for, unless there are concurrent primaries

in operation, lunar or secondary directions fre--

quently pass with little or no result.

Primary directions and transits appear to answer

to all the more important events in life.

At the same time we have to consider the duration

of effects, and in regard to this it has been observed


that the process of formation of an arc of direction

should be considered. For the longer a direction

may be in forming, the longer will those events

endure which it signifies. Here we have Fitzroy's

old maxim again in evidence : " Long foretold,

long last : short notice, soon past."

Thus an aspect to the Ascendant formed during

the rising of a sign of short ascension such as

Aquarius, Pisces, Aries, Taurus in northern lati

tudes, and the opposite signs to these in southern

latitudes, will be speedily formed and over. On

the other hand, a similar direction formed to the

Ascendant when in a sign of long ascension will be

formed more slowly, and will dissolve more slowly.

In such case we might expect the signified event

to begin to happen earlier and to end later than in

the former case.

One finds in experience, however, that men

frequently trace years of toil and suffering to a

sudden disaster overtaking them in a moment.

In my theory of transits, this could not happen in

earlier years, but might easily occur at maturity

when the accumulated results of a man's labour

were heaped around him. (See Transits.)

The following illustrations will, however, suffi

ciently prove that there is adequate coincidence

between arcs of direction and the events they are

held to signify, to warrant the measure of time

1° = 1 year as scientifically valid.

CHAPTER IX

ILLUSTRATION

In the example horoscope given in these pages we

have a singularly interesting subject. The chief

events of the life are well defined and closely

indicated by the attendant arcs of direction.

Hundreds of horoscopes, whether pertaining to

individuals in high walks of life or of modest

position in the world, could be adduced to show

that this coincidence of direction and event is

not fortuitous, but regular and consistent, and as

dependable as any astronomical formulary. The

student will find pleasure and instruction in work

ing out the following arcs of direction in the present

instance.

John Ruskin leapt into fame and became a

" lion " in the world of art in the autumn of 1843

under the direction of

Sun sextile Midheaven mundo 24° 37'

He was married on the 19th April 1848, and, while

on his honeymoon, took a chill while sketching

in Salisbury Cathedral and was seriously ill. This

happened under the adverse directions—

57


Moon oppos. Venus mundo conv. 29° 16'

Moon square Venus mundo dir. 29° 16'

The nearness of these adverse arcs to the event of

marriage proved unfortunate for such a domestic

change. The danger of his choice of a wrong time

and a wrong partner for marriage was radically

indicated by the Moon's opposition to Mars and

Mercury, and nothing but constant bickering could

have been expected from such indications.

The first serious break in Ruskin's health was in

May 1840, for which we have the direction—

Moon oppos. Saturn zod. 21° 46'

He received honours from the University of Cam

bridge in May 1867 under the appropriate direc

tions of

Ascendant trine Venus mundo 48° 2'

Ascendant sextile Moon zod. 48° 22'

He was elected Slade Professor of Fine Art on the

10th August 1869, and commenced his course of

lectures under the following directions :

Ascendant trine Jupiter zod. 50° 35'

Midheaven par. Jupiter zod. 50° 57'

Ascendant par. Jupiter zod. 51° 14'

Moon rapt par. Jupiter . 51° 22'

In the following year his health gave way, and his

mother died in December of that year, 1871. The

arc for that year measured from 51° 53' to 52° 53',

and within these limits we have the significant

directions—

ILLUSTRATION 59

Ascendant square Saturn zod. con. 51° 59'

Moon square Mars mundo . . 52° 0'

Sun par. Uranus zod. con. . . 52° 0'

Ascendant square Jupiter mundo . 52° 41'

followed by Moon par. Mars zod. 53° 3', close upon

the death of his mother.

His health completely broke down again in 1888,

under the directions—

Sun opposition Uranus zod. . . 68° 49'

Sun opposition Uranus mundo . 69° 14'

Moon rapt par. Saturn . . .69° 30'

Here the Sun is hylegliacal, and, being so heavily

afflicted from angles of the horoscope, and the

Moon also afflicted by Saturn, only disastrous

illness and misfortune could have been signified.

Nevertheless, he survived this affliction, and

further added to his reputation as a man of letters

and exponent of fine art during some ten years,

until eventually, with declining vitality laying him

open to attack, he was afflicted by influenza and

succumbed on 20th January 1900, the arc for that

date being 80° 57'. The following significant train

of directions was then in force :

Sun par. Uranus zod. . .80° 10'

Ascendant square Saturn mundo .81° 2'

Ascendant sesquiq. Sun zod. . 81° 11'

Ascendant par. Uranus zod. . . 81° 27'

Moon square Mars zod. con. . . 81° 30'


In view of these directions, it cannot be said

that we are not duly signalled by the celestial

bodies, not only of the approach of evil times, when

more than usual care and attention are due to

health and fortunes, but also of those periods of

good fortune when the sun smiles upon all our

efforts and stimulates us to greater endeavours.

The fault is altogether ours if we do not regard

these portents. The beneficent Creator, having

established these celestial bodies " for signs and for

seasons," is ever faithful. He puts up the signals

on every occasion. It is for us to apprehend and

read them.

In King Edward VII. 's horoscope we have the

attachment which led to his marriage indicated by

Venus conjunction Moon mundo . 19° 25'

Moon conjunction Venus con. . 20° 7'

The attempt on his life by the maniac Sipido, when

as King he was travelling in Germany, measures

to an arc of 58° 25', and the appropriate direction

was—

Sun opposition Neptune zod. 58° 21'

The death of the Empress Frederick (Princess

Royal) in August 1901 was indicated by the

direction—

Midheaven conjunction Saturn 59° 43'

The death of his royal mother, Queen Victoria,

ILLUSTRATION 61

requires an arc of 59° 14', and we find the appro

priate directions—

Midheaven square Moon zod. . 58° 58'

Ascendant opposition Moon . . 59° 19'

Saturn semisq. Ascendant . . 59° 22'

Midheaven conjunction Saturn zod. 59° 42'

These illustrations will doubtless serve for all

practical purposes, and they can be worked out at

leisure by those who wish to exercise themselves

in this art.

Other methods than that here illustrated must

claim our attention, inasmuch as they have con

sistently been advocated by various authors. There

are, moreover, several points which may be con

sidered as debateable, and these also have to be

considered before our work is rendered complete.

We must therefore pass on.

CHAPTER X

PTOLEMY AND PLACIDTTS

It is generally conceded that the system of direct

ing which has so far occupied our attention first

originated as a measure of time in the mind of

Claudius Ptolemy, the famous geographer, mathe

matician and astronomer of Alexandria, who

flourished in the second century of our era, and

wrote a standard work on the subject of astrology

called in the Greek Tetrabiblos, and in the Latin

Quadripartite, being four books on the Influence

of the Stars. He also wrote the Syntaxis and

the Almagest, which, together with his work on

astrology, have been translated into every language

in Europe and into many Oriental languages

also.

From the writings of Sir Isaac Newton we have

evidence that there were many sources of informa

tion open to Ptolemy in the pursuit of astrological

knowledge, and there is no reason to suppose that

he did not avail himself of them fully, for none

has ever suggested that astrology as a science was

first promulgated by him. But it may certainly be

62

PTOLEMY AND PLACIDUS 63

affirmed that Ptolemy gave to the Western world

the first scientific exposition of the subject. There

are two Latin editions of the work and one in

Greek. The best translation that we have is the

paraphrase of Proclus from the Greek text rendered

into English with extensive commentary by J. M.

Ashmand, and recently published as a supplement to

Coming Events. Ashmand has followed the Elzevir

text, dated 1635.

The name of Claudius Ptolemy will be revived

wherever astronomy and astrology are studied. It

is enough for the purpose of this sketch to note

that he was born at Pelusium in Egypt, and

became a brilliant disciple of the Alexandrian

School. It appears that he was born about the

year 80 a.d., flourished during the reigns of Adrian

and Antoninus Pius, and died in the seventy-eighth

year of his age.

Of Placidus de Titus, who first rendered a studied

version of Ptolemy's work on astrology, we have

very little information. It appears that he was

known as Didacus Placidus, and was a native of

Bologna, became a monk, and was appointed

mathematician to the Archduke Leopold William

of Austria. He wrote in the early part of the

seventeenth century a work entitled the Primum

Mobile, in which he gives a thorough digest of the

teaching of Ptolemy. The best English transla

tion is by Cooper. Placidus showed that Ptolemy

recognised two sets of directions arising out of


two sets of planetary positions, one in the zodiac

and the other in the world, i.e. in the prime vertical.

To Placidus remains the credit of having elaborated

that part of directional astrology which has regard

to directions in mundo.

Ptolemy makes it clear in his chapter on the

" Number of the Modes of Prorogation " (bk. hi.,

ch. xiv.) that " when the vital prerogative is

vested in the Ascendant, the anareta or killing

planet may be brought to it by oblique ascension ;

and if it be vested in the Midheaven or a body there

situate, then direction is to be made by right

ascension. If on the occidental horizon, the

degrees of oblique descension are to be reckoned.

But if not in either of these three places, but in

some intermediate station, it should be observed

that ' other times ' will bring the succeeding place

to the preceding one, and not the times of ascension

or descension nor of meridian transit as already

declared.

" For, if it be desired to calculate agreeably to

nature, every process of calculation that can be

adopted must be directed to the attainment of one

object—that is to say, to ascertain in how many

equatorial times the place of the succeeding body

or degree will arrive at the position preoccupied at

the birth by the preceding body or degree, and,

as equatorial times transit equally both the

horizon and the meridian, the places in question

must be considered in regard to their proportionate


distances from both these, each equatorial degree being

taken to signify one year."

Here Ptolemy makes it clear that he directs a

body in the heavens to one that precedes it, or a

body to a degree that precedes it, which direction

is formed by the diurnal rotation of the Earth on

its axis from west to east. He also makes it clear

that he uses the proportionate distances of bodies

from both the horizon and meridian as the basis

of the calculation, and the arc of direction is

the intervening degrees (equatorial) between them,

at the rate of one equatorial degree for a year

of life.

It is evident, therefore, that he takes a proportion

of the semiarcs, or, as he calls them, " the horary

times," of the planets involved. These arcs he

describes as parallel to one another and to the

Equator, but cutting the circle of the horizon at

various degrees of obliquity.

Obviously, therefore, we have to take proportion

of their semiarcs and meridian distances, exactly

as we have been instructed in the foregoing ex

position ; and as these semiarcs are regulated by

the latitude of the place of birth and the corre

sponding ascensional differences of the planets, the

positions of the bodies will have respect to the prime

vertical and will be their apparent places in the

plane of that circle. But it is important to note

that Ptolemy says nothing concerning converse

directions, whether in mundo or in the zodiac.

5


That he recognises the mundane position of a body

as distinguished from the apparent place of its

" degree " of longitude is obvious from his men

tioning both in the same sentence ; and we dis

tinguish ourselves between the mundane and zodi

acal conjunctions only by reference to the body of

the planet in the first instance and its longitude

in the other case.

To Claudius Ptolemy, therefore, may rightly be

accorded the honour of having set astrologers upon

the right track with regard to the correct measure

of time by reference to the equatorial degrees

separating one body from another, or one body

from the longitude or aspect of another, as seen

from the place of birth.

There is little doubt, from the illustrations of

his method that Ptolemy gives, that he uses the

" ascensional " times in all cases due to the latitude

of the place of birth ; and this method serves very

well not only for directions to the Ascendant and

Descendant, but also for intermediate positions

when the planets are in the same or different

quarters and on the same side of the meridian, for

then their arcs may be measured with great facility

and approximate accuracy from the Tables of

Houses alone.

Illustration

1. Bring the Sun to the place of Mars in the

horoscope of Ruskin.


h. m.

The sidereal time on the Midheaven

when Mars' place rises is . . 15 49

That when the Sun rises is . 16 44

Difference in R.A. on the Mid-

heaven in S.T. . . 0 55

Divided by 4, this gives 13° 45' as the arc of

direction.

The same arc of direction when exactly calculated

by the semiarc method is 13° 49'.

2. Bring the Sun to the conjunction with Venus

in zodiac.

h. m.

The S.T. at sunrise (as above) is . 16 44

That when Venus' place rises is . 14 35

Difference . .29

This gives an arc of 32° 15'.

3. Bring Saturn to the place of Sun in zodiac.

The declination of Saturn is 6° 54' S.; and this

answers to the longitude of Pisces, 12° 37'.

h. m.

S.T. on Midheaven when this point

rises 17 30

S.T. on Midheaven when Sun rises . 16 44

Difference . 0 46


4. Bring the Moon to the opposition of Venus

in zodiac.


The declination of the Moon is 25° 39', which

exceeds that of any degree of the zodiac owing

to the Moon's extreme latitude north added to the

declination of its longitude. But reference to the

Tables of Ascensional Difference and Right Ascen

sion will show that its oblique descension answers

to the twelfth degree of the sign Leo, which is the

same as the oblique ascension of Aquarius 12°.

Then the arc between the place and Venus in

zodiac and Aquarius 12° will be the arc of direc

tion. Thus :

h. m.

S.T. on Midheaven when Venus long.

rises . . . . 14 35

S.T. on Midheaven when the 12th of

Aquarius rises . . . 16 30

Difference . 1 55


5. Bring the Sun to the opposition of Uranus in

zodiac.

Take the opposite degree of the zodiac to that

held by Uranus, and bring the Sun to it by oblique

arc.

h. m.

S.T. when Gemini 23° 25' rises . . 21 21

S.T. when Sun rises . . . 16 44

Difference . 4 37


6. Bring Sun to par. Uranus in zodiac direct.


The decimation of Uranus is 23° 24', which

answers to that of Cancer 4°. Find the arc be

tween this and the Sun.

h. m.

S.T. on Midheaven when Cancer 4°

rises 22 6

S.T. on Midheaven when Sun rises

in Aquarius 18° 45' . . . 16 44

Difference . 5 22


These examples will serve to show that without

recourse to the elaborations of a speculum or the

use of proportional logarithms in the computation

of proportional arcs, Ptolemy could, by the mere

use of a table of ascensions under any latitude,

find the time of an indicated event within an arc

of 30' and even less, which, having regard to the

approximations which are frequently adduced as

" arcs for the event " when both are accurately

known, show that they would serve for all practical

purposes. I most frequently calculate arcs of

direction in this manner, bringing out the results

to the nearest quarter of a degree, which measures

to three months of time. Ptolemy had constructed

such tables, as appears from his Almagest, and this

is obviously the method he used. In other words,

he recognised no other directions than those that

could be calculated by the difference of the oblique

ascensions of the planets and of their longitudes,


taking the oblique ascension of their opposite

degrees when the arc was formed by descension

of a body.

A table of oblique ascensions such as that

published by Worsdale enables the calculation to

be made with even closer exactness. It has only

to be remembered that when we are directing the

body of a planet to the body or longitude of an

other, the longitude corresponding to its declination

must be dealt with, and not the longitude of the

body itself, as the above examples will sufficiently

indicate.

CHAPTER XI

DIRECTIONS UNDER POLES

This method has been much advocated, and especi

ally by Mr R. C. Smith, the first of the almanac

writers under the pen-name of " Raphael." It con

sists in directing a significator under its own pole

instead of under the pole of the place for which

the horoscope is cast.

To find the Pole of a Planet

Take its R.A., declination, and semiarc.

Then say :

As the semiarc is to 90°,

So is its meridian distance

To the difference of its circle of position and

the meridian.

And this difference, compared with its meridian

distance, will give its ascensional difference under

its own pole.

Then having this and also its declination,

from the sine of its ascensional difference under

71


its own pole take the tangent of its declination,

and the remainder will be the tangent of its

pole.

Example.—In the horoscope of Ruskin find the

pole of the Sun.

The R.A. of Sun is 321° 12', the meridian dis

tance (below) 108° 44', the semiarc 110° 1', and

the declination 15° 13'.

Semiarc 110° 1' . . prop. log. 0-21381

Arith. comp. . 9-78619

Quadrant of 90° . . . . 0-30103

Meridian distance . 108° 44' 0-21891

Difference . 88° 57' 0-30613

Asc. diff. under pole 19° 47' log. sine 9-52951

Sun's declin. . . 15° 13' log. tang. 9-43458

Pole of Sun . . =51° 13' log. tang. 10 09493

It is thus seen that the pole is measured along

the tangent by its distance from the meridian or

nadir, according as the body may be above or below

the Earth at the time. At the meridian the pole

would be 0, and at the horizon it would be the

same as the latitude. Here " pole " is the same

as polar elevation. The difference 88° 57' in

dicates the place of the circle of position from the

DIRECTIONS UNDER POLES 73

plane of the meridian circle. Circles of position

are small circles which are parallel to the great

circle of the meridian and at right angles to the

great circle of the horizon. They are like lateral

circles of latitude in relation to which the meri

dian stands as equator and the Ascendant and De

scendant as poles. Hence, if a planet be on the

cusp of a house, it will have the same pole as that

house.

Having calculated the poles of all the planets,

and of the Sun and Moon, direction of one to

another of them is thus made.

Rule.—Take the oblique ascension (or descension,

as the case may be) of the promittor or body

directed to under the pole of significator, and the

difference of this from the oblique ascension (or

descension) of the significator under the same pole

is the arc of direction.

To find the oblique ascension of a body under

the pole of another directed to it, to the log. tang,

of its declination add the log. tang, of pole of the

body directed, and the sum will be the log. sine

of its ascensional difference under that pole. From

this its oblique ascension can be found by referring

it to its R.A. according to the rule (see "Defini

tions," Chapter I.).

Example.—Direct the Sun in the example horo

scope to the place of Venus in the zodiac.

The declination of Capricorn 5° 49' is 23° 20'.

The Sun's pole is 51° 13'. Then—


Pole of Sun, 51° 13' . . log. tang. 10 09493

Dec. Venus long. . . log. tang. 9-63484

Asc. diff. of aspect 32° 28' log. sine 9-72977

R.A. of aspect . 276° 20'

O.A. of aspect . 308° 48' under pole of Sun.

O.A. of Sun . . 340° 59' under its own pole.

Diff. . 32° 11' =arc of direction.

Applying this method to the hint I have already

given as to the use of tables of oblique ascension,

or tables of houses for various latitudes, we can

calculate this arc perfectly well with a table of the

houses for latitude 51° 13', which is the pole of the

Sun. And we can calculate all the solar arcs by

this means from the same table. Then if we find

the pole of the Moon, and refer to the Table of

Houses for equivalent latitude, we shall be able

to take out all the directions of the Moon under

its own pole. The directions of the Ascendant

will, of course, be made under the pole of the place

of birth, and those of the Midheaven by right

ascension only. So that what appears at first a

complex and exhaustive piece of work can readily

be done by tables of houses, or tables of oblique

ascension for various latitudes, in next to no time,

as the saying is. And this, I think, may be ad

judged the most popular contribution to the theory


and practice of primary directions that I have been

able to make.

Example.—Direct the Sun under its own pole to

the opposition of Uranus in the zodiac.

The Sun's pole is 51° 13'. Therefore take in

hand the Tables of Houses or the Tables of Oblique

Ascension for latitude 51° 13' N.

The opposition of Uranus falls in Gemini 23° 25'.

h. m.

S.T. on Midheaven when Gemini

23° 25' rises . . . 21 21

S.T. when Sun's place rises . 16 43

4 38

This converted into arc of R.A. = 69° 30'=arc of

direction.

Example.—Direct the Sun under its own pole to

Venus in the zodiac. Pole of Sun=51° 13'.

h. m.

S.T. on Midheaven with Sun

rising . . . . 16 43

S.T. on Midheaven with Capri

corn 5° 49' rising . . 14 35

Arc of direction, Sun conj. Venus

zodiac =difference . .28

This is equivalent to 32° 0'.

By exact calculation we found it formerly to be

32° 11'. The difference is inconsiderable from the

point of view of probable time of the event.


As to the merits and demerits of these divergent

systems of directing, I leave my readers to decide

for themselves. Experientia docet. I hold no brief

for either system, my business being merely to

represent and to simplify. This I think I may

claim to have done.

The system of directing under the semiarcs in

the prime vertical is that which was followed by

Ptolemy. The system of directing under the poles

of the planets is of considerably more recent origin,

and dates to the seventeenth century only. It

consists, as will be seen, in directing in the circle of

observation due to the pole of the significator or

planet directed. The difference is that which one

may note as between the tables of houses for one

latitude and another. Nothing is simpler or more

demonstrable. I leave it at that.

But in general practice it will be found that

equally close results may be obtained by simple

proportion and the use of the tables. Take the

following hint for what it is worth. I am quite

satisfied in my own mind that what we call primary

directions seldom or never operate exactly to time,

and if we correct the observed time of birth by

one direction for an event we shall find that sub

sequent directions are not on schedule time. We

have to allow a latitude for the operation of these

directions. Such being the case, and, in the experi

ence of the best artists, the import of primary

directions being accelerated or retarded by the


secondary directions and transits, we do not need

to observe scruples. Approximations are always

valuable.

The following may be regarded as the via Icetitia

in primary directing :—

Rule 1.—As the semiarc of the planet whose

pole is required is to 90° of the prime vertical, so

is the distance of the body in right ascension from

the meridian (upper or lower as the case may be) to

its proportional distance in the prime vertical.

Rule 2.—From the sine of their difference sub

tract the tangent of the planet's declination. The

remainder is the tangent of its pole.

Rule 3.—For all directions under the pole of

that planet or significator use the Tables of Houses

for that latitude which answers to its pole.

Rule 4.—Find the difference between the ascension

of the body (by sidereal time or right ascension

on the Midheaven) and that of the planet directed

to. This will be the arc of direction.

Note.—If the planets involved or the positions

involved are between the tenth and fourth westward,

take the ascensional degrees of the opposite places.

Rule 5.—Direct the Midheaven by right ascen

sion only, and the Ascendant by oblique ascension

under the latitude of birth. Direct the Sun under

its own pole and the Moon under its own pole.

This completes the entire scheme of primary

directing.

Example.—In the horoscope of Ruskin the Sun


was found to have a pole equal to the latitude

of 51° 13' N. (see p. 72). It must therefore be

directed under the Ascendant of 51° 13'. Similarly,

the Moon, whose pole is 47° 27', must be directed

under the latitude of that degree. A significator

on the Midheaven would thus be directed by right

ascension only, as stated by Ptolemy (see p. 64) .

For directions of the Sun to other bodies, there

fore, we use the Tables of Houses for 51° 13'.

Those for Taunton are 51° 1', which is deemed

near enough.

1. Direct the Sun to Jupiter in the horoscope.

h. m.

S.T. on Midheaven with Sun rising . 16 41

S.T. on Midheaven with Jupiter's long.

rising 15 55

Arc of direction = 11° 30', equi

valent to S.T. . . 0 46

2. Direct the Sun to Mars.

h. m.

Sun rising as before, S.T. on Midheaven 16 41

Mars rising, S.T. on Midheaven . . 15 43

Arc of direction =14° 30' . .0 58

3. Direct the Sun to Mercury in zodiac.

h. m.

Sun's rising as before . . . 16 41

Mercury's longitude rising . . . 15 39

Arc of direction = 50° 30' 1 2


4. Direct the Sun to Venus' longitude.

h. m.

Sun's rising as above . . . 16 41

Place of Venus rising . . . 14 30

Arc of direction = 32° 45' . .2 11

5. Direct the Sun to Neptune in zodiac.

h. m.


Neptune's long, rising . . . 13 59

Arc of direction =40° 30' . .2 42

6. Direct the Sun to Uranus in zodiac.

h. m.

Sun's rising as above . . . .16 41

Uranus' long, rising . . . 13 36

Arc of direction =46° 15' . .35

7. Direct the Sun to opposition of Moon in zodiac.

h. m.


Rising of Capricorn 27° 8', S.T. . . 15 47

Arc of direction = 13° 30' . .0 54

The various aspectr to these promittors can be

picked up en route as we bring the Sun from the

horizon to the Midheaven, which it reaches in an

arc of 69° 59' =70 years nearly.

We cannot direct Sun to Saturn by the diurnal

motion of the Earth, and so we must bring Saturn


up to the Sun's place. This involves knowing the

pole of Saturn.

We may also bring Saturn to the Ascendant

under its own pole. But if we were to bring the

Sun to Saturn under the Sun's pole, that would

be a prenatal direction, for the Sun cannot go back

from the position it has attained and sink below

the eastern horizon. We have therefore no alter

native but to regard these directions as invalid,

or to admit the thesis already suggested, that in

these directions, made contrary to the apparent

motion of the bodies in the heavens, we are dealing

with the locabsed impress of the planet at the

moment of birth, which impress is carried by the

Earth up the western heavens and down the eastern

heavens, so that the Sun's localised imprint is here

carried down to the place of Saturn. And this is

conformable to the theory of directions under the

poles of the significators.

CHAPTER XII

THE PART OF FORTUNE

For a considerable time there was much discussion

as to the correct method of finding the place of

the Part of Fortune. This, it should be explained,

is one of the old Arabic points, which, like the

Pomegranate, the Sword, and others, were regulated

by the distances of the several bodies from the Sun

in the zodiac, the particular point referred to being

the same distance in zodiacal degrees from the

Ascendant.

It was when astrologers came to apply this theory

to the system of primary directions in vogue that

the trouble arose as to the correct method of

computing this point.

I think that the easiest expression of the case

is this :—the Part of Fortune is a mundane point

answering to the distance of the Moon from the

Sun in the zodiac. Thus in the horoscope of

Ruskin the Moon wants 21° 38' from the opposition

of the Sun, and therefore the Part of Fortune will

be 21° 38' below the western horizon in mundo.

81 6


Its mundane position will therefore be 8° 22' inside

the 6th house.

Its meridian distance will be 68° 22', and its

pole 39° 13'. Under this pole we may direct it to

aspects in the zodiac, and in mundo. It has been

suggested that the Part of Fortune cannot be

directed, but can only receive directions from other

significators and the planets. This is surely

nonsense. Any point in the heavens having been

denned and located is carried by the motion of the

Earth on its axis from its radical place to others

successively in a direction that is contrary to the

rotation of the Earth. Hence the Part of Fortune

will here be carried down the heavens from the

6th to the 5th and from that to the 4th house

successively, forming both mundane and zodiacal

aspects under its own pole. The pole of the Part

of Fortune and that of Saturn being near to one

another, they must be near a mundane parallel,

on the same side of the horizon.

There are, however, other suggested methods of

taking the place of the Part of Fortune.

Ptolemy says (bk. iii., ch. xii.) : " The Part of

Fortune is ascertained by computing the number

of degrees between the Sun and Moon, and it is

placed at an equal number of degrees from the

Ascendant in the order of the signs. It is in all

cases, both by day and night, to be computed and

set down, that the Moon may hold with it the

same relation as that which the Sun may hold with

THE PART OP FORTUNE 83

the Ascendant ; and it thus becomes, as it were,

a lunar horoscope or Ascendant."

It is therefore clear that Ptolemy intended

degrees of oblique ascension or descension, and not

merely degrees in the zodiac, the relations of which,

in regard to the horizon of any place, are continually

changing.

Thus in the horoscope of Ruskin we have—

O.A. of Sun . . 341° 13'

O.D. of Moon 157° 26'

add 180° 0' 337° 26'

3° 47' Moon to oppos. Sun.

O.D. of 7th . . 159° 56'

156° 9' O.D. of Part of

Fortune.

This gives us a position answering to the 10th

degree of Leo, and therefore close to the Moon.

Placidus says : " Let the Sun's oblique ascension

taken in the Ascendant be subtracted always from

the oblique ascension of the Ascendant, as well in

the day as in the night, and the remaining difference

be added to the Moon's right ascension ; the sum

will be the right ascension of the Part of Fortune,

which will have the Moon's declination."

In the example horoscope the oblique ascension

of the Ascendant is 339° 56', from which take the

Sun's oblique ascension 341° 13' (adding 360 for

subtraction), and the remainder is 358° 43', which


add to the right ascension of the Moon 120° 17',

and the sum is the right ascension of the Part of

Fortune 119° 0'.

The right ascension of the imum cadi being

69° 56', the meridian distance of the Part of Fortune

-will be 49° 4', and its semiarc will be that of the Moon,

52° 51', as it has the same declination as the Moon

in all cases. Then semiarc 52° 51' -49° 4' = 3° 47',

which is the same as we derived from the method

of Ptolemy. For there we found the oblique

descension of the Part of Fortune to be 156° 9';

and the oblique descension of the 7th being 159° 56',

the difference is 3° 47'.

The method of Placidus appears preferable in

that we derive at once the right ascension and

meridian distance of the Part of Fortune.

The question is, however, whether either is true,

and only directions made by the position as thus

derived can settle the point in debate.

To enable the student to at once work out the

primary arcs, we here append the speculum in the

example horoscope

R.A. Ner. Dist. Semiarc. Horiz. Arc. Cusp. Dist.

119° 0' 49° 4' 52° 61' 3° 47' 3° 47'

These elements at once suggest that the pole

of the Part of Fortune can be found, and direc

tion made by the Part of Fortune in mundo and

THE PART OF FORTUNE 85

zodiac to the planets, just as if it were a definite

body.

The fact that it is merely a symbol, a point in

space, does not in the least invalidate its significance

in human affairs, as some impulsive students have

suggested. For what else are the degrees of the

zodiac known as the Midheaven and Ascendant ?

They are points in space which bear a definite

relationship to a particular place at a given time.

They do not need to be identified with a star in

the heavens in order to obtain a significance in the

horoscope. Every tyro in astrology knows as an

absolute fact that these points have a very demon

strable significance in a horoscope, and that transits

of the major planets over these points, and the

passing of these points by planets in direction, are

attended by events which leave no shadow of doubt

that they are an essential part of the signalling

apparatus by which we are forewarned of coming

events. And if these, why not the Part of Fortune ?

Call it a " myth " if you like, but understand that

a myth is a " veil " designed to hide a truth which

a symbol is said to embody. The symbol handed

down to us is identical with that used in China

and also in Egypt to indicate " land, territory,

a field."

CHAPTER XIII

LUNAR PARALLAX AND SEMI-DIAMETER

Among the problems modernly confronting the

student of directional astrology, that of the hori

zontal parallax of the Moon is perhaps one of the

most important and at the same time most per

plexing.

The places of the planets as indicated in the

horoscope are the geocentric longitudes. They are

computed from the standpoint of an observer.

But as the place of observation is on the surface

of the Earth and not at its centre, the observed

position of the Moon will not exactly coincide with

its computed geocentric longitude. In the case

of the Sun and planets, the distances from the

Earth are so great as to render the parallax in

considerable, that of the Sun being only 9", and

the parallaxes of other bodies beyond it being

proportionately less. But in regard to the Moon,

its nearness to the Earth renders its parallax of

importance if we are to regard the Moon as affecting

us by its direct ray. The nearer the Earth it may

be, the greater is the angle of parallax. It is

86

LUNAR PARALLAX AND SEMI-DIAMETER 87

therefore greatest at the perigee and least at the

apogee of the Moon.

As the amount of parallax depends on the Moon's

place in its orbit, we make use of the apogee as a

point of departure, and the Moon's distance from

that point in its orbit where it is furthest from

the Earth is called its anomaly.

By comparing the calculated place with the ob

served place it has been found that the difference

of the two at the apogee is 53' 53", and at perigee

61' 23". It will be sufficient for our purpose if we

call these 54' and 61' respectively. By the use of

the " Ready Reckoner " the amount of the anomaly

can always be found for any date or hour, and the

corresponding parallax is set against it. The table

is here repeated for convenience.

[Table

88 DIRECTIONAL ASTROLOGY"

Table op Anomaly.

Epoch 1800, Jan. Qi 0h 0m=98 20° 20'.

Years. Add Days. Add. Anom. Hor. Par.

• 0 • 0 i O

1 2 28 43 1 0 13 4 0 0 54

2 6 27 27 2 0 26 8 6 55

3 8 26 10 3 1 9 12 12 55

4 0 7 67 4 1 22 16 18 55

6 3 6 40 5 2 5 19 24 55

8 6 0 24 6 2 18 23 1 0 55

7 6 4 7 7 3 1 27 6 55

8 0 I5 64 8 3 14 31 12 65

9 3 14 38 9 3 27 36 18 55

10 6 13 21 10 4 10 39 24 56

20 1 9 46 11 4 23 43 2 0 56

40 2 19 32 12 5 6 47 6 56

50 0 2 63 13 6 19 51 12 56

60 3 29 18 14 6 2 66 18 57

70 10 12 39 16 6 16 58 24 57

80 5 9 3 16 6 29 2 3 0 67

90 11 22 24 17 7 12 6 6 58

100 6 18 49 18 7 26 10 12 58

Months. Add 19 8 8 14 18 59

20 9 21 18 24 59

January 0 0 0 21 9 4 22 4 0 59

February 1 16 1 22 9 17 26 6 69

March . j 60

April . 3 6 61 23 10 0 30 12 60

May . 4 7 48 24 10 13 34 18 60

June 0 22 49 25 10 26 37 24 60

July . 6 24 46

26 11 9 41 o 60

August 8 9 47 27 11 22 45 6 60

September . 9 24 48 28 0 5 49 12 60

October 10 26 46 29 0 18 63 18 61

November . 0 11 46 30 1 1 67 24 61

December 1 13 42 31 1 16 1 6 0 61


Example.—Find the Moon's anomaly for 8th

February 1819, and the corresponding horizontal

parallax.

8 O '

Epoch 1800 . . . 9 20 20

Add 19 . . 9 27 59

February . . . 1 15 1

8 days . . . . 3 14 31

Anomaly=0 17 51

The Moon is therefore within 18° of its apogee or

furthest distance from the Earth, and its parallax

will therefore be near its minimum. Our table

shows that the parallax due to this anomaly is 55'.

This would be the difference between the Moon's

geocentric longitude and its observed position

from the surface of the Earth if it were exactly

on the horizon. At the meridian the parallax is 0,

and at the horizon it differs, as stated, from 54' to

61' according to the distance of the Moon from the

Earth, i.e. its place in its orbit.

Now, as the horizon is at all points 90° from the

zenith or nadir, we can make one of these the

apex of a triangle, of which the zenith distance of

the Moon at transit is the perpendicular and the

base its meridian distance. From these we may

find the hypotenuse, which will be the Moon's

zenith distance at the time of birth.

Thus, in the example horoscope the latitude of

the place is 51° 30' N., and the Moon has latitude


5° 1' N., which therefore must be subtracted,

leaving 46° 29' as the zenith distance of the Moon

at transit of the nadir. Its meridian distance is

found from the speculum to be 50° 21'. Then

Log. cosine 50° 21'. . 9-80489

Log. cosine 46° 29'. . 9-83794

Log. cosine 63° 52'. . 9-64283

And as 90° is to 55', so is 63° 52' to 39', which is

the Moon's parallax, and by which amount she is

apparently depressed further below the horizon

than she is computed to be. This will affect its

meridian distance, etc. The directions of the

Moon, if operating dynamically by right lines of

energy upon any part of the Earth instead of via

the centre of the Earth, will hence be affected ; and

it remains a problem worth some close study and

consideration as to what view ought to be taken.

It is sufficient here to have indicated the method

of calculation. It is one of the factors in the

vexed problem of " the uncertain Moon," which

has frequently been charged with an inconstancy

altogether absent from the directions of the Sun

and planets.

The semi-diameters of the Sun and Moon have

often been resorted to in order to accommodate a

directional arc to the date of an event. Allowing,

as is undoubtedly the case, that primary directions

have an orb of influence within the limits of which


it may be said they begin to operate, attain their

maximum, and pass off, there yet remains the fact

that one would naturally expect the maximum to

coincide with the most marked phase of a crisis in

the life. This appears to be acknowledged, inas

much as practitioners in the art of directing make

use of arcs of direction, measured from the centres

of bodies as determined by their longitudes, in order

to correct approximate times of birth. This cor

rection can only be legitimately made on the

supposition that arcs of direction are close, if not

exact, to the time of the events they are held to

signify.

And unless there were this fundamental integrity

of the system of direction advocated, unless there

was a close agreement throughout a life between

the arcs of direction and the events portrayed,

there would be no use in making the calculations.

Our longitudes are geocentric and apply to the

apparent centre of the bodies. The apparent

diameter of the larger planets, on account of their

great distance from the Earth, is inconsiderable.

But when we come to the Sun and Moon, which

are the chief significators, and the bodies that are

directed to form the aspects of the promittors, we

are concerned with orbs that have a visible diameter.

The Sun on account of its immense size, and the

Moon on account of its close proximity, appear to

have a diameter of about half a degree, or from the

centre to the limb about 15'. This becomes an


important consideration when we are directing

either of them to the aspect or conjunction of one

of the planets, inasmuch as from first to last

contact of the disc of the luminary with the said

planet or aspect there will be an included arc of

half a degree, and this means six months of time

according to the Ptolemaic measure of 1° = 1 year.

Hence it may well be that a direction is increscent

for three months before it attains its actual cen-

trality and maximum strength, and another three

months may transpire before the effects wear off.

And if to this we add the fact that directions

formed at the tropics, i.e. near Cancer or Capricorn

0, are very slow in formation (as may be seen

from the Tables of Declination), 4° of longitude

including only 1' of declination, it will readily be

understood that there is ample room for " latitude "

in the timing of events.

It seems desirable, therefore, that a few cases

of very well-observed birth-times should be taken,

and the arcs of direction computed very closely ;

and then that these arcs should be compared with

the course of events, so that an estimate of the value

of the semi-diameters of the Sun and Moon may

be made.

The apparent semi-diameter of the Moon is

controlled by the same factor as the parallax,

namely, its place in the orbit and consequent

distance from the Earth. It may be useful to

mention that the semi-diameter of the Moon is


approximately twenty-seven one-hundredths of

the parallax. Therefore multiply the parallax by

27 and divide by 100. Thus, when the parallax is

54', the semi-diameter of the Moon is 54 x 27 -f 100

=14$', and when the parallax is 60, the semi-

diameter is 60 x 27 -f 100 = 16'.

The Moon directed to the opposition of the

Ascendant in the example horoscope works out at

2° 30' ; but as the horizontal parallax of the Moon

is 55', its semi-diameter will be nearly 15', and

therefore the direction would read :

Asc. oppos. Moon in mundo, first contact 2° 15'

middle 2° 30'

„ „ last contact 2° 45'

thus giving a possible range of 30', or six months for

the duration of this indication. This may help

to account for the variability that has been noticed

in regard to lunar directions, and possibly we may

also have to consider taking the parallax into

account. The solar directions will be affected by

semi-diameter of the Sun, but not appreciably by

parallax.

CHAPTER XIV

LUNAR EQUATIONS

Under this head I propose to examine a problem

of some interest which appears to have escaped

general recognition, but which may very well be

considered with the questions of parallax and semi-

diameter as having some connection with the noted

irregularity of primary lunar directions.

Take an illustration from the horoscope already

submitted. We would direct the Moon to conjunc

tion with the nadir, which direction is known as

" Midheaven opposition Moon in mundo." It is

measured by the arc of the Moon's meridian dis

tance, 50° 21', and is formed by the rotation of

the Earth on its axis, by which the Moon is carried

down the western heavens until it makes its

meridian transit.

The theory underlying this direction is that there

is a permanent significance and value attaching

to the radical positions of the Midheaven, Ascen

dant, and other significators, which is unaffected by

the subsequent changes taking place amongst the

planets, either on account of their apparent motions

94

LUNAR EQUATIONS 95

in the heavens or their real motions in the zodiac.

But we have now to consider whether there may

not be some value attaching to these subsequent

motions of the bodies in the zodiac. These motions,

within the narrow limits of time comprised in the

formation of directions in a life of ordinary length,

would not be appreciable in the case of the planets

or the Sun, but in the case of the Moon there would

be a quite appreciable increment owing to the

velocity of that body in its orbit.

Thus the arc of 50° 21' cited above would occupy

the interval of 3 hours 25 minutes, during which

the Moon will have increased its longitude by

about 1° 42', so that it would not actually make

the meridian transit for another 7 minutes, although

its radical place would then be exactly on the nadir.

Its right ascension will be increased by about the

same amount, and therefore the actual arc of

direction from the time of birth until the bodily

transit of the nadir would be about 52° 3'. So far

as this case is concerned it is worthy of notice

that this arc of the second distance of the Moon

to the opposition of the Midheaven, and therefore

to the mundane square of the Ascendant, coincided

exactly with a period of serious illness and trouble

in the life of Ruskin, whereas the arc M.C. opposi

tion Moon in mundo, 50° 21', exactly coincided

with the election of Ruskin to the Slade Professor

ship of Fine Art, a distinction which brought him

into the highest position in his sphere of life.


Obviously, therefore, the second distance of the

Moon is by far the most appropriate.

Let us look at another direction from the same

point of view. Direct the Moon under its own

pole to the opposition of Saturn.

The Moon's pole is 47° 27', and its

ascensional difference under that

pole, derived in the process of find

ing the pole, is 31° 32'

Its right ascension 120° 17'

Its oblique descension under its pole . 151° 49'

Add 180° 0'

Oblique ascension of opposition Moon =331° 49'

Then for Saturn's oblique ascension under the

same pole—

Pole of Moon

tang. . . 10 03712

Tang. Saturn's

decl. . . 9 08283

Ascl.diff. Saturn

sine . . 9- 11995= 7° 31'

R.A. of Saturn . . 348° 54'

OA. of Saturn . . 356° 25' under Moon's

pole.

O.A. of Moon's oppos. . 331° 49'

Arc. of Moon oppos. Saturn= 24° 36'

LUNAR EQUATIONS 97

This corresponds with Ruskin's leap into public

estimation and fame, for which we have the arc of

direction Sun sextile Midheaven in mundo. Most

certainly the Moon to opposition Saturn could not be

regarded as in the least degree akin to the nature of

events then current in the life of the great artist.

But this arc took lh. 38m. 24s. to complete, and

during that time the Moon had increased its R.A.

by some 49' ; and as we are bringing Saturn up to

the opposition of the Moon under the pole of the

Moon, we shall have to curtail the direction by

49', which results in an arc of 23° 47'. This is

nearly a year in advance of Ruskin's great advent,

and may very well have coincided with a period

of stress and indisposition.

The Moon to the opposition of Venus comes into

force at about thirty years of age, or in the thirtieth

year of life, when he married ; but by adding the

increment due to the time of direction to the radical

place of the Moon we get an arc which falls out a

whole year later, when it is certain Ruskin realised

his disappointment.

The directions of the Sun during the course of

sixty years would only be affected by an increment

of 10', and they can always be relied upon ; but

the directions of the Moon are at present very

unsatisfactory, and it has been thought that this

question of second distances may serve not only

to indicate why lunar primary directions are in

constant, but why also they appear to have a more

7


durable influence than those of the Sun. The

suggestion is that from the time the direction is

formed to the radical position of the Moon to the

time that it is formed to the actual position of that

body in the heavens, may be the extent of its dura

tion ; and during this period, which naturally in

creases in length as the age increases, transits and

other secondary indications may come up repeatedly

to reinforce the portents of the lunar direction and

bring them into play. Certain it is that there are

many conditions affecting the directions of the Moon

which arise out of its velocity, and to maintain its

ancient reputation for inconstancy and fickleness

it appears to have jealously guarded its secret even

from the lynx eye of the practical astrologer.

Whether we have succeeded in compassing the

fickle goddess by this exposition remains to be

decided by constant experiment conducted by

several independent workers. In the cause of a

scientific astrology this is worth carrying out, and

it is to be hoped that qualified and unprejudiced

students will communicate their experience.

It may assist the average student to know that

all directions of the Moon to succeedent places will

fall out sooner, while those to precedent places will

fall out later, than indicated by the radical or first

distance of the Moon, and the arc of direction must

therefore be increased or decreased at the rate of

2' for every degree of the arc of direction. Thus an

arc of 39° 15' requires 1° 18J'.

CHAPTER XV

CTJSPAL DISTANCES

When giving instructions as to the method of

directing bodies to aspects of the Ascendant and

Midheaven in mundo, it is customary to affirm that

one-third of a planet's semiarc is equal to a house-

space, so that a planet that is one-third of its semi-

arc above the horizon is held to be on the cusp

of the 12th house, and when two-thirds of its

semiarc above the horizon it is on the cusp of the

11th. But if this were actually the case, we

should find that when on the cusp of a house the

oblique ascension of an ascending planet is the

same as the oblique ascension of the cusp of that

house. Such is not the case.

Example.—Direct the Sun in Ruskin's horoscope

to the sextile of the Midheaven in mundo. This

aspect falls on the cusp of the 12th house.

The semiarc diurnal of the Sun is 69° 59', and

one-third of this is 23° 20', to which add the Sun's

distance under the horizon, 1° 17', and we get the

arc of direction = 24° 37'. The Sun is then on the

cusp of the 12th house presumably. Let us see.

90


The R.A. of the Midheaven is 249° 56', to which

if we add 60 we shall have the oblique ascension

of the cusp of the 12th house, 309° 56'. Now,

when the R.A. of the Midheaven is increased by

an arc of 24° 37', the oblique ascension of the cusp

of the 12th will be increased by the same amount,

and will then be 334° 33', while the oblique ascen

sion of the Sun is 341° 13'. Wherein lies the

error ?

It lies in the fact that we are directing the Sun

under the pole of the Ascendant, whereas we should

direct it under the pole of the 12th house cusp.

I here give a table of the polar elevation due to

the various houses in several latitudes, from which,

by proportion of their parts, we may derive the

pole of any house for any minute of the included

latitudes.

Poles of Houses.

Lat. Cusps of 3, 5, 9, 11. Cusps of .2, 6, 8, 12.

0 0 / o /45 18 57 34 11

46 19 37 35 10

47 20 19 36 10

48 21 2 37 10

49 21 46 38 12

50 22 33 39 15

51 23 21 40 16

52 24 12 41 24

53 25 5 42 31

54 26 1 43 39

55 26 59 44 48

CUSPAL DISTANCES 101

The pole of the 12th house for the latitude

51° 30' N. is seen to be 40° 51', and if we direct the

Sun under this pole we shall have the

Ascensional difference of Sun

under pole of 12th . . 13° 36'

Right ascension of Sun . . 321° 12'

Oblique ascension of Sun under

pole of 12th . . 334° 48'

Oblique ascension of cusp of the

12th house.... 309° 56'

Arc of direction . . 24° 52'

This, although not exact, is certainly nearer, and

seems to justify the method of directing under the

poles of planets.

The fact, however, is that if we take a fixed pole

for any house in a given latitude we shall always

be in some degree of error, and for the simple reason

that the semiarcs of the planets, being parallel to

the equator, do not lie in the same plane as the

prime vertical, which is the circle we divide into

twelve equal parts to form the houses of the heavens.

Therefore an equal division of the prime vertical

will not result in an equal division of the semiarcs,

and either we have to consider the poles of the

houses as movable, or, as seems more consistent

with the facts, we must regard the house-spaces

as unequal. In other words, we shall find that the


time (measured by degrees of R.A.) that the Sun

remains in successive houses is unequal, and the

same is to be said of any other body. When,

therefore, we take one-third of the semiarc of a

planet as equal to one house-space, we are indulging

in a free use of the metaphysical concept that " all

circles are equal to one another," as defined by the

doctrine of Correspondences. Against this I have

nothing to say except that it is not mathematics.

Now, just as we take the Sun's oblique ascension

under the pole of the Ascendant in order to find

its distance from the horizon, so we must take

its oblique ascension under the pole of the 12th

house in order to find its distance from the cusp

of the 12th, and its oblique ascension under the

pole of the 11th to find its distance from the

cusp of the 11th. Its right distance from the cusp

of the 10th will be its arc to that cusp, since the

meridian has no polar elevation. Thus :

The pole of the Ascendant is . 51° 30'

The pole of the 12th house . . 40° 51'

The pole of the 11th house . . 23° 46'

The Sun's declination is 15° 13', log. tang. 9-64380,

and if to this we add the tangent of the poles

of the houses successively we shall have the sine

of the ascensional differences of the Sun under

these poles, which, added to its right ascension,

will give its oblique ascension under those poles.

These are :


O.A. of Sun under pole of 1st house . 341° 13'

O.A. of Sun under pole of 12th house 334° 48'

O.A. of Sun under pole of 11th house 327° 59'

R.A. of Sun under pole of 10th house 321° 12'

Then, to find the arc of direction between the

Sun and any of these cusps, we merely subtract

the oblique ascension of the one from the other.

The oblique ascensions of the cusps are :

Of the Ascendant . . 339° 56'

Of the 12th . . . 309° 56'

Of the 11th . . . 279° 56'

Of the Midheaven R.A. 249° 56'

Thus we have the following true arcs of direction

of the Sun in mundo :

O.A. Sun under pole of Ascendant . 341° 13'

O.A. of the Ascendant . . . 339° 56'

Arc of Sun to conjunction Ascendant 1° 17'

O.A. of Sun under pole of 12th . 334° 48'

O.A. of 12th house cusp 309° 56'

Arc of Sun to sextile Midheaven mundo 24° 52'

O.A. of Sun under pole of 11th . 327° 59'

O.A. of cusp of 11th .... 279° 56'

Arc of Sun to sextile Ascendant mundo 48° 3'

R.A. of Sun under Meridian 321° 12'

R.A. of Midheaven .... 249° 56'

71° 16'


And in all these cases the Sun will have the same

oblique ascension as the cusp of the house to

which it is directed, at the time of direction being

completed. This is what we argue for and obtain.

Also we may find the degrees of R.A. which pass

under the meridian while the Sun passes from the

cusp of one house to the next, and thus the house-

space of the Sun at its present declination.

As the whole diurnal arc of the Sun is less than

90, the house-space will be less than 30°.

Subtract the arc of direction of Sun conjunct

Ascendant from the arc of direction Sun conjunct

12th =Sun sextile Midheaven. There remains 23°

35', the house-space of 12th house.

Subtract the direction of the Sun to the 12th

from that to the 11th; there remains 23° 11', the

house-space of the Sun in the 11th. Subtract

the arc of direction Sun cusp of the 11th from the

Sun conjunct Midheaven ; there remains 23° 13',

the house-space of the Sun in the 10th.

And the three house-spaces added together=

69° 59', which is the diurnal semiarc of the Sun.

Hence it appears that the mundane directions

of planets must be taken in terms of the pole of

the cusp to which they are directed. The cuspal

distances of the planets must also be measured

according to the same rule. This will affect all

directions calculated by primary arcs on the semi-

arc method now commonly in vogue.

But what appears of most vital importance as


a legitimate conclusion drawn from this critique is

that the correct method of directing to any body

is by oblique ascension under the pole of that body,

which is quite different from taking the direction

under the pole of the body directed. At the same

time, it appears to dispose of the semiarc method,

except as a valuable approximation. For nothing

can be more certain than that the cusps of the

houses, measured in the prime vertical, are 30°

distant from one another by oblique ascension.

These conclusions agree entirely with our mathe

matics, for we have seen that the house-space of

the Sun in the 12th, due to its declination, is 23° 35' ;

and if to this we add the Sun's direction (from

below) to the Ascendant= 1° 17', we have an arc

of direction, Sun to conjunction cusp of 12th =

Midheaven sextile Sun in mundo, 24° 52', which is

exactly what we found the direction of the Sun

to be by oblique ascension when taken under the

pole of the 12th house.

This proves, if anything can, not only that the

correct method of directing is under the pole

of the planet or position directed to, but also that

the house-spaces are variable and depend on the

several declinations of the planets, and thus on

their oblique ascensions and descensions, taken

under the poles of the successive houses.

By the semiarc method, taking one-third of a

semiarc as equal to a house-space, we are deal

ing with an approximation which, although useful


and facile, is not mathematically correct. Rather

than that bad habits should become popular, I

have undertaken a somewhat lengthy demonstration

of this point, which I consider to be now settled

beyond further debate.

CHAPTER XVI

SUGGESTED METHOD OF TRUE DIRECTING

As the result of this examination of the various

methods of directing, both by semiarc proportions

and by oblique ascensions under the poles, we may

come to the conclusion that all the disparities

which vitiate the present methods can be disposed

of if we proceed along the lines to which our con

clusions point. For this purpose we shall require

a speculum containing :

1. The right ascension of a planet.

2. Its declination.

3. Its pole.

4. Its ascensional difference under its own

pole.

The first of these will, of course, be worked as usual.

The declination will be that given in the ephemeris.

The pole of the planet will be that derived in the

usual way from the ascensional difference of its

proportional place in the prime vertical taken under

its own declination, as already shown. Its cuspal

distance will be the difference between its oblique

107


ascension (or descension) taken under the pole of

the cusp to which it is nearest and the oblique

ascension of the cusp in the prime vertical. These

are all the elements required for a complete cal

culation of all legitimate arcs of direction.

Directions must be made under the pole of the

body to which we are directing another. The pole

is the same as geographical latitude. It represents

the latitude (geographical) or polar elevation (astro

nomical) at which the cusp of the house cuts into

the circle of the prime vertical, or at which a circle

of position cuts into it.

Thus in the following diagram let the great

circle NZHS, etc., be the sphere of the Earth, of

which N is the north pole, S the south pole. Also

let ZN be the great circle of the prime vertical at

an elevation from the Equator of 51° 30' N., and

H-H the horizon intersecting it at right angles.

Then HNZH will be the upper meridian and

HSNH will be the lower meridian, the points Z and

N marking the zenith and the nadir. The cusps of

the 10th, 11th, and 12th houses are shown by the

great circles cutting through the prime vertical

at different elevations, and these answer exactly

to the geographical latitudes (north) of the same

values. Thus the pole of the Ascendant is 51° 30',

that of the 12th, 40° 51', that of the 11th, 23° 46',

and that of the 10th, 0° 0', as shown in the diagram,

the ascensional difference being the arc in R.A.

between N-S and H-H.

SUGGESTED METHOD OF TRUE DIRECTING 109

A circle of position is thus seen to be one which

passes through a body and converges upon the

N

S

horizon north and south exactly like an inter

mediate cusp of a house.

Rules for Directing

Rule 1.—Find the pole of the body or ecliptic

position to which direction is to be made. Find

the ascensional difference under this pole of the

body to be directed. Apply this ascensional

difference to the right ascension of the body to

be directed, and obtain its oblique ascension (or

descension, as the case may require) under the


pole of the body to which direction is made. The

difference between this and the oblique ascension

of the body to which direction is made, taken under

its own pole, will be the arc of direction.

Rule 2.—In mundane directions take the body

of the promittor, i.e. body directed to. In zodiacal

directions take its longitude.

Rule 3.—In directing to the aspect of a planet

in mundo, its cuspal distance taken under its own

pole must be directed to under the same pole.

This rule also serves for mundane parallels.

Here is the Speculum required for Ruskin's

horoscope.

Speculum

Planet. R.A. Declin. Pole. Ascen. Diff.

0 / O 4 o /

Sun . 321 12 15 13 51 13

10-09493

19 47

9-43458

Moon 120 17 25 39

9-68142

50 21

10-08147

35 24

Mercury 296 47 21 34 44 55 23 13

9-69688 9-99885

Venus 276 6 18 10

9-51606

27 13

9-71125

9 43

Mars . 299 6 21 45

9-60013

46 22

10-02066

24 44

Jupiter 302 37 20 26 47 13 23 44

9-57119 10-03355

Saturn 348 54 6 54

9-08283

45 56 •

10-01423

7 11

Uranus 262 49 23 24

9-63623

3 13

8-74904

7 27

Neptune 267 47 22 14 3 48 9 20

9-61148 8-82147

SUGGESTED METHOD OP TRUE DIRECTING 111

Examples

Direct the Sun in mundo to the conjunction

with Venus mundo. The pole of Venus is 27° 13',

its ascensional difference under that pole is 9° 43',

which added to its R.A., 276° 6' (as Venus' declina

tion is S.), gives its oblique ascension under its

own pole =285° 49'.

The oblique ascension of Sun under the same

pole is—

Pole, log. tang. . 27° 13' 9-71125

Decl., log. tang. . 15° 13' 9-43458

Asc. diff. log. sine 8° 2' 9-14583

R.A. of Sun . 321° 12'

O.A. of Sun . 329° 14' under Venus' pole.

O.A. Venus . 285° 49'

Arc of direction = 43° 25' Sun conj. Venus in mun.

Note.—All the tangents being inserted in the

speculum under the declinations and poles of the

planets, they can be extracted as required.

Direct Uranus to the conjunction with the Moon

in mundo.

The pole of the Moon is 50° 21', its ascensional

difference under that pole is 35° 24', and its oblique

descension 155° 41'.


The declin. of Uranus

Pole of Moon

Asc. diff. under pole

Uranus' R.A. .

is 23° 24' tan. 9-63623

. 50° 21' tan. 0-08147

. 31° 28' sine 9-71770

. 262° 49'

O.D.Uranus . . 231° 21' underMoon'spole.

O.D. of Moon. . 155° 41' „

Arc of direction= 75° 40' Uranusconj. Moon

in mundo.

These directions take very much less time to

calculate than to set out in writing, and with the

speculum at hand they are readily figured out in a

minute or two.

Direct the Moon to opposition of Venus in

mundo.

Oblique descension of the opposition of Venus

= 105° 49'.

This is taken under the pole of Venus, from

Venus' oblique ascension less 180°=oblique ascen

sion of the opposite point.

Oblique descension of Moon under Venus'

pole 134° 37'

Oblique descension of Venus under same

pole 105° 49'

Arc of Direction, Moon oppos. Venus

mundo 28° 48'


These examples will doubtless serve for all

conjunctions in mundo. For zodiacal directions

it will be necessary to find the declination of the

degree of the ecliptic held by a planet to which

direction is made, or of its aspect, and add the log.

tang, of this declination to the log. tang, of its

pole. This will give the ascensional difference

under that pole. Apply this to the right ascension

to get its oblique ascension or oblique descension

under that pole. The difference between this and

the oblique ascension (or descension) of the planet

directed, taken under the same pole, will be the arc

of direction.

Planets having the same pole are either in mun

dane conjunction or in mundane parallel. This

gives us the hint as to the calculation of mundane

parallels.

Find the oblique ascension or oblique descension

of the planet on which the parallel is formed, taken

under its own pole. Find the oblique ascension

or oblique descension (as the case may require)

of the planet forming the parallel, under the

same pole. The difference will be the arc of

direction.

Example 1. — Bring Saturn in the example

horoscope to the mundane parallel of the

Moon.

This direction is formed by Saturn coming up

to the pole of the Moon on the other side of the

meridian.

8


249° 56'

155° 45'

94'

249'

11'

56'

Right ascension of the Midheaven

Oblique descension of Moon under

its own pole

Moon's distance from Midheaven

westward ....

Added to R.A. of M.C.

Oblique ascension of the parallel,

eastward 344° 7'

Oblique ascension of Saturn under

Moon's pole .... 357° 18'

Arc of direction =difference . 13° 11'

This arc of direction, when computed by the

semiarc method, is seen to be 8' short of the actual

figures, which throws the time out nearly two

months. The arc by that method is 13° 3' as

compared with 13° 11', the true arc.

Example 2.—Bring Uranus to the mundane

parallel of Sun in mundo. Here the planet descends

the western horizon until it comes to the same pole

westward as the Sun holds eastward.

Oblique ascension of the Sun under

its own pole, 51° 13' . . . 340°

Subtract 180 . . .180°

Oblique descension of aspect below

west horizon .... 160° 59'

Oblique descension of Uranus under

pole of Sun .... 230° 14'

Arc of direction, Uranus parallel

Sun mundo . . .69° 15'

59'

0'


This arc of direction by the semiarc method is

found to be 70° 57', which shows an error of 1° 42',

equal to one year and eight months of time.

Time Measure for Arcs

This remark brings me back again to the question

of the equation of time, so much in dispute among

astrologers. I think there can be little doubt that

the true method is " a day for a year," which is

certainly the most ancient method, as it is also

the most uniform. In twenty-four hours the Earth

revolves on its axis and the Sun comes again to

the same meridian, having in the interval increased

its longitude by more or less than a degree according

to its apparent place in its orbit, i.e. the season of

the year. The mean rate of its motion is 59' 8".

Then, as all our calculations are made in terms

of equatorial degrees, we have to make a proportion

59' 8" to 60', and this gives 24h. 21m. = 1 year

5-334 days = l year 5d. 8h. for each 1° in the arc of

direction. Thus every 6° in the arc of direction

will give an extra month, to be added to the time

at the rate of 1° = 1 year, which is the measure of

time used in the semiarc method. If we add

5' for every 6° of arc it will come to the same

thing approximately. The measure of a degree

of R.A. for a year is due to Placidus. That of the

Sun's mean motion, or 1° R.A. = 1 year 5 days, is

due to Valentine Naibod. Both are a compromise

with facts. The probability is that we ought to


take the measure according to the season of the year

in which the birth takes place, and hence the Sun's

actual increase of R..A. on that date, since the Sun

is in every natural sense the great chronocrater,

or time-maker. Thus, in the case of Ruskin, who

was born on the 8th February, the Sun's diurnal

increase of R.A. is 3' 57" = 59' 15" in arc, but its

increase in longitude is 60' 43", and this being an

excess 1' 35" over the mean motion in the zodiac,

an arc of direction, at the rate of a day for a year,

would measure to so much less, at the rate of about

l\ minutes for every complete degree of the arc.

It will thus be seen that the question of the validity

of one method over another in primary directions

does not rest entirely on the astronomical facts,

but also upon the value we attach to the arcs of

direction when obtained. As to the astronomy

of the case, there is not the slightest doubt in my

mind that the method of directing under the pole

of the significator is the correct mathematical

scheme. But as to the measure of time from arcs

thus derived, this is a matter of experiment, and

one needs to exhaust all the evidence before coming

to a conclusion.

CHAPTER XVII

CONCLUSION

In the foregoing pages I have endeavoured to set

out and critically examine the methods of directing

advocated by Ptolemy and Placidus as modernly

represented ; and I have further sought to establish

their validity on general principles. I have not

been blind to their imperfections, and have clearly

indicated my view of the semiarc method, derived

from the principles laid down by these great

pioneers of a scientific astrology, when I speak

of them as valuable approximations. The discrep

ancies are those due to incorrect use of words in

describing the facts. The term " corresponding

to " should be more frequently used in the semiarc

method in place of the term " equal to." It is

admitted that in both systems—that of proportional

semiarcs and that of direction under poles—we are

concerned with the apparent places of the planets

in the prime vertical, and therefore when we speak

of planets as being directed to a conjunction we

mean an apparent conjunction as seen from the

place of birth, and not either in the zodiac or by

117


right ascension, but solely in the prime vertical or

circle of observation, which coincides neither with

the Equator nor the Ecliptic. Therefore, when we

come to the test we find without doubt that the

only way of doing this is to bring the directed body

along its own arc or parallel of declination to the

same pole as the promittor or body directed to. Also,

it is apparent that as polar elevation is measured

from the zenith in the plane of the prime vertical,

planets having the same pole must be in mundane

conjunction if on the same side of the meridian,

or in mundane parallel if on opposite sides, which

fact renders the calculation of mundane parallels

a process of such extreme simplicity that I wonder

it has never been pointed out before.

To correct the errors arising out of the methods

of Ptolemy and Placidus, I have made a complete

statement of the true doctrine of polar directions

in the plane of the prime vertical, and have supple

mented this by a speculum drawn according to the

principles laid down, so that by mere inspection

of the same, and very little figuring, all directions

in mundo can be calculated. For directions in

the zodiac it will be necessary to have the pole of

the aspect or position in the zodiac, which can be

determined by the longitudinal distance from the

cusp of the house taken in proportion to the

degrees of the ecliptic included in that house

from the Table of Poles of the Houses, and from

this we get its oblique ascension or oblique de

CONCLUSION 119

scension under its own pole, and direct to it as

in mundane direction.

In effect, it will be found that with a set of

tables of oblique ascension, and one of tables of

poles, all directions can be correctly calculated

in a fraction of the time usually devoted to them,

even by the very facile but faulty method of pro

portion of semiarcs. I have fairly stated both cases,

and criticised only where criticism was necessary

to correct error. In this I have done no hurt to

the cause of scientific astrology, and I conclude this

treatise in the earnest belief that I have even done

some small service.

TABLES FOR THE USE OF

ASTROLOGICAL STUDENTS

INCLUDING TABLES OF LOGARITHMIC

SINES, TANGENTS, ETC., TABLES OF

RIGHT ASCENSION, DECLINA

TION, AND ASCENSIONAL

DIFFERENCE, AND TER

NARY PROPORTIONAL

LOGARITHMS

9

TABLES OF LOGARITHMIC

SINES, TANGENTS, ETC.

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-!- rt rt r rt M rt rt rt c rtrtrt to rt rt m« rt m rt rt m rt rt to rt t-s rt rt to

to m OsON00 soNO NO NO

r-. io rtw m

O 00 NO i*- rt 0 tS mOoor-.NO Ni-

ONND -o oa r- •*

|

rt o Os 00 MA, ih ON00 m rt X osoo r- NO M t3

J00 00 00 00 00 00 00 oo 00 00 00 oo 00 00 00 00 OO OO 00 00 00 00 00 0C 00 00 00 00ON ON ON Os ON ON ON ON ON Os Os .Os ON ON Os ON ON ON ON ON ON Os On Os ON ON ON Os os Os Os

}

NO NOM OsNO

--o Os -*o?-no "Ssrtrtrt

r^s00 rt f- rt r— mNO M ioO Woo so fo

0 •* ON Os moom o oo *noo oo r- r-

1f? "f 4-

M 00 NO M m 00M 11 O

NO fN

rrr

M 00 NOON0O 00

O O O 0 0 o o o o O 0 o o o o o o o2 2°o o o 8 8 8 8 8 8 8

O O O o 0 o o o o o o o bbo o o o bbo o 0 o O 0 o o o o o p

13 rt rt J rt rt r rtrt rtrtrt rtrtrt-D rtrt rtrtrt t rt rt 0 rtrtrt rtrtrtc

J -4- os 0 vN ONO OO i^

us r- NO ~ r-^rt r-. « oo ON Osn-sNO 00

us O W ONO m NO m t- H-»00 0

so"* NOOO « fO NO 00 a m -+NO

-e ?rt J

!

1oo oo oo 'osoos"os

Os ON O^

ia.<Ovioi

Os ON Os

oq oo oo 00 00- ooON ON ONON ON ON

rJ-Too--ÎII P-

SsSsO^SsON ON Os Os I

ON ON ONON ON ON

ON ON ONON ON ON

ON ON ON ON ON ONON ON ON "os Os OsON ON ON ON ON ON

-O M M W r*1 -O MM .o M M rt cs i*i M"i 1 1 MM 1n rt M M

r- o for- os o

so Os rt w Os rt U100 ihOs O ft

-+ 0 to vsoo O csNO os rt woo o m

OO O MNO

00 00 00 00

S6ne.m H t+- U-iN0 00

0O 00 OQ

r-oo Os

00 00 oo

BUM

$•£i*-8

5- 5- "*rt rt rt-•4- rt m

$IVl oo oo

-4- t*-00 OO 00

•* -i-oo oo oo 00 oo oo 00 00 00 00 00 OO oo oo oo

Os Os Os OsON ON ON ON Os Os ■ ON Os ON Os Os Os Os Os ON ON ON ON Os Os os Os ON Os

O - rt i m * io so 1-.00 ON O « rt to tj- usNO r— 00 ON ort -rt rt" M

-rt rt rtrtrt

12

TABLES OF RIGHT ASCENSION,

DECLINATION, AND ASCENSIONAL

DIFFERENCE

VHaiqctNaexiuy

•qtoqjojsuieseq}aiv

■J)ICI,:>SVPna'ojpsa8tU.'seuyjoeeaSsp

suitjssqt0}o08TPPawqni°'VH»HJ0J

•33Q U90SV->H uopuoT ui,8u]uzj»g [OOdZ9A|1

0 0 0 t 0 t 0 t 0 J

0 0 0 0 0 0 0 0 0 0 0

T 0 fZ 0 99 0 08 0 T8 0 38

2 0 8f T 09 T 0 T 2 t *

8 T 2T 2 Qf T 08 T 88 T 78

f T 98 8 0* Z 0 2 f E 6

9 T 69 f 98 2 08 2 98 2 If

9 2 82 9 08 8 0 8 9 8 81

7 Z 9 92 8 08 8 7S 8 5*

8 8 OT 7 T2 f 0 \ 8 f 7T

6 8 fS 8 91 08 f 68 Bf

OT 8 89 6 TT 9 0 9 10 9 21

TT T2 OT L 9 08 9 Tt 9 89

2T 9* TT 2 9 0 9 2T 9 98

8T 9 8 TT 89 9 08 9 8f- 9 L9

n 9 18 2T 89 I 0 I n L 6Z

9T 9 99 8T 6f L 62 7 9f 8 T

9T 9 81 fl ff 7 69 8 9T 8 88

7T 9 If 9T Of 8 62 8 9t> 6 5

8T 7 f 9T 98 8 89 6 LI 6 18

6T 7 27 7T 28 6 82 6 8t 0T 8

O2 7 6* 8T 82 6 Li OT 81 0T 0*

T2 8 2T 6T fZ OT 72 OT 6* TT 2T

22 8 W O2 O2 OT 99 TT 61 TT

82 8 79 T2 17 TT 92 TT 6* ST 9T

fZ 6 61 ZZ 81 TT 99 2T O2 2T 94

92 6 Tf SZ OT 2T fZ 2T 09 81 7T

92 OT 8 fZ 9 2T 89 ST O2 8T 6*

72 OT W 92 8 8T zz 8T 09 n O2

8S OT 9* 92 0 8T T9 H O2 n 19

62 TT 7 92 79 n O2 fX 09 91. 22

08 n 6S 7s 99 fl 8? 9T 6T ex 89

mi

oiaaoogonasnnnvj. aoNaaaJHiQlanoisKaosy

•qtoqjojauiBS3q;axe

.JB?ao3svpireonipaGsqj,'sainexjoeaaSsp

aiiiaSeqi,o;o08tdpuoidjoogjo-yH«SS

-8»a -udssvW uopuoTa»t3uJtnjtg

[oodjven

0 0 t 0 4 0 4 O i 0 i

0 TT 65 75 99 n St 91 61 91 89

T TT 09 85 39 91 LX 91 6* 91 82

2 51 01 65 6f 91 9f 91 61 9T *9

8 3t 18 08 Lf 91 n 91 Sf 71 fZ

f 31 19 18 9f 91 Zf 7T LI 71 99

9 81 51 58 Sf 17 10 7T 9* 81 92

9 81 58 88 If 71 88 81 91 81 99

L 81 19 *e 68 81 9 81 ff 6T 92

8 fl TT 98 88 81 88 61 51 61 W

6 fl 08 98 78 61 0 61 05 >5

10 tl 6f 78 98 61 72 05 6 05 89

TT 91 8 88 *8 61 f<3 02 78 T5 2o

31 91 75 68 88 05 21 15 9 12 is

81 91 Qf Of 88 05 If 21 58 55 02

fX 91 8 If 58 15 fX 15 69 55 9f

91 9T 13 Zf 58 T2 Of 53 95 86 9T

91 91 88 2f 58 55 9 55 69 85

17 9T 99 n 58 55 18 82 05 fZ 51

81 71 51 Qf. 38 S5 99 85 9* fZ 68

61 71 65 9f 88 85 21 fZ 51 95 9

05 71 9f Lf 88 85 9f fZ 78 95 88

21 81 T 8* fB fZ 10 95 8 95 69

55 81 £1 6* 98 fZ *8 95 85 95 62

82 81 58 09 98 fZ 79 95 59 95 19

fZ 81 Lf 19 78 95 T5 95 91 72 9T

95 61 I 59 68 95 8? 95 Of 27 Tf

95 61 91 89 Of 95 9 75 f 85 9

75 61 08 W Zf 95 82 75 75 82 68

85 61 Sf 99 ff 95 6* 75 6* 85 89

62 61 75 99 Lf 75 TT 85 TT 65 91

08 05 10 79 6f 75 18 85 88 62 69

Gemini & Sagittarius Ascensional Difference

Deg. Declin. Rt. Ascen. London Birming'm Liverpool

Q o r 0 r 0 r 0 t o t

0 20 10 57 49 27 31 28 33 29 89

1 20 22 58 52 27 52 28 54 30 1

2 20 35 59 54 28 12 29 15 30 28

S 20 46 60 57 28 31 29 35 30 44

4 20 57 62 0 28 46 26 54 31 4

5 21 8 63 8 29 8 80 8T 31 24

6 21 19 64 7 29 25 80 32 31 43

1 21 29 65 10 29 42 80 50 32 2

8 21 39 66 14 29 59 31 7 32 20

9 21 49 67 18 30 15 81 23 32 87

10 21 58 68 22 30 30 31 40 82 54

11 22 6 69 26 30 45 31 55 33 10

12 22 14 70 30 30 58 32 9 33 26

18 22 22 71 84 81 11 32 23 33 40

14 22 29 72 39 81 24 32 87 33 54

15 22 36 78 43 31 36 82 49 84 7

16 22 43 74 48 81 48 33 1 34 20

17 22 49 75 52- 81 58 33 12 34 81

18 22 55 76 67 32 8 33 22 34 42

19 23 0 78 2 82 17 33 32 34 52

20 23 4 79 7 32 25 33 41 85 1

21 23 9 80 12 82 33 83 49 35 10

22 23 13 81 17 82 40 33 56 35 17

23 23 16 82 22 32 46 34 2 35 24

24 23 61 83 28 32 51 34 7 35 80

25 23 21 84 83 82 55 34 12 35 85

26 23 23 85 38 82 59 34 16 85 39

27 23 25 86 44 33 2 34 19 35 42

28 23 26 87 49 33 4 34 21 85 44

29 23 27 88 55 88 5 84 22 85 45

30 23 27 90 0 88 6 34 23 35 46

tS" For the R.A. of Sagittarius add 180° to the

same degree of Gemini. The Declin. and

Asc. Diff. are the same for both.

Iv

Cancer and

CapricornusAscensional Difference

Deg. Declin. Rt. Ascen. London Birming'm Liverpool

e

0

O f o t o r o t O 9

23 27

23 27

28 26

28 25

23 23

23 21

90 0 88 6

33 5

83 4

33 2

82 56

32 55

84 23

84 22

84 21

34 61

34 16

34 12

35 46

35 45

35 44

35 42

35 89

35 35

1 91 5

2

8

4

6

92 11

93 16

94 22

65 27

6

7

8

9

10

23 19

28 16

28 8T

23 9

23 4

96 32 82 51

82 46

32 40

32 83

32 25

34 7

84 2

33 56

83 49

88 41

35 80

85 24

85 17

35 10

85 1

97 38

98 43

99 48

100 53

11

12

13

14

15

23 0

22 55

22 49

22 43

22 86

101 58 32 17

32 8

31 58

81 48

81 86

33 82

83 22

83 12

83 1

32 49

34 52

34 42

34 31

34 20

34 7

103 3

104 8

105 12

106 17

16

17

81

19

20

22 29

22 22

22 14

22 6

21 58

107 21 81 24

81 11

80 58

SO 45

80 30

32 87

32 23

82 9

81 55

81 40

33 54

33 40

33 26

33 10

82 54

108 26

109 30

110 34

111 38

21 21 49

21 89

21 29

21 19

21 8

112 42

118 46

80 15

29 59

29 42

29 25

29 8

81 23

81 7

80 60

80 82

30 13

82 37

82 20

32 2

31 48

81 24

22

23

24

25

114 50

115 53

116 57

26

27

28

29

30

20 57

20 46

20 35

20 22

20 10

181 0 28 49

28 81

28 12

27 52

27 31

29 54

29 35

26 15

28 54

28 83

31 4

30 44

80 28

80 1

29 89

119 3

120 6

121 8

122 11

IS* For the R.A. of Capricornus add 180° to the

same degree of Cancer. The Declin. and

Asc. Diff. are the same for both.

Ivi

sniHvnSyanyoht HOMHHaddIQTVKOISN33Sy

•qtoqjojsuicssqt3jb-jjiq

•osypua"niioecieqx-°8T!J°ssjSadsuits

aqi°;0O8TPP*snmsnby}o-yaeq*joj«sf

•8ea •U35BV-JH uopuoT ta.Sutuutg

O 0 1 0 i .O t 0 i 0 1

0 O2 01 212 TT 72 18 82 88 62 68

T 6T 57 82T 8T 72 TT 82 TT 62 91

5 6T St *2T 9T 95 6* 72 6* 82 89

8 61 08 92T 81 95 8S 72 72 82 63

6T 91 912 O2 95 e 7S t 82 9

5 61 X 27T T2 25 e* 62 0* 7s »

9 8T Lt 812 85 25 21 92 91 27 91

7 81 58 62T fZ fZ 57 92 25 92 T5

8 81 17 08T 52 tz *e 52 82 95 9Z

6 8T T T8T 92 *2 01 25 8 SS 69

10 7T 5* 28T 72 85 9* fz 78 25 88

TT 17 65 881 7S 85 21 fZ 2T 9Z 9

5T 7T 2T fSX 85 22 95 es 9* fz 68

81 9T 56 58T 85 22 18 es O2 fZ 51

tx 9T 88 981 82 22 9 22 89 85 ft

9T 91 15 78T 85 T2 Of 22 95 es OT

91 91 8 881 85 T2 fX 21 65 22 8*

17 5T 5t 681 72 O2 Lt I2 58 22 20

8T 91 27 OfX 72 20 21 T2 9 T2 19

6T 5T 8 XfX 95 61 w 20 78 T2 55

05. tx 6i> ZfX 25 61 72 O2 6 O5 86

15 tx 08 en 85 61 0 61 Xf O2 ts

55 tx TT ftx 22 81 88 61 zx 61 W

85 81 T5 9fX T2 81 9 81 ft 6T 92

tz 81 58 9fX 61 17 88 81 91 81 99

«5 81 2T 7H 7T 7T ox 17 9f 81 91

95 51 T5 8H 5T 91 Zf 17 LX LX 55

72 12 18 6H 8T 91 fX 91 Bt 7T fZ

85 51 OT O5T n 5T 9t 91 61 9T W

65 TT 09 15T 8 91 17 91 6* 91 855

08 TT 65 25T 9 n 8* 15 6T fiT 89

!!AI

Virgo and Pisces Ascensional Difference

Deg. Declln. Rl. Ascen. London Birming'm Liverpool

0 a r 0 i 0 1 0 i 0 1

0 11 29 152 5 14 48 15 19 15 58

1 11 7 153 8 14 20 14 50 15 22

5 10 46 154 0 8T 51 14 20 14 51

« 10 24 154 57 13 22 18 50 14 20

4 10 8 155 54 12 53 13 20 13 49

6 9 41 156 50 12 24 12 50 13 17

6 9 19 157 47 11 55 12 20 12 46

7 8 57 158 43 11 26 11 49 12 15

8 8 84 156 40 10 56 11 19 11 48

9 8 12 160 36 10 27 10 49 11 12

10 7 49 161 82 9 57 10 18 10 40

11 7 27 162 28 9 28 9 48 10 8

12 7 4 163 24 8 58 9 17 9 87

13 6 41 164 20 8 29 8 46 9 5

14 6 18 165 16 7 59 8 16 8 88

15 5 55 166 11 7 29 7 45 8 1

16 5 81 167 7 7 0 7 14 7 29

17 5 8 168 2 6 80 6 43 6 57

81 4 45 168 58 6 0 6 12 6 25

19 4 21 169 53 5 30 5 41. 5 58

20 S 58 170 49 5 0 5 10 5 21

21 3 34 171 44 4 80 4 39 4 49

22 8 10 172 89 4 0 4 8 4 17

23 2 47 173 34 8 80 8 37 8 46

24 2 23 174 30 8 0 3 6 8 18

25 1 59 175 25 2 SO 2 85 2 41

26 1 36 176 20 2 0 2 4 2 9

27 1 12 177 15 1 80 1 33 1 87

28 0 48 178 10 1 0 1 2 1 4

29 0 24 179 5 0 80 0 81 ,0 82

80 0 0 180 0 0 0 0 0 \o 0

IS" For the R.A. of Pisces add 810° to the same

degree of Virgo. The Declin. and Asc. Diff.

are the same for both.

Iviii

TERNARY PROPORTIONAL

LOGARITHMS

Ternary Proportional Logarithms

10°

0 Infinite

1 403342

1 373-i39

3 355630

4 343136

5 3 33445

6 325527

7 3-18833

8 3oJ3033

9 3-07918

10 303342

:t 2"99203

12 2-95424

13 2-91948

i4 288730

:J 285733

16 282930

«7 280297

: 8 2-77815

:9 2 7546720 273239

11 271120

22 2-69I00

2} 267170

»4 265321

»3 263548

26 2-61845

27 260206

28 258627

»9 2-57X03

30 255630

3« ».54»°6

32 2 52827

33 25M91

34 250194

33 2-48936

J6 2-477I2

37 246522

38 245364

39 2-44236

40 243136

4< 242064

4' 2-41017

43 2 39996

44 2-38997

43 2-38021

46 2-37067

47 236133

48 2-35218

49 234323

30 2-33445

S: 232585

3' 2-3t742

33 2-309I5

34 2-30103

33 229306

36 2-28524

37 2-27755

38 2-27000

39 2-26257

63 2-25527

2-213882207352-2009I2194572I8833

2-152612-146932-14I332I35802 t3O33

2I24942.X:9D12-114352-109142-10400

2-098932-093902-088942-084032-07918

2074382-069642064942 060302.05570

2051152046652-042202 03779203342

2-029tO2O24822-O20602-016392-01223

2-O08122-OO4O42-000001-996O0r99203

1-988IO1-98421t 98035t-97652197273

t 96897t 965241-96t541 95788195424

: 954241-95064t-94706t 94352t .940001 93651

1 93305t929621-92621I .922831-9I948

1-916151912851909571-906321-90309

1-899881-896701.893541-8904:1-88730

1-884201-881141 878091-87506187206

1869071-866u1-86316I .860241 85733

t- 85445I -85I581 848731 84590I 84309

I .840301-837521-834771832031 82930

1826601-823911-821241-8I8581-8I594

1-81332t.8I07I1808111 80554I 80297

I-8oo43179790t-795381792871 79039

1-78791t-78545178300178057177815

3°1 778151 775751 773351 770971 768611 76625

1 76391176158175927175696175467

1-752391750121-747871745621-74339

174117173896173676173457173'39

1-730231-7280?1725931723791 72167

1 71956t 717451 71 536171328171120

1-70914170709170504t -70301170099

1-698971-696961-694971692981-69100

1-68903t 6S7071-685121683181-68124

1-679321 677401-675491-67359167 1 70

1-66981t 667941-666071664211 66236

t.66o5I1-6586*I.656H51 655031 65321

4°

1-6532I1-65t4I1'64961I 647821646031 64426

1-642491 640731-63897I -637221-6^548

1 633751-632021'630301 628591-62688

1-625181 623491-621801-620121-61843

1616781-615I21-6I3471611821-61018

1608541-60691t 60529t .603671 .60206

1600451-598851-597261 59567t 59409

1-59»511-590941589381-587821-58627

t-584721583171-58164t .5801 11 57858

1-577061-575541-574031-57253157103

1 569531-568041-566561-565081 56360

1-562131 -560671-559211 55775155630

5°

I 55630I 554861-55342I 551981-55055154912

t 547701546291 544871-543471-54206

1-540661 539271-53788t 536491-53511

1-533741532361531001-529631 52827

1-52692t-525571 524221-522881-52154

1-520211-51888:-5t7551-516231-51491

1-51360'1-5I2291-5Jo981-50968I 50838

I -507081-505791-504511-503221-30194

1-500671 499401-498131-49687t-4956o

1-494351-493091-491841-490601-48936

1-488121486881-485651-484421-48320

t-48t97t 48076

:47954: 478,3t 47712

8°

1-477121 475921-474721 473521 472321 47113

1 410171-409141 408111-407081 406061 40503

1-4&994 1 4040141-46876 1-403001-46758 1 401981-46640 1-400971 46522 1 39996

1-464041 462881 461711 460551 45938

1 458241 457081 455931-45478145364

1452501-45 1 36t 45022144909t-447.96

1-44684t 445711-444591-44347t 44236

1-441251-44014: 43903i.437931-43683

t.435731-434631-433541-43245143136

1-430281-429201-428121-427041-42597

1-424901-423831-422761-421701-42064

1 419581-4185-14 1 7471-41642141538

1414J31413291 41225141121t.4JoJ7

1 398951 .397941-396941 395931 39493

1 393941-39294139195t 39096t 38997

1388991-388001-387021-38604t -38506

1-384091-383121-382151-381181-38021

t 37925t 378291-37733t 376371 37541

t 37446t-3735t137256t -371611-37067

1-369721-368781-367841-3669:: 36597

1-365041-364111-363181-36225.1-36I33

1 o36040

1-359481 358561 357651 35673

1-355821 35491t 354001 35309t 35218

8°

1352181-351281- 350381349481348581 34768

1 346791345891 345001-344111 34323

1-342341-341461 340581-33970133882

1-337941-33707I-336I91-335321-33445

1-33359t 332721331861-33099133013

t 32927t 328421327561-32671t 32585

1325001-3»4151-323311-322461-32162

l-320771-31993131909131826131742

t-3t6591 31 5751 314921314091-31326

1-312441-311611310791-30997130915

1 30833t-3075t1 306701 30588130507

1-304261 303451 302641 30183tJOt03

9°

1-301031-300231299421-298621-29782129703

1-296231-29544t 29464t 293851 .29306

1-292271-291481-290701-289911-28913

1-288351287571-286791-286011-28524

1-284461-283691-282921282 15t 28138

1-280611-279841-279081-278311-27755

1-276791-276031 275271 27451I- 27376

1273001 272251-27I501 270751-27000

1 269251-268501-26776.1-267011-26027

1-265531 264791-264051-26331126257

T26t84X-261101-26037t- 250641-25891

1-258181-257451-256721-256001 25527

lxi


11

:3M

»3

16

19

2223

»4»3

16

1282930

S<3*333433

*3738

39

4«

4:4»434443

4«474*4930

5I

3»333433

3«5758

5960

10°

t255271-I5+5J1-253831253111-23239:.25167

1-250951250241-240511-248811 24809

1 247381 246671 243961-245261*4455

1-243841-243141 242441-24173124103

1-240331 239631238941-238241-«734

1-236851 236161-235461-»34771 23408

1-233391 232711-232021231331 23065

1-229971 229281-228601-227921-22724

1 226571-225891-22521122454122386

1-223191-22252t 221851-221181-22051

I 219841-ltgt81-218511-217851-21718

1-216521-215861-215201214541 21388

11°

:-113881-213221212571-211911-211261-2Io6o

1209951-209301-20865t .20800t 20735

t .206701-206051-205411-20476120412

I .203481-202841-202191-201551 -20091

1-200281-19964r190001-198371-19773

1197101196471 195841 19520tt9457

1- 19395I- 193321192 691-19206119144

1-190811-190191 189571 188951-18833

1-187711-187091186471-18585118523

1-184621-184001183391-182781-18217

1-181551180941-1803311/9731-17912

1-178511 177901 177301-176691-17609

12°

117609117349117489117429117369117309

1172491-171891-171291-17070117010

1I69311 168911-168321 167731-16714

:•16655

1-165961165371- 164781-16419

1-163611-163021162431161851-16127

1-160681-160101-139321-158941-15836

1 157781-1372I1 156631156051 15548

1134901 I5433

1-1537JII53t8115261

1- 152041151471 150901-150331- 14976

1-149191 148631-148061 147501 14693

1-146371-14581I• 14524

1144681-14411

t- 143361-14300114244

1-14189114133

18°

1-14133J- 140771140221139661-13911113855

113800:-137451136901 13635113580

:•:35->5

1I34701-13415IJ336o1- 13306

1-I325I1131971-13142II3o881 13033

1 I 29791-t29251-128711-»2817112763

II2709t- 126551-J26ot1125481- 12494

1-124401 123871-1»3331-122801 12227

1-111731-121201-t20671-10O14t-U961

1-"908t-"855:.tI8o2111750ttt697

1-11644t-tt5921115391"4871-IM35

1-113811113301-112781-11226111174

1-111221-11070

1-"oI81-109661-10914

14°

1I09141 10863

1-io8:t1-Io76oI• 10708

I 10637

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/84° 85° 88° 87° 88° 89° 90° 91° 92° 93° 94° 95°

0 33099 32585 32077 31575 31079 30588 30103 29623 29148 28679 28214 27755

t 33091 32577 32069 31567 31071 30580 30095 29615 29141 28671 28207 27747

2 33082 32568 32061 31559 31063 30572 30087 29607 29133 28663 28199 27740

3 33073 32560 32052 31550 31054 30564 30079 29599 29125 28656 23191 27732

4 33065 32551 32044 31542 31046 30556 30071 29591 29117 .28648 28184 27724

5 33056 32543 32035 31534 31038 30548 30063 29583 29109 28640 28176 27717

6 33048 32534 32027 31525 31030 30539 30055 29575 29101 28632 28168 27709

7 33039 32526 32019 31517 31021 30531 30047 29567 29093 28625 28161 27702

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9 33022 32509 32002 31501 31005 30515 30031 29552 29078 28609 28145 27686

10 33013 32500 31993 31492 30997 30507 30023 29544 29070 28601 28138 27679

it 33005 32492 31985 31484 30989 30499 30015 29536 29062 28593 28130 27671

12 32996 32483 31977 31476 30980 30491 30007 29528 29054 28586 28122 27664

13 32987 32475 31968 31467 30972 30483 29999 29520 29046 28578 28 1 14 27656

14 3»979 32466 31960 31459 30964 30475 29991 29512 29038 28570 28107 27648

15 32970 32458 3 195 1 31451 30956 30466 29983 29504 29031 28562 28099 27641

16 32962 32449 31943 31442 30948 30458 29975 29496 29023 28555 28091 27633

17 32953 32441 31935 31434 30939 30450 29967 29488 29015 28547 28084 2762618 32944 32432 31926 31426 30931 30442 29958 29480 29007 28539 28076 27618

:9 3293S 32424 319*8. 31418 30923 30434 29950 29472 28999 28531 28068 2761020 32927 32415 31909 31409 30915 30426 29942 29464 28991 28524 28061 27603

21 32919 32407- 31901 31401 30907 30418 29934 29456 28984 28516 28053 2759522 32910 32398- 31893 31393 30898 30410 29926 29448 28976 28508 28045 2758823 32902 32390 31884 31384 30890 30302 29918 29441 28968 28500 28038 2758024 32893 32381 31876 31376 30882 30393 29910 29433 28900 28493 28030 27572

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26 32876 32365 31859 31360 30866 30377 29894 29417 28944 28477 28015 2755727 32867 32356 31851 31351 30857 30369 29S86 29409 28937 28469 28007 2755028 32859 32348 31842 31343 30S49 30361 29878 29401 28929 28462 27999 2754229 32850 32339 31834 31335 30841 30353 29870 29393 28921 28454 27992 2753430 32842 32331 31826 31326 30833 30345 29862 29385 28913 28446 27984 27527

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35 32799 32288 31784 31285 30792 30305 29822 29346 28874 28407 27946 27489

36 32790 32280 31775 31277 30784 30296 29814 29338 28866 28400 27938 27481

37 32782 32271 31767 31269 30776 30:88 29806 29330 28858 28392 27930 2747438 32773 32263 31759 31260 30768 30280 29798 29322 28851 28384 27923 27466

39 32765 32255 31750 31252 30759 30272 29790 29314 28843 28376 27915 27459

40 32756 32246 31742 31244 30751 30264 29782 29306 28835 28369 27908 27451

41 32747 32238 31734 31236 30743 30256 29775 29298 28827 28361 27900 2744442 32739 32229 31725, 31227 30735 30248 29767 29290 28819 28353 27892 27436

43 32730 3*221 31717 31219 30727 30240 29759 29282 288 1 1 28346 27885 27429

44 32722 32212 31709 31211 30719 30232 29751 29275 28804 28338 27877 27421

45 32713 32204 31700 31203 30710 30224 29743 29267 28796 28330 27869 27413

46 32705 32195 31692 31194 30702 30216 29735 29259 28788 28322 27862 27406

47 32696 32187 31684 31 186 30694 30208 29727 29251 28780 28315 27854 2739848 32688 3»t79 31675 31178 30686 30200 29719 29243 28772 28307 27846 27391

49 32679 32170 31667 31170 30678 30192 2971 1 29235 28765 28299 27839 27383

50 32671 32162 31659 31161 30670 30183 29703 29227 28757 28292 27831 27376

51 32662 32153 31650 3"53 30662 30175 29695 29219 28749 28284 27824 2736852 32654 32145 31642 31145 30653 30167 29687 29211 28741 28276 27816 27360

53 32645 32136 31634 31137 30645 30159 29679 29204 28733 28268 27808 27353

54 32636 32128 31625 31128 30637 30151 29671 29196 28726 28261 27801 27345

55 32628 32120 31617 31120 30629 30143 29663 29188 28718 28253 27793 27338

56 32619 32m 31609 31112 30621 30135 29655 29180 28710 28245 27785 27330

57 32611 32103 31600 31104 30613 30127 29647 29172 28702 28238 27778 2732358 32602 32694 31592 31095 30605 301 19 29639 29164 28695 28230. 27770 27315

59 32594 32086 31584 31087 30506 301 1 1 29631 29156 28687 28222 27763 2730860 32585 32077 31575 31079 30588 30103 29623 29148 28679 28214 27755 27300

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3 27278 268:18 26382 25942 25506 25074 24646 24222 23803 23388 22976 22569

4 27270 26820 26375 25934 25498 25066 24639 24215 2379S 23381 22969 22562

5 27262 26813, 26368 25927 25491 25059 24632 24208 23789 23374 22963 22555

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7 27247 26798 26353 25913 25477 25045 24618 24194 23775 23360 22949 22542

8 27240 26790 26346 25905 25469 25038 24610 24187 23768 23353 22942 22535

9 27232 26783 26338 25898 25462 25031 24603 24180 23761 23346 22935 22528

10 27225 26776 26331 25891 25455 25024 24596 24173 23754 23339 22928 22521

n 27217 26768 26323 25883 25448 25016 24589 24166 23747 23333 22922 22515

12 27210 26761 26316 25876 25440 25009 24582 24159 23740 23326 22915 22508

13 27202 26753 26309 25869 25433 25002 24575 24152 23734 23319 22908 22501

M 27195 26746 26301 25861 25426 24995 24568 24145 23727 23312 22901 22494

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16 27180 26731 26287 25847 25412 24981 24554 24131 23713 23298 22888 22481

17 27172 26723 26279 25840 25404 24973 24547 24124 23706 23291 22881 22474

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19 27157 26709 26265 25825 25390 24959 24533 24110 23692 23278 22867 22461

20 27150 26701 26257 25818 25383 24952 24526 24103 23685 23271 22860 22454

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24 27120 26671 26228 25789 25354 24923 24497 24075 23657 23243 22833 22427

25 27112 26664 26220 25781 25347 24916 24490 24068 23650 23236 22826 22420

26 27105 26656 26213 25774 25339 24909 24483 24061 23643 23229 22819 22413

27 27097 26649 26206 25767 25332 24902 24476 24054 23636 23223 22813 22407

28 27090 26642 26198 25759 25325 24895 24469 24047 23629 23216 22806 22400

29 27082 26634 26191 25752 25318 24888 24462 24040 23623 23209 22799 22393

30 27075 26627 26184 25745 2531 1 24881 24455 24033 23616 23202 22792 22386

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32 27060 26612 26169 25730 25296 24866 24441 24019 23602 23188 22779 22373

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35 27037 26590 26147 25709 25275 24845 24420 23998 23581 23168 22758 22353

36 27030 26582 26140 25701 25267 24838 24413 23991 23574 23161 22752 22346

37 27022 26575 26132 25694 25260 24831 24405 23984 23567 23154 22745 22339

38 27015 26567 26125 25687 25253 24824 24398 23977 23560 23147 22738 22333

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44 26970 26523 26081 25643 25210 24781 24356 23935 23519 23106 22697 22292

45 26962 26516 26074 25636 25203 24774 24349 23928 23512 23099 22690 22286

46 26955 26508 26066 25629 25196 24767 24342 23921 23505 23092 22684 22279

47 26947 26501 26059 25621 25188 24760 24335 23914 23498 23086 22677 22272

48 26940 26493 26052 25614 25181 24752 24328 23908 23491 23079 22670 22265

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53 26902 26456 26015 25578 25145 24717 24293 23873 23457 23044 22636 22232

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Documents

Gift of The People of the United States Throughthe Victory … · 2017. 2. 26. · 4 DIRECTIONAL ASTROLOGY Significators, in this scheme, are the Midheaven, Ascendant, Sun, and Moon