The Scientific Basis of the Predictive

Art commonly called Astrology : to

which is added a Complete Set of

Tables with Emendations and New

Rules for the use of Students.

By " SEPHARIAL "

Author of The Manual of Astrology, Lectures on Astrology, Hindu Astrology after Pardshara, etc.

L. N. FOWLER,

7, IMPERIAL ARCADE, LUDGATE CIRCUS, E.C.

CONTENTS.

CHAPTER I. The Use of an Ephemeris.-Nautical Almanack. The Speculum ; Latitude ; Declination ; Rt. Ascension ; Meridian Distance ; Semi-arc ; Horizontal Arc ; Cuspal Distance ; Use of Tables ; Proportional Logarithms.

CHAPTER n. The Horoscope of King Edward VII.-Figure of Heavens at Nativity; Speculum of Planets' Elements; Signs of Accession.

CHAPTER 111. Primary Directions,-Vhat a Direction is ; Mun- dane Directions ; Zodiacal Directions ; How Arcs are formed ; Illustration of Planetary Arcs ; Direct and Converse Directions.

CHAPTER IV. Mundane Directions.-The Conjunction in Mundo ; Examples : Venus to conjunction Moon ; Sun to conjunction Jupiter ; Uranus to conjunction Ascendant ; Saturn to conjunction Mid-heaven.

CHAPTER V. Aspects in Mu?ido.-How measured ; Examples : Sun to trine Neptune; opposition and sesquiquadrate aspect of same ; Converse Solar directions to Neptune; Why converse directions cannot be pre-natal as asserted ; Saturn to Aspects of Ascendant ; Venus to Aspects of Mid-heaven; Mid-heaven to Aspects of the Sun in Mundo.

CHAPTER VI. Parallels in Muttdo.-The nature of Mundane Parallels ; Validity of Horizontal Parallels ; Examples : upiter to

parallel Neptune; Sun to horizontal parallel Saturn. I parallel Moon ; Moon to parallel Jupiter ; Sun to orizontal

CHAPTER VII. Rapt Parallels.-Direct and Converse Parallels ; Rule to compute Rapt Parallels; Examples : Moon and Saturn to Rapt Parallel on upper meridian ; Moon and Sun to Rapt Parallel on the same ; Sun to Rapt Horizontal Parallel : Jupiter to Rapt Horizontal Parallel.

CHAPTER VIII. Zodiacal Directions. -Similar to Mundane Direc- tions ; direct and converse ; Why Parallels are not valid.

CHAPTER IX. Conjunctions in Zodiac.-Method of directing; Examples : Mid-heaven to conjunct Moon in Zodiac; Mid-heaven to conjunct Saturn ; Ascendant to conjunct Uranus ; Ascendant to

conjunct Sun ; Venus to conjunct Moon ; Sun to conjunct Saturn ; An unique direction of Moon to conjunct Moon.

CHAPTER X. Aspects in Zodiac.-Aspects of longitudes ; Method of directing ; Examples: Mid-heaven square Moon in Zodiac ; Mid- heaven sextile Sun ; Ascendant sextile Jupiter ; Ascendant opposi- tion Moon ; Sun to opposition Neptune ; Moon to square Sun ; Venus to sextile Moon ; Direct and converse directions.

CHAPTER XI. Order of Directing. Necessity for Method in work ; Order of Procedure ; Mundane category ; Zodiacal category ; Use of terms Mid-heaven and- Meridian, Ascendant and Horizon ; Concluding remarks.

CHAPTER XII. Effects of Directions.-House position ; Good and evil aspects ; Significators : Mid-heaven, Sun, Moon, Ascendant ; Effects of Uranus' directions; Saturn's effects-Jupiter's, Mar's, Venus's; Effects of Sun, Moon, and Mercury; The Measure of Time ; When directions operate.

CHAPTER XIII. S1mnaary.-Sir Isaac Newton, Kepler, Tycho Brahe in relation to Astrology ; Every Astrologer in honourable company. *

CHAPTER XIV. The Part of Fortune.-An Ancient Symbol ; i ts signification ; How to calculate its position in the Prime Vertical; Example from Royal Horoscope; Serni-arc of Part of Fortune; Examjles of directions to Part of Fortune ; Jupiter to conjunction ; Moon to square aspect ; Uranus to square aspect.

CHAPTER XV. Lunar Parallax.-Definition of Parallax ; Parallax of Sun and planets ; Of the Moon ; Illustration of Parallactic angle: Apogee and Perigee; Moon's Anomaly; Motion of Apogee of Moon; Parallax determined by Anomaly; Anomalistic Tables ; Example of their use ; Sepharial's Chord of Parallax ; Example of its use; Part of Parallax due to Zenith distance ; Correction of Moon's place by Parallax ; An open question ; Semi-diameters of Sun and Moon to be applied to arcs of direction.

CHAPTER XVI. The Houses of the Heavens.-Truth sacrificed* for convenience ; House-space of a planet not uniform ; Illustration of inequality of House-space ; Calculation of the Cusps of Houses ; Illustration of unequal House-space ; Proofs of the new statement ; Effect upon Arcs of Direction.

'CHAPTER XVII. Lunar Equation.-Planetary influence continues after birth ; Directions to the places a t Nativity and to the actual places ; Example of Moon's place directed to Western horizon and compared with Moon's setting.

A P P E N D I X . - T ~ ~ ~ ~ S of Right Ascension and Declination, and Ascensional Difference for London, Birmingham and Liverpool.

Tables of Proportional Logarithms.

FOREWORD

I N publishing this short treatise on Primary Directions for the use of students of Prognostic Astronomy, I am conscious of invading systems already in repute, but I 'trust I have not done so without due cause. Most books on the subjec't, while aiming at mathematical precision, embody too much of what is already weighted with traditional error, and they fail entirely to convey a simple conception of what is being done and the reason 'for doing it. I have therefore endeavoured to render 'every operation a s intelligible as possible by means of -diagrams relating to the case I have chosen to illustrate the subject ; and a set of tables has been added to the work in order to facilitate calculations. I t is presumed that the reader is already acquainted with the elements of the science and can set a figure of the heavens for any given time and place. Unlike the majority of ¥writers who bewilder the student with technical terms and explain them at the end of a work, I have thought fit to begin with a Glossary of Terms.

Having written for the past eighteen years on the subject of planetary influence in human life, it will hardly be necessary to elaborate the¥argumen in this place. Those who deny such influence esteem their premature opinion as of greater weight than the mature conclusions of those who have given the matter long and arduous study, and i t is not a n uncommon ex- perience that such egotists have but the most superficial knowledge of the subject they contemn.

I t remains for 'the intelligent truth-seeker to construct his own horoscope and compute the various arcs of direction b y the methods herein set forth, before pro- nouncing a verdict on a subject- which has fascinated

the minds of many great men in all ages, and for which, not without reason, is claimed a place among the sciences as an essential part of natural physics-possibly also the key to much that goes under the names of psycho- logy and metaphysics.

Those who are acquainted with the nature of Hertzian waves and the phenomena attaching to wireless tele- graphy, will have little difficulty in conceiving the idea of planetary actions, v i a the ether of space, upon the brain-cell batteries of human beings. If the planetary bodies by their conjunctions and aspects are capable of creating disturbances in the Earth's atmosphere, as follows from the concept of the solidarity of the Solar System and that of the continuity of Matter, they are also capable of producing electrical disturbances in highly-charged brain cells by means of the Earth's atmosphere; and that one brain can affect others is a fact well within our knowledge. Every act of cerebra- tion is accompanied by an electrical discharge and the breaking down of the walls of brain cells. The electro- static condition of the Earth's atmosphere at the moment a child draws its first breath is the basis of individual brain activity. I t is like the charging of a battery of a given capacity and quality. Any subsequent change in the Earth's condition will be expressed by the individual in terms of his particular brain development. Influences which create great disturbance in one brain will be scarcely registered by another, for there are qualities as well as quantities of electrical action, and astral science has already tabulated 6,132 different modes of planetary action. When these modifications of the ether of space are related to the wide diversities of brain development, the complex of human thought and action is fully accounted for.

The system of Prognostic Astronomy explained in these pages is primarily due to Claudius Ptolemy, who' lived in Alexandria in the time of Antoninus, about the beginning of the second century A.D. H e rendered immense service to his time, and, indeed, to modern science, by compiling the longitudes and latitudes of all known places, and in laying the foundation of the

method of projecting geographical charts. H e was also th6 author of a treatise upon optics, in which he explains the cause of the refraction of light, and also wrote upon music, chronology, the Gnomon, and mechanics. His genius was as diverse as his intellect was great, and to his patient toil modern Astronomy owes the Almagest, which gives- an account of ancient eclipses and their connection with current events, observations of stars, and a canon of the kings of Assyria, Persia, Greece and Rome, and which, "considered as a depository of ancient observations, is one of the most precious monuments of antiquity " (Laplace: Systeme dzi Monde).

Astronomy is to Astrology what the body is to the soul that quickens and inspires it. The dry facts of Astronomy are of interest and value only to the extent that they may be brought into relation with the daily life of mankind. The gospel of true science is utility. Sir Norman Lockyer is at present engaged in an attempt to apply the phenomena of Sun-spots to the times and places of great drought and famine, believing to have observed a relationship of the celestial and terrestrial facts. H e has given some years of study to the subject and hopes, in measurable time, to be able to locate the exact provinces in which the Sun-spots will do their sterilising work. Further, Sir Norman has discovered a coincidence between the prevalence of Sun- spots and the Nile tides, which reduced to a word is this: Famine years in India are low-tide years in the Nile, and both are controlled by the prevalence of Sun- spots.

This is the true Evangel of Science, for, as Lord Bacon said: "The real use of all knowledge is this, that we should dedicate the reason which was given u s by God to the use and advantage of man." Sir Norman Lockyer will take his place among the ranks of the prophets and scientific astrologers will give him a warm welcome. In ancient days the Nile tides were studied by the Hyksoi-Shepherd-Kings and Patriarchs -and by the Egyptian Eshpayim, in relation tocelestial phenomena, and in course of time, as the search pro- gresses, it will be found that the rents in the luminous

envelope of the Sun, commonly known as '& Sunkpots," have direct relation to the periodic ratios of the planets Jupiter and Mars.

In regard to planetary action upon individuals, it ¥woul appear that, as the direct rays of the celestial bodies are more powerful than their oblique rays, the electrical disturbances due to the planets when acting in conjunction, or a t certain angles called 4 6 aspects," will be greatest in the Equatorial region. Thence the energy generated would be distributed towards the Poles. From varied and continuous observations it is evident that the geocentric configurations of the planets affect the world generally, according to the natures of the planets involved. But this affection is reflected by the individual according to the positions of the planets as seen from the place of his nativity, and at the moment of that event. Thus all inter-planetary action is universally "distributed and reflected by the individual, according to natural susceptibility or predisposition, at times which are measured by the arcs of direction, L e . , the degrees of Right Ascension between one body and another, or one body and the aspect o f another, as seen from the place of birth.

This measure of Time in reference to the events of life is the main purpose of this work, which 1 trust will attract the attention of competent critics.

SEPHARIAL.

PROGNOSTIC ASTRONOMY

- -

C H A P T E R I.

THE USE OF EPHEMERIDES AND TABLES

AN Ephemeris, to be of much use to the student of Prognostic Astronomy, must contain the geocentric ¥longitudes the declinations and latitudes of all the celestial bodies of the solar system for each day at noon throughout the year.

The Nautical Almanac is a reliable Ephemeris and contains all the elements necessary for computing a figure of the heavens for any given time. But the French Ephemeris known as the Connaisance de T e e s is preferable, since it gives the geocentric longitudes of the planets, as well as the apparent Right Ascension and other elements contained in the British Nautical Almanac. The equation of longitude due to any meri- dian other than that of Paris is of course readily effected by simple proportion of the diurnal motions of the several bodies. , From this, or any other reliable Ephemeris, the plane- :tary Speculum is constructed., The following definitions of the elements of the speculun~, and the method of their calculation, will be of service to the beginner.

The first column will contain the Symbols of the bodies ¥o the Solar System, viz..: T h e Sun, Moon, Neptune, fUranus, Saturn, Jupiter, Mars, Venus, and Mercury.

The second column will contain their Latitudes.

Celestial latitude is the distance of a body North or South of the Ecliptic or Sun's path in the heavens. The Sun, therefore, has no latitude. The Ecliptic crosses the Equator of the Earth at an angle of about 23O27', subject to a slight annual din~inution of no practical account for many years together. The points of intersection are known as the Equinoxes. The Ephemeris gives the latitude daily at noon and by pro- portion it can be found for any intermediate hour.

The third column will contain the ~ecl inat ions . De- clination is distance N. or S. of the Equator, expressed in degrees and minutes of a circle. The declinations of the planets and of the Sun and Moon will be found for noon each day in the Ephemeris.

The fourth column will contain the Right Ascensions. The Right Ascension of a body is its distance from the vernal Equinox measured in degrees and minutes on the Equatorial circle. In the Nautical Almanac the apparent Right Ascension of the different bodies is ex- pressed in hours, minutes and seconds. In these terms the whole circle of the Equator is equal to twenty-four hours. Thus:

34 hours = 360 degrees. I hour = 15 degrees. 4 minutes = I degree.

The tables constructed for the appendix of this treatise give the Right Ascension of every degree of the Ecliptic, and a body without latitude has the same Right Ascension as its longitude. For a body having latitude the Right Ascension has to be calculated by the formula : - Log . cos. (arith. comp.) declin. + log. cos. latitude + log. cos. distance in longitude from nearest Equinox = log. cos. of the Right Ascension from the same Equinox.

The fifth column will contain the Meridian Distances of the planets. . The Right Ascension of the meridian degree of the horoscope beingknown,together with the Right Ascension of the various bodies,,the degrees and minutes of Right

Ascension which separate these bodies from the nearest meridian constitute their meridian distances, which will always be less than go0.

The sixth column will contain the Semi-arcs of the planets. '

The semi-arc of a planet is half the time (expressed in degrees and minutes) that the body remains above or below the horizon; That arc which the planet describes above the horizon is called the " diurnal " semi-arc, while that below is called the " nocturnal " semi-arc. The one taken from 180Â will give the other.

T o find the semi-arc of a body : Log. tang. of the latitude of place of observation +

log. tang. declination of planet = log. sine of the A scensional Difference.

I . If the planet be above the horizon in South declination, or below the horizon in North declination, take the Ascensional Difference from go0.

2. If the planet be above the horizon in North declination, or below the horizon in South declination, add the Ascensional Difference to go0.

The result is the semi-arc of the planet, diurnal if above and nocturnal if below the horizon.

The seventh column will contain the Horizontal Arcs. The horizontal arc is the distance a body is in degrees and minutes of Right Ascension from the nearest horizon. The semi-arc, less the meridian distance of a planet, is its horizontal arc. The semi-arc is, in fact, composed of the meridian distance and the horizontal distance, since the semi-arc is the course traversed by a body from its meridian passage to the point where it rises or sets.

The eighth and last column of the Speculum will contain the Cuspal Distances of the planets.

The cuspal distance is used to locate the position of a planet in the circle of observation or prime vertical, and is required in calculating mundane aspects. In passing from the horizon to the meridian, or from the meridian to the horizon, a planet passes through the houses. The time it takes to pass from the cuspof

one house to that of the next on the same side of the horizon is called its house-space, and this arc is, approximately, one-third of the planet's semi-arc.

Therefore to find the cuspal distance : Of a planet in a cadent house, i.e., the ninth, sixth,

third or twelfth, take its meridian distance from one- third of its semi-arc if in the ninth or third; but the horizontal arc from one-third of its semi-arc if in the sixth or twelfth.

Of a planet in a succedent house, i.e., eighth, fifth, second or eleventh, take its meridian distance from two- thirds of its semi-arc..

Of a planet in an angle, i.e., first, tenth, seventh or fourth houses, take its meridian distance, or its horizontal arc only, and this, in each case, will give its distance from that cusp to which it is next proceeding.

These are all the elements required for the construc- tion of a celestial or horoscopical speculum.

THE 'TABLES'

Appended to this treatise contain the Right Ascension and declination of every degree of the Ecliptic from Aries to Virgo, inclusive. The opposite degrees have the same declination, as, for instance, 8 go has declina- tion 14~31' N., so that q g O will have the same declination S. The Right Ascension of the Southern signs of the Ecliptic are found by adding 180 to the same degree of the opposite Northern sign. Thus the Right Ascension of nlsO is 73'43' arid, therefore, f 15O has Right Ascension (73O43' + I 80° = ~53~43 ' .

Against each degree of the Ecliptic is found also its Ascensional Difference for the cities of London, Birming- ham and Liverpool, whose latitudes ,are 5i03.z', 52O28', and ~ 3 ~ 2 5 ' N.,respectively. All places in the same lati- tudes will have the same amount of Ascensional Difference for the same'point of the Ecliptic. - By subtracting the Ascensional Difference from the Right Ascension of any degree between Aries oo and Virgo 30° or adding it to the Right Ascension of any degree of the Southern 'signs, we have the Oblique Asbeision' of that degree-and also of any celestial body

having the same declination as that degree. T h e opposite process will give the Oblique Desce~zsio~z. The Ascensional Differences can also be used to find the semi-arcs of the planets, since the semi-arcs is always go0. plus or minus the Ascensional Difference due to the declination of the body.

The tables, therefore, will be found of extreme- utility and by means of simple proportion all the elements. of the speculum, beyond those given in the Ephemeris, can be readily calculated. The chief object of their construction, however, is for use in the calculation of Directions in the Zodiac.

PROPORTIONAL LOGARITHMS

In dealing with fractional quantities of a quadrant,. the process of making a proportion is greatly facilitated by the use of these logarithms. Thus in the proportion : As 72'5' is to 3'52' so is 85'9' to x , we should reduce. all the quantities' to minutes, multiply the second and third terms together and divide the result by the first term, and this-operation in its simplest expression would.

be 232 51°9 The process would certainly occupy- 4325 '

several minutes even for a quick calculator. In the use of logarithms we take out the separate-

logarithms for the three terms, add the second and third terms together, and subtract the first ; or take the: first from 10-ooooo and add it to the second and third. term logarithms. Thus :,

2nd. 3 O 5 2 ' log. 1.66794 3rd. 85'9' 1,' -32509

Or. thus :

(Arith. cornp.) 9.60256 and. 3O52' 1.66794 3rd. 850g1 -32509

-- Ans. 4O34' 1.59559

Note-The arithmetical complement of a logarithm is what it lacks of ten.

As all directions are worked by proportional arcs it will be found expedient to extract the logarithms of the planets' semi-arcs and cuspal distances from the tables, and set them under their proper heads in the columns.

The constant logarithm of a body is obtained by adding together the arithmetical complement of the logarithm for its semi-arc, and the ,logarithm of its meridian distance, thus :

semi-arc 1) 85O28I log. - *32348

(Arith. cornp.) 9-67652 Merid. Dist. 1) 32'37' log. .74183

-- Constant log. of Moon - .41835

Whenever the T) is the body to which direction is made, the constant log. 941835 will supply the place of the first and second terms of the proportion. W e have then merely to add to it the log. semi-arc of the body which moves to form the arc of direction, to obtain the log. of its proportional distance.

The use of the constant log. will be found a great economy of labour, but for the sake of lucidity I shall not make use of it i n t h e Examples of Directions given in the following pages.

W e may now proceed to the calculation of Arcs of Directions, taking a worthy horoscope as the subject of our study.

CHAPTER 11.

THE HOROSCOPE OF H.M. KING EDWARD VII.

ACCORDING to the Official Bulletin published a t the King's birth, this event took place a t ioh. 48m. a.m. on the 9th November, 1841, at Buckingharn Palace, in latitude 51~32' N. and longitude om. 3gsec. W.

The calculation of the horoscopical Mid-heaven is as follow :

Sidereal Time, noon, 8th November - 15 10 o Time since elapsed - 22 48 o Acceleration at 10 sees. - 3 48

38 1 48 Less Circle 2 4 0 0

Rt. Asc. of Mid-heaven at Birth - 14 I 48

This corresponds to 210~27'. By adding go0o' we obtain 3o0°27' which is the Oblique Ascension of the Ascending degree. By subtracting 180 from the Right Ascension of the Mid-heaven 210'27' we have 30°27 for the Right Ascension of the Nadir, or lowest point of the heavens a t the moment of the King's birth.

The following are the horoscopical figure and speculum.

1 I 1 I St. 1 Mer.

Planet. Long. Lat. Declin. Asc. Dist.

0 16111.541 - 16s.541224 251 13 58 Log. 1.11018

Semi- Hor. A r c A r c . ---

O f O f

67 31 53 33 -42586 -52651 -- 85 28 52 51 '32348 '53223 --

112 14 38 39 -20515 "66812

cusp Dist.

0 I

13 58 1~1i018

4 8 1.63597

1 14 2-16419 -- 6 54' 1-41642

I t will be seen that the planet Saturn is the most potent in the horoscope, its influence being very sinister. Not only is Saturn rising, being only i033'from the horizon, but it is also in close zodiacal square to the Moon and semi-square to the Sun. The Sun is also afflicted by a square of Neptune, and because of this great affliction of the luminaries it was thought by some astrologers that H.R.H. would never fully assume the office and title of

King. But not only are the luminaries in elevation, but the Sun has the sextile of Mars from its exaltation sign Capricornus, its action being strengthened from its being angular and rising. The Moon is proceeding to the mundane trine aspect of Jupiter, while the Mid- heaven is supported by the trine aspect of Neptune in mundo and the sextile of Saturn in the Zodiac. The Sun is near the mundane parallel of Venus and the Ascendant has a mundane trine of the Moon and a near influence of Jupiter. The mundane positions are certainly very strong and with five planets above the horizon and no less than seven rising, the full title and honours of kingship would follow as a consequence of this horoscope being that of the true and rightful heir t o the Throne, which God defend.

Taking this horoscope as the illustration of our study, we may pass on to the subject of Primary Directions in Mqndo and in Zodiaco, by which the periods of all great changes in health and fortune may be determined with great accuracy.

C H A P T E R

AN arc of direction is the distance which separates one body from another, or one body from the position of another, or its aspect. Such distance is measured by the Equatorial degrees which pass under the meridian from the moment of birth to the moment when the direction is completed.

The original position of a body, either in the zodiac or in the circle of observation, is always that to which direction is made.

Mundane Directions are those which are made to the apparent position of a celestial body, or its aspects, in the circle of observation, or Prime Vertical.

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.

All Directions are formed by the rotation of the Earth on its axis, by which the planets are apparently carried from East to West, rising, culminating and setting in the circle of observation ; or by which a localised impress of a planet is carried from W. to E. against the apparent motion of the heavens. The lines thus traversed by these bodies are practically parallel to the Equator, and a t distances determined by their declinations.

The horizon of any place cuts the Equator at an angle equal to its geographical latitude.

Careful study of the figure annexed to Chapter XVI. will make the preceding observations perfectly clear.

Both the Mundane and Zodiacal Directions may be either direct or converse. Mundane " Direct Directions " are those which are formed by a body moving West-

ward when above the horizon and Eastward when under the horizon.

" Converse Directions " are exactly the reverse of this. Some writers have deemed these directions to b e pre-natal, and on first sight it would appear that they are so. Thus, in the horoscope before us, if we bring the Moon to a conjunction with Venus conversely, we direct the Moon along its own arc till it reaches a meridian distance (proportionate to its semi-arc), equivalent to that held by Venus. Here it looks as if we took the Moon backwards to a position it held about an hour before the birth.

Such, however, is not the case. The fact is that every planet throws a direct ray to the place of birth a s well as oblique rays in other directions. The direct ray is called its Earth-line, and it is this line which, by the rotation of the earth on its axis, is carried from West to East, conveying th-3 localised influence of that one body to a point wheie it meets the localised influence or Earth-line of another body that is following i t in the heavens.

Therefore all directions are formed by the one natural fact of the Earth's rotation. The more important directions are those made to the meridian, horizon, their zodiacal equivalents8(the Mid-heaven and Ascend- ant), and the Sun and Moon. All these Significatovs, as they are called, are themselves directed to the planets.

The method of calculating Arcs of Direction may now be explained, and examplesof every kind of direction adduced in illustration.

CHAPTER IV.

A SIGNIFICATOR or planet may be directed in mundo t o a conjunction, aspect, parallel, or rapt parallel of another.

The body (or its aspect) to which direction is made, is supposed to remain stationary, while the directed body moves to it along its own arc.

The universal formula for all directions, whether mundane or zodiacal, is as follows :-

As the semi-arc of the stationary body or aspect Is to its meridian, horizontal, or cuspal distance, So i s the semi-arc of the moving body To its proportional distance.

The difference between this proportional distance of t he moving body and its original distance is the

Arc of Direction.

CONJUNCTION I N MUNDO

Bring the body directed along its own arc till it reaches the body of another a s seen from the place of birth.

EXAMPLES

I . Direct Venus to conjunction with Moon in mundo. As Semi-arc D 85'28' p. log. -32348

(a.c.) 9.67652 To Merid. Dist. ) 32'37' p. log. - .74183 To Semi-arc ? 82'26' ,,

--- -33917

To Prop. Dist. ? 31'28' ,, ¥7575 1st Dist. ?12' 3' ,,

Are of Direction 19'25' ? d D mundo.

This is a d i m < direction of Venus in mundo. I t produced pleasant experiences abroad and led toward marriage. Venus is in the ninth house (foreigners) and the T) on its cusp.

2. Direct the Sun to conjunction mundo.

Semi-arc V 57O44' log.

(a.c.) Merid. Dist. ~ 9 6 ' ,, Semi-arc 667031' ,,

Prop. Dist. . 058~47' ,, - 1st Dist. 0 13~58' ,,

Arc of Direction 4404gr 0 rf m. con.

with Jupiter i n

This is a converse direction of the Sun. The Sun's. Earth-line is carried Eastward by the rotation of the Earth till it coincides with Jupiter's Earth-line. I t was fortunate in relation to equine sports, l(. being in the twelfth in 1.

3. Direct Uranus to conjunction Ascendant in mundo. The meridian distance subtracted from the semi-arc

of Uranus will give the planet's distance from the horizon, or horizontal arc, as shown in the speculum, viz . ,

Arc of Direction, I# d Asc. 56'51'.

This direction signifies accidents to the limbs and feet, also complications in finance, as tf is in the second house at birth.

4. Direct Saturn to conjunction Mid-heaven in mundo. The Right Ascension of Saturn minus Right Ascen-

sion of Mid-heaven will give the meridian distance of Saturn, as already shown in the speculum. This is the

Arc of Direction, 5 rf M.C. 5g043'.

This influence is evil for life and fortunes, liable to. generate serious illness and to produce depression in affairs of State. Saturn afflicting the Ascendant at birth renders its influence more evil.

CHAPTER V.

MUNDANE aspects are measured from the cusps of the houses. Thus : a planet being on the cusp of the eleventh house will be in mundane sextile 60Â to the Ascendant, and in square go0 to another planet which may be on the cusp of the eighth house. A planet in the middle of the second house would be in semi-square 45O to the Ascendant, and in sesquiquadrate lyjO to the Mid-heaven. t

Therefore to direct a planet to the aspect of another in mundo, we have to bring it to an equivalent distance from the cusp of that house in which the aspect is formed.

EXAMPLES

I. Bring the Sun to a trine of Neptune in mundo. Neptune is i014' inside the cusp of the second house ;

we must .therefore direct the Sun to an equivalent distance inside the cusp of the tenth.

Semi-arc (~ÈIIZOI~ log. .205 15

(a.c.) 9.79485 Cusp. Dist. V 1'14' ,, 2-16419 Semi-arc 0 67'31' ,, .42586

-- Prop. Dist. 0 0'45' ,, 2.38490 1st Dist. 0 13'58' ,, -- Arc of Direction 13~x3' O A Y m.

Having determined the arc of any one aspect in

mundo we have only to add or subtract, successively, one-sixth, one-third, one-half, or two-thirds of the setni- arc of the directed body, in order to obtain all its other aspects, both direct and converse. Thus :-

Arc of Direction - 13 13 Q ~ y r n u n d o . & Semi-arc - 11 15

Arc of Direction - 24 28 0 Q y mundo. A Semi-arc - 33 45

Arc of Direction, - 58 13 0 8ql mundo.,

These are direct directions in mundo. For the converse we bring the Sun along its own arc into the eleventh and twelfth houses.

Sem'i-arc Mer. Dist.

Dist. from 11th Add Prop. Dist.

Arc of Direction Semi-arc

Arc of Direction Semi-arc

A rc of Direction

- , 8 3 2 - 0 45 - - g 17 0 u y m. con., - 22 30 - - 31 47 0 36 V m. con. - 11 15 - - 43 2 0 ~ y m . c o n . -

These are converse directions, and are formed by the rotation of the Earth on .its axis from W. to E., the localised influence of the Sun, which is originally 13'58' E. of the meridian, being carried eastward, to points in the circle of observation where it meets the localised influence of the planet Neptune.

Note.-If, as some have erroneously stated, these converse directions are pre-natal, the Sun itself being directed to a place it occupied so many hours and minutes before birth, then the. whole process is falsely conceived. For it must be apparent to the meanest intellect that kh'en the' Sun was 0°45 from 'f the cusp of

the twelfth house, Neptune had not yet arrived at the equivalent distance from the cusp of the second-where we find it at the birth-but was close to the cusp of the third house.

Therefore the Sun itself cannot be conversely directed to the sextile of Neptune's radical place in mundo, for how can a body support a position that is not yet assumed ?

I t is the local impress of the solar influence at birth which is carried backward to form aspects with the radical place of Neptune, and the single axial motion of the Earth from W. to E. is the sole basis of all directions, whether direct or converse, mundane or zodiacal. -

2. Bring Saturn to its aspects of the Ascendant in mundo.

0 I

Hor. Arc of $ I 33 $ d Asc. m. 4 Semi-arc - 29 5

Arc of Direction - 30 38 $ L Asc. m. Semi-arc - 9 42

Arc of Direction - 40 20 ^ * A S C . ~ . 3 Semi-arc - I9 23

Arc of Direction - 59 43 1? ASC. m.

Note.-The mundane conjunction of Saturn with Ascendant 1 ~ 3 3 ' is also the arc of 5 a Mid-heaven in mundo, and 5 a Ascendant m. 59'43' is also the arc for 5 rf M.C. in mundo.

For the converse directions of Saturn in mundo we have to take the contra-semi-arc (Nocturnal) of Saturn as he is below the horizon when forming these aspects :

0 I

From 180 o Diurnal Semi-arc - 58 10

Nocturnal ,, - 121 50

One-half ,, - 60 55 Hor. Arc $ - - 1 33

Arc of Direction - 59 22 12, f Asc. m. Semi-arc - 20 18

Arc of Direction,

3. Bring Venus 10

mundo.

Venus Semi-arc One-half ,, Mer. Dist. . .

Arc of Direction & Semi-arc

Arc o/Direction 3 Semi-arc

Arc of Direction

- 79 40 '2 * Asc. m.

aspects of the Mid-heaven. in,

- 29 10 ? f M.C. m. - 1 3 4 4

- 42 54 ? M.C. m. - 27 29

- 70 23 ? a M.C. m.

This latter aspect of $ to M.C. is the same as the mundane opposition to the Ascendant, and is measured by the horizontal arc of Venus.

These mundane directions of the planets to the Mid- heaven and Ascendant are extremely simple and facile, being merely a part of the semi-arc less the meridian distance of each planet.. The conjunctions, oppositions and quadratures are already included in the speculum under the meridian distance and horizontal arc of each planet.

4. Bring the Mid-heaven to aspects of the Sun in mundo.

Here we have to bring the meridian degree "nfs038' along its own arc to equivalent distances from the cusps of the houses in proportion to the Sun's distance, 13v' from tenth.

Semi-arc 067 31 log. - -42586

(a.c.) 9'57414 Mer. Dist. 013 58 ,, 1~11018 Semi-arc M.C. , 73 56 ,, - -38643

Prop. Dist. M.C. 15 18 log. 1.07075 A Semi-arc 36 58

A re o f Direction Semi-arc

Arc of Direction & Semi-arc

Arc of Direction

The Ascendant dane aspects by a the planets.

21 40 M.C. L o mundo. 12 19 ,

- 33 59 M.C. * 0 mundo. 24 39

58 38 M.C. 00 mundo. - is directed in the same way to mun- proportion of its semi-arc to those of

CHAPTER VI.

A MUNDANE parallel is formed by one planet coming to an equivalent distance on one side of the meridian or horizon as another body on the other side of the same meridian or horizon. A parallel can therefore be formed by the approach of a body to the upper and lower meridians and to the east and west horizons,

Note.-Some writers on this subject have repudiated the parallels formed upon the horizon, but without adducing adequate reason for so doing, and, indeed, tradition has been allowed too much weight on many points of vital moment. Yet the same writers have not denied the validity of parallels formed on the same side of the meridian, one south and the other north, as in the fourth and ninth houses, the tenth and third, nor have they seen that planets thus placed must be at equal distances from the horizon !

The rule is the same as for the aspects., i.e., as the semi-arc of the stationary body is to its meridian distance (or horizontal arc), so is the semi-arc of the moving bodyto its proportionate meridian or horizontal distance.

EXAMPLES

I. Bring Jupiter to a meridian parallel of the Moon. The Moon is near the cusp of the ninth house. W e

must, therefore, bring Jupiter up to the eleventh to form the mundane parallel.,

0 r

Semi-arc D 85 28 log. -32348 --

( a , ~ . ) Mer. Dist.

9'67652 D32 37 s *

- .74183 Semi-arc 11-57 44 * S '49385

Prop. Dist. . 22 2 log. .91220 1st Dist. 50 16 - Arcpf Direction 28 14 3 par. D mundo. -

2. Bring the Moon to the meridian parallel of Jupiter. This is the reverse of the above problem.

0 I

Semi-arc 357 44 log. -49385

(a.c.) 9'50615 Mer. Dist. 2/50 16 ,, - -55399 Semi-arc £8 28 - .32348

Prop. Dist. D74 25 11 - -38362 1st Dist. D32 37 - Arc of Direction 41 48 1) par. 2j mundo.

3. Bring the Sun to the horizontal parallel of Neptune. 0 1

Semi-arc Y112 14 log. - ,20515

(a.c.) .- 9-79485

Hor. Arc f 38 39 9 . .66812 Semi-arc 0 67 31 I S .42586 -- Prop. Dist. 0 23 15 . I *88883 1st Dist. 0 53 33

Arc ef Direction 30 18 0 par. (f mundo.

This is a converse direction of the Sun to an equiva- lent distance from the horizon to that of Neptune.

4. Bring the Sun to a horizontal parallel of Saturn.

Semi-arc 5121 50 log. - -1 695 I 8

(a.c.) 9.83049 Hor. Arc. '? 1 33 , a 2'0'5494 Semi-arc 0 67 31 -42586 - Prop. Dist, 0 0 52 ,, 2.32129 1st Dist. 0 53 '33 - Arc of Direction 52 41 0 par. 5 mundo

,-

The nocturnal arc of Saturn in relation to its hori- zontal distance is here taken as in the preceding case of Neptune, and the Sun is brought conversely to an equi- valent distance from the horizon on the south side as Saturn is on the north. Whatever may be the opinion of others, in my experience these parallels are of consider- able efficacy and fall naturally into line with other directions of similar import occurring at or about the same time. L L Raphael " (R. C. Smith) in his Manual, after defining the mundane parallel as the same dis- tance on opposite sides of the meridian, remarks that he has not found those formed upon the horizon to be significant.

Later writers, however, are not of the same opinion, for we continually find that a parallel formed upon the same side of the meridian but in different quadrants, is admitted into the category of operative directions. Now, two bodies at equivalent distances on the same side of the meridian, and in different quadrants, are at equiva- lent distances on opposite sides of the same horizon ; and as the parallel is more correctly defined by " an equivalent distance on opposite sides of an angle," I have employed the horizontal distance instead of the meridian distance of the Sun in directing it to a mundane parallel with Saturn. The result is the same if we bring 0 to an equivalent from the tenth as Saturn is from the fourth.

Semi-arc 5 121 50 log: - -16951

(a.c.) 9.83049 Mer. Dist. '? 120 17 # I - ¥I750 Semi-arc 0 67 31 ,, -42586

Prop. Dist. 0 66 40 ¥4314 1st Dist. 0 13 58

Are a/ Direction, 52 42 0 par. 5 mundo.

I t will be expedient to distinguish between parallels formedon the meridian and those on the horizon, thus: 3)m.p. -U. 41' 48', @ h.p. 5 52' 42'.

CHAPTER VII.

RAPT parallels are formed by the apparent motion of the heavens, or by the rotation of the Earth, whereby any two bodies, or their places, are carried to an equal distance on opposite sides of the same angle, whether it be the meridian or the horizon.

In making this statement I am extending the observa- tion of former writers who recognise only the rapt parallel formed by direct direction upon the meridian angle. My experience includes also those formed conversely on the same angle, and I include the horizon in this observation. The student may follow me in one or two illustrations. The rule for the calculation is as follows :

Rule.-As half the sum of the semi-arcs of the two bodies is to half the sum of their meridian (or horizontal) distances, so is the semi-arc of the body applying to the angle to its distance from that angle at the formation of the parallel.

EXAMPLES

I. Bring the Moon and Saturn to a rapt parallel upon the upper meridian.

Here we propose to bring the Moon down the western sky and Saturn up the eastern sky by the apparent motion of the heavens. At the formation of the parallel, Saturn will be applying to the meridian, while the Moon will be separating from it.

Semi-arc ~ 8 5 28 I # $ 5 8 10

2) 143 38

sum of S.A. - -39905

(a. c.) 9.60095 Mer. Dist. . D 32 . 37

I s s t b59 43 . . . . . 2) 9 2 20

sum of M.D. 46. 10 - '59094 Semi-arc >? 58 10 "49060

*Prop. Dist. b37 24 I S . -68249 1st Dist. $59 43

Arc of Direction 22 19 rapt. par. 1)

As Saturn is above'the horizon at the time of this parallel, we have taken its diurnal semi-arc. 2. Bring the Moon and Sun to a rapt parallel upon

the, upper meridian. 0 I

Semi-arc 067 31 I I 185 28

2) 152 59 -- sum S.A. 76 29 log. - -37171

(as.) 9-62829 Mer. Dist. 013 58

t t s t 132 37

& sum M.D. . 23 17 log. - ~88823 Semi-arc ~ 8 5 28 ,, -32348

Prop. Dist. , T) 26 I - *8400o 1st Dist. D32 37

Art of Direction , 6 36 D rapt. par. 0

This is a converse direction, formed by the rotation of the Earth from W. to E., whereby the mundane places of the Moon and Sun are carried eastward t o equivalent distances on opposite sides of the upper meridian.

3. Bring the Sun to a rapt parallel with Saturft on . .. the east, horizon.

Semi-arc 0 67 31 I s $121 50 --

2) 189 21

4 sum of S.A. 94 40 1%. - .27908 -- (a.c.) 9.72092

Hor. Arc 0 53 33 I f I f T? 1 33

* sum of H.A. 27 33 log. -81515 Semi-arc 0 6 7 31 -42586

Prop. Dist. 0 1 9 39 9 , ,96193 1st Dist. a 5 3 33

Arc of Direction 33 54 0 rapt. par. 5

I t will be observed that, as Saturn is below the horizon when the parallel is formed, his nocturnal arc is employed, while the Sun being above the horizon, his diurnal arc is that used.

4. Bring Jupiter to a rapt parallel with the Sun on the E. horizon.

Semi-arc I I

sum of S.A.

Hor. Dist. I > Ã ˆ

2) 61 I sum H.A.' 30 30 10% - '77097

Semi-arc 0 67 31 ,. - -42586

Prop. Dist. 0 21- 42 1 ,, . '91875 1st Dist. 0 53 33

Arc of Direction 3s 51 0 rapt. par. if.

The nocturnal arc of l(. is employed in this problem, as he has to pass below the horizon to form this parallel, i.e., the mundane places of the Sun and Jupiter are carried eastward by the Earth's rotation till they come to an equal distance on opposite sides of the horizon.

This concludes the directions termed " Mundane." In effect they are very powerful, being formed by the direct rays of the various bodies to the place of birth.

CHAPTER VIII.

THESE directions are in all respects similar to the mundane, save that, instead of bringing the significator to the body of a planet we direct to the longitude of that planet, taking the meridian distance and semi-arc of that longitude or ecliptic degree.

Directions in zodiaco may be direct or converse. Thus, if we direct a body in Libra to the longitude of one in Scorpio, the direction is direct; but when directing a body in Libra to the longitude of another in Virgo, the direction is converse, being contrary to the order of the signs.

In all cases we direct the body of a planet to the longitude of another. In this sense the meridian and horizon are considered as "bodies," and are directed to the longitudes of the planets.

Directions may be to conjunction or aspect. The zodia- cal parallel is also included by most writers on this subject. Personally, I conceive the direction to a parallel to be ill-founded and extremely difficult of scrutiny. The method consists in taking the declina- tion of the planet to which direction is made ; finding a degree of the zodiac whose declination is the same; and then taking the semi-arc and meridian distance of this longitude, after which the body directed is brought to a conjunction with this degree in the manner already explained. Excepting t h e equinoctial and solstitial points there are four degrees in the zodiac having the same declination as each planet. The Moon, however, sometimes has greater declination than the Tropics, in which case the planets cannot, by this method, be

brought to a parallel of the Moon. But all this seems beside the mark, for it is obvious that a parallel of declination is equal distance above and below the Equator. Not by any mathematics can a body having 13O of declination be brought by direction (i.e., by the rotation of the Earth) to 7 O or 15' of declination. I t has already been explained ' that the rotation of the Earth causes the planets to traverse arcs from E. to W. which are parallel to the Equator, and at distances which are determined by the declinations of the several bodies.

To bring a body to the conjunction of a degree in the zodiac (as seen from the place of observation) is not the same as bringing that body to the same distance from the Equator. The fact is, these parallels form no part of a true system of Primary Directions, but belong solely to Secondary directions. I t is conceivably possible that the correct method of dealing with these zodiacal positions of the planets so as to form parallels, would be to direct them by their semi-arcs, to equivalent distances on opposite sides of the angles and also to rapt parallels in the same way. Thus, the Sun's place q16O54' could be brought along its semi-arc to an equivalent distance on the East of the meridian as is the Moon's long. ng2g027' on the West of it.

In the same manner q16O54' and q2g027' could be brought to a rapt parallel on the upper meridian. The theory presumes the planets to be operative in the degrees of their respective longitudes, and their influences to be thence reflected to the individual-neither of which concepts are contrary to the principles of the science. I have not, however, had opportunity for testing this theory.

CHAPTER IX.

CONJUNCTIONS IN ZODIAC

FOR the Mid-heaven, take the Right Ascension of the longitude of the planet to which direction is made. The difference between this and the R.A. of the Mid-heaven, will be the Arc of Direction.

For the Ascendant, take the Oblique Ascension of the longitude of the planet. The difference between this and the Oblique Ascension of the Ascendant will be the Arc of Direction.

For the Sun, Moon, and Planets, find the R.A. and declination of the longitude to which direction is made, and calculate thereby its meridian distance and semi- arc.. Then proceed as for the calculation of a conjunc- tion in mundo. As the semi-arc of the lotzgitude is to its meridian distance, so is the semi-arc of the moving body to its proportional distance from the meridian. Take this from that body's original distance, and there remains the

Arc of Direction.

EXAMPLES

I. Bring the Mid-heaven to conjunction with Moon in zodiac.

0 I

J) 's long. ~ 2 9 ~ 2 7 ~ R.A. - - I79 29 R.A. of Mid-heaven - 210 27

Arc of Direction M.C. d p 30 58

2. Bring the Mid-heaven to conjunction with Saturn in the zodiac.

f^ 's long. VJ oOg' R.A. - - 270 9 R.A. of Mid-heaven - 210 27

Are of Direction M.C. d i; 59 42

The first example-is a converse direction, the second is direct.

3. ring the Ascendant to conjunction with Uranus in zodiac, direct.

0 ' 3's long. xzo037' R.A. - - 351 23 Asc. Diff. (add) - - 4 42

Obi. ASC. ~20'37' 356 5 Obi. ASC. of Ascdt. - 300 27

Arc of Direction Asc. d 55 38

If we add 55'38' to the Right Ascension of the Mid-heaven 2 io027', we shall obtain Right Ascension 266O5' which is equivalent to f 26'24'30", and when this comes to the meridian of London, x20°37' the longitude of Uranus is rising.

4. Bring the Ascendant to conjunction with Sun in zodiac, converse.

0 ' s long. 7ti.16~54' R.A. - - 224 25 Asc. Diff. (add) - 22 29

Obi. Asc. of in16O54' - 246 54 Obi. ASC. of Ascdt. - 300 27

Arc of Direction Asc. d O 53 33

Note.-As the Sun is on the ecliptic, its Oblique Ascension and that of its longitude are the same. The direction is therefore identical with the converse mun- dane direction of 0 d Ascendant 53'33'.

5. Bring Venus to conjunction with the Moon in zodiac, converse.

The p's longitude is q2g027', the Right Ascension of which is i7g02g', its meridian distance 30°58 (see Exam. I of this series). The declination of q 2 g 0 q ' is 0°13' its ascensional difference is 0°17 for London, and its semi-arc is therefore go017'. Then we say :-

0 I

AS Semi-arc go 17 log. ,29967

(a.c.) 9.70033 To Mer. Dist. 30 58 , I .76438 So Semi-arc ? 82 26 ,, . -33917

T o Prop. Dist ? 28 16 -80388 Subt. 1st Dist. 9 12 2

Arc of Direction 16 14 ? d T) zod. con.

6. Bring the Sun to conjunction with Saturn in zodiac, direct.

Saturn's longitude is ^yoOgt, which has Right Ascen- sion 270°g' its meridian distance being 5g042' (see Exam. 2 in this series). The declination of woOgt is 23O27', its ascensional difference 33O6' for London, and its semi-arc - - ~ 6 ~ 5 4 ' .

Note.-We take the diurnal semi-arc of WOOQ' and its - - d

distance from the upper meridian for convenience of proportion to the known factors of the Sun.

0 ' Semi-arc 56 54 1%- ¥5001

(a.c.) .49984 Mer. Dist. 59 42 S t ¥4793 Semi-arc 067 31 .. *42586

--- Prop. Dist 070 50 Ã '40500 1st Dist. 013 58 -- Arc of Direction 56 52 0 d 12 zod. d.

7. Bring the Moon to conjunction Moon in zodiac, converse.

This unique direction is inserted for the purpose of illustrating the fact that from the point of view of an observer, the body of a planet having latitude is not in

the same position as the longitude of that planet, and consequently an Arc of Direction may'be measured in all such cases. Owing to the inclination of the Moon's orbit to the Ecliptic being greater than that of the other bodies, the difference between its Right Ascension and the R.A. of its longitude is more marked. As to what effects may be due to the direction of Moon to Moon's place in zodiac, I must defer judgment, but the Moon to its own aspects in zodiac produces changes and favour or disfavour of women, the public, etc.-accord- ing to the nature of the aspect and attendant directions.

But here is the calculation :- D'S long. m 29'27' has R.A. 17g0zg', its meridian

distance being 3oC58'. Its declination 0°i3 gives Asc. Diff. 0°i7 and its semi-arc is therefore 90~17'.

Semi-arc go 17 log. .29967

(a.c.) 9.70033 Mer. Dist. 30 58 , , -76438 Semi-arc D85 28 i i -32348

Prop. Dist. D29 19 i i *78819 1st Dist. D32 37

Are of Direction 3 18 D d D zod. con.

Note.-Possibly a direction of this nature imports the influence of the D'S radical aspects, developing those changes in the constitution which are so often effected by infantile complaints.

CHAPTER

WE have already directed the Mid-heaven, Ascendant, etc., to the longitudes of the planets for the conjunction in zodiac, and we now have to direct them to aspects of those longitudes. The process is in every way similar, the Mid-heaven being directed by R.A., the Ascendant by Oblique Ascension, and the planetary bodies (includ- ing 0 and I)) by proportion of their semi-arcs.

EXAMPLES

I. Bring the Mid-heaven to the square of Moon in zodiac, direct.

The Moon's long. is vy^2g027', its squar,e falls in f 2g027', the R.A. of which is 26g025'.

G I

R.A. f2Q027' - - 269 24 R.A. of M.C. - - 210 27

Arc of Direction 58 57 M.C. a I) zod.

2. Bring the Mid-heaven to the sextile of Sun in zodiac, converse. 1

The Sun's long. is 1~16~54 ' , the converse sextile being vy 16O54', the R.A. of which is 167'57', its meridian distance (210~27'-167~57') 4z030' ; Arc of Direction M.C. ¥X @ zod. con.

3. Bring the Ascendant to sextile Jupiter in zodiac, direct.

Jupiter's longitude f 21~28' has its sextile in ,%c¥21~28' the Right Ascension of which is 323O52', and its

ascensional difference 18O47', gives its Oblique Ascen- sion 34203g1.

O f .

Obi. Asc. of Aspect - - 342 39 Obi. &c. of A~cdt. - 300 27

Arc of Direction Asc. * 42 12

4. Bring the Ascendant to opposition Moon in zodiac, direct.

We have already found the Right Ascension of 1)'s longitude n12g027' to be i7g02g', and its ascensional difference to be 0°i7' W e therefore proceed :

R.A.n~zg~z7 ' - - I79 29 180Â + Asc. Diff. - 180 17

Obi. Asc. of x 29'27' 359 46 Obi. ASC. of A~cdt . - 300 27

Arc of Direction Asc. 8 D 59 19

Here we bring the opposition point of the 1)'s longi- tude to conjunction with the Ascendant, which is the same as directing the Ascendant to opposition Moon.

5. Bring the Sun to the opposition of Neptune in the zodiac, converse.

Neptune's longitude is Z Z I ~ O ~ I ' , the opposition of which is &i402if, its Right Ascension 136¡50f and its meridian distance 73O37'. I ts ascensional difference is 21~58'~ which gives a diurnal semi-arc of I I 1'58'. Then :

0 I

Semi-arc 111 58 log. -20618 -- (a.c.) 979382

Mer. Dist. 73 37 - # .38830 Semi-arc 067 31 .. .42586

Prop. Dist. 044 23 B~ -60798 1st Dist. 0 1 3 58 -- Arc of Direction 58 21 0 <? V zod. con.

Note.-As the Sun has to cross the meridian to form this aspect we add its first distance, 13'58', to its pro- portional distance on the other side of the meridian, to obtain the full arc of the Sun's direction.

6. Bring the Moon to the square of Sun in zodiac, converse.

The square of 0 (converse) falls in &16O54', the Right Ascension of which is 13g022', its meridian distance being 71~5'. I ts ascensional difference is 20°5i' which gives its semi-arc I 10~51'. Then :

0 I

Semi-arc 110 51 log. -21054

(a c.) 9-78946 Mer. Dist. 71 5 9 , -40350 Semi-arc I185 28 e l .32348 .-- Prop. Dist. D54 48 ,I 31644 1st Dist. 5 3 2 37 - Arc oJDirection 22 11 D a 0 zod. con.

7. Direct Venus to the sextile of Moon in zodiac, direct.

The direct zodiacal sextile of the D'S longitude is n^,2g027', the Right Ascension of which is 237O13~, meridian distance 26O4.6'. Its ascensional difference is 27O21', and its semi-arc 6203g1. Then :

Semi-arc 62 39 log. -45835

(a.c.) 9.54165 Mer. Dist. 26 46 * I .82768 Semi-arc 982 26 ,, -33917

-- Prop. Dist. 935 I3 , I -70850 1st Dist. ? 12 2

Arc of Direction 47 15 ? * D zod. d.

Note.-As Venus has to cross the meridian to form the aspect, the proportional distance on the E. side of the meridian is added to its original distance on the W. side to obtain the arc traversed.

I t will be noticed that the directions in the zodiac direct are formed by the same natural fact as mundane converse directions, viz.i the axial rotation of the Earth. The body of a planet is believed to impress its influence upon the Earth at the moment of birth, by a right line of influence. By the Earth's rotation, the locality thus impressed is brought eastward till it forms its conjunc- tion with the rays of another body, or comes into line with a zodiacal point, as seen from the place of birth,

W e have now taken examples of every kind of direction, both mundane and zodiacal, which can be accommodated to the principles of primary direction in the circle of observation.

The TABLES will be found of great use in computing the semi-arcs of the planets, the Right Ascensions of zodiacal positions and aspects, and the Oblique Ascen- sions of all zodiacal points.

CHAPTER XI.

THE student will do well to employ some definite order of calculation, otherwise he will be sure to over- look many directions which, belonging to a series, become very important in association with others of a like nature, or of contrary nature. For instance, in a series or train of evil directions falling out in a particular year of life, a good direction of the hyleg to Jupiter will generally convert a judgment of death into one of serious illness, from which the native recovers. In short, such a direction would indicate a favourable crisis. I t is therefore important to have all the directions calculated.

The ' following is suggested as the most convenient order of procedure.

I. Take the Mundane Directions first. I. Direct all the bodies to aspects and conjunctions

with the Ascendant : ( a ) from E. to W. ; ( b ) from W. to E. 2. Direct all the bodies to aspects and conjunctions

with the Mid-heaven: ( a ) from E. to W. ; ( b ) from W . to E.

3. Direct the Sun to the other bodies in mundo : (a) from E. to W . ; ( b ) from W. to E.

4. Direct the Moon to the other bodies in mundo : (a) from E. to W. ; ( b ) from W . to E.

5. Do the same with each of the planets, directing them separately and in turn to the 0 and to the Moon, first from E. to W., and next from W. to E.

6. Direct the a to mundane parallels with the I) and planets.

7. Direct the Q to rapt parallels with the T) and planets.

8. Direct the Moon to mundane parallels with the @ and planets.

9. Direct the Moon to rapt parallels with the 0 and planets.

This completes the Mundane Directions. 11. Take next the Zodiacal Directions. Follow the same order as for Mundane Directions,

omitting classes 6, 7, 8, and 9, which are not formed in the zodiac.

Remember that in Zodiacal Directions a body is always moved to a longitude to form a conjunction or aspect, and that the meridian and horizon are in this sense regarded as bodies. A longitude is never directed to a body.

Note.-The meridian and horizon are, for convenience, called the Mid-heaven and Ascendant, though these latter terms really refer to the ecliptic degrees which, at birth, occupy those angles. The meridian and hori- zon have fixed relations to the place of birth, which is not the case with the zodiacal positions associated with them at the moment of a nativity.

All this may appear very tedious, and no doubt it does require patience and method. But once done it serves for a lifetime, a point to be remembered, more especially when, by the possession of such a chart, we may wisely direct our course in such way as to beware of dangerous shoals, sandbanks, and breakers-or, if not able to do this, at least to make proper provision against the evil hour, and to redouble our efforts when under benefic influences, and so to order our affairs wisely and bring our lives to a peaceful end. Sudden death cannot overtake the man who foresees his end years in advance, and the keen edge of many afflictions, to which a 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 unhurt. Therefore, rather than pray that what is foreordained by the laws of life in regard to the inscrutable ends thereof, may be averted, let us say with the Psalmist : " Teach me the number of my days that I may apply my heart unto wisdom," for "the wise man foreseeth the evil and hideth himself the ignorant pass on and are hurt."

CHAPTER XII.

THE EFFECTS OF DIRECTIONS

OBSERVE the house originally occupied by the body that is moved to form the aspect, and take this as a general indication of the source of good or evil. That house to which the body moves in order to form the Arc of Direction is also of some significance, as also the sign to which it is radically related.

Good Aspects : the sextile, quintile, trine, biquintile, the conjunction and parallel of the henefics, denote good effects. The Sun, Moon, and Mercury in conjunction or parallel are also benefic when well aspected at birth.

Evil Aspects, such as the square, sesquiquadrate, etc., and the opposition of all planets, the conjunction and parallel of y, I#, +, <y (and of the Sun, Moon, and Mercury when radically affected by ill aspects), denote evil effects.

The MID-HEAVEN and the S U N have general significa- tion of honour, credit, position, and family fortunes.

The ASCENDANT and MOON hold general signification of health, changes and personal fortunes.

The SUN denotes the father and male relatives, the MOON denotes the mother and female relatives.

N~pTuN~.-Events due to this planet are chaotic and mysterious, sometimes due to treachery, fraud or im- position. I t produces an involved state of affairs, and voluntary or enforced seclusion frequently follows. I ts influence is seductive, sybaritic, and disposes to the use of narcotics. The good aspects of Neptune bring benefits connected with art and the exercise of special faculty.

U~~Nus.-Sudden and unexpected events transpire

under the influence of this planet. Strange coincidences, romantic episodes, estrangements, bereavement and accidents are attributed to its aspects. I ts good aspects give favours from governmental and civic bodies.

SATURN has a lingering influence and, when he afflicts, he gives one plenty of time for reflecting. His good effects are lasting and the planet has a steadying in- fluence on the fortunes, when not depressing. H e hurts by cold, contraction, privation, and obstruction ; some- times by blows from heavy bodies or by falls producing contusion, broken bones, insensibility, etc. Favours from aged persons or benefits from old associations may be expected from his good aspects.

JUPITER in good aspect brings increase of fortune, advancement, honours, confidence, and good judgment in affairs of life. His ill aspects bring losses, errors of judgment, vanity or excessive confidence, disfavour of judges, priests and nobles. H e hurts by excess, surfeit, congestion, etc., giving "too much of a good thing," and disposing to what is popularly known as "the swollen head."

MARS brings activity, daring, enterprise, and decision. I t increases the executive powers and stimulates to expression of inherent faculty when in good aspect. His evil aspects bring loss of blood, burns, abrasions, cuts, and inflammatory action in the body. Also theft or loss by fire or other sudden disaster or loss. Military men, marines, surgeons, and workers in fire and iron are under his influence.

VENUS has chief influence in domestic affairs, and social life, and is the signification of the affections. I ts conjunction or good aspect denotes engagement or marriage, or the birth of a child if married. Its evil aspects are productive of bereavement, grief, disappoint- ment, 'domestic trouble, and evils resulting from young females.

' The SUN brings honours and advancement by his good aspects ; and by his evil aspects displeasure of superiors, governing bodies, masters, etc., also fevers and reversal of fortune.

The MOON brings changes, and benefits or troubles

through females of mature years, public bodies, and the populace, according to its aspect.

MERCURY is controlled in its effects by that planet to which it is in nearest aspect at birth, or if in no aspect, by the ruler of the sign it occupies. Its good aspects bring activity, increase of business, profitable jour- neys, gain by writing, etc., and its evil aspects produce worry, annoyances, evil news, sleeplessness, irregularity of life.

If Mercury at birth be in closest aspect to a benefic its conjunctions and good aspects will be much enjoyed ; but if associated with a malefic at birth, its conjunction, parallel or evil aspect can work great ill, and it may even prove to be the messenger of death.

THE MEASURE O F TIME

Allow one year for every degree of the Arc of Direc- tion and one month for every five minutes. The longer a body may be in the process of forming an arc of direc- tion, the longer will its effects be noticeable, not infre- quently beginning to operate several months before the climax of the Direction. A careful study of the nature of a direction, z.e., of its process of formation, is the only key to a correct time-measure of the duration of effects. Thus, for example, aspects to the Ascendant from signs of short ascension are rapid in formation and dissolution, while those from signs of long ascension are slower in passing the horizon : as, in the Royal Horoscope, T) 8 Ascendant in zod. 5g0xg' should register its effects promptly, owing to Pisces, a sign of short ascension, being then on the Ascendant; while @ 6 Ascendant zod. d. 53'33' should be more lasting in effect, as then the sign Scorpio would be associated with the horizon and is a sign of long ascension.

CHAPTER XIII.

IN reviewing the Arcs of Direction which have been used in illustration of our subject, it is impossible at this date to overlook the extreme significance of those attending the death of Queen Victoria, and those also preceding and following it.

Lhave collected them into order of their formation, and the array is certainly startling.

0 I

Uranus conjunct. Asc. mundo - 56 51 Ascdt. conjunct. -0 zod. - - 57 47 Sun opposit. if mundo - - 58 I3 Sun opposit. if zod. - 58 21

Mid-heaven square 0 mundo - 58 38 M.C. square T) zod. 58 58 Ascdt. semi-square if zod. - - 59 18 Ascdt. opposit. 1) zod. - - 59 I9 Saturn semi-square Asc. mundo - 59 22 M.C. conjunct. \ zod. - - 59 42 Saturn conjunct. M.C. mundo 59 43

The Arc of Direction for the King's age at the date of Queen Victoria's death is 5g014'.

ASC. 8 D zed. =5g019'

That of Sipido's attempt upon the King's life measures to 58'25'.

0 oppos. if z0d.=58~21'

The death of the Empress Frederic (Princess ~ o y a l ) which occurredin August, 1901, requires an arc of 5g045', and this is close to the Directions of Saturn to the M.C. in zod. and mundo 59'42'-43'.

This very untoward series of Directions could not fail

t o produce a succession of very disastrous effects. The Arc of Ascendant T) extends to February, 1902, before which there is an Eclipse of the Sun close to the Sun's place a t the nativity. The effects of Eclipses upon important places in the horoscopes cannot be over- estimated as they have a most baneful action upon the health and fortunes.

Thus, in the case of Empress Frederic, the Eclipse of Sun in November, 1900, fell close to the Sun's place a t her birth ( ~ 1 s t November, 1840) and that of May, 1901, fell in still closer opposition to the radical Sun.

I have in these pages illustrated every kind of direction that can legitimately be said to result from the apparent motion of the heavens in regard to a particular place of observation.

If the axial rotation of the Earth from West to EaGt be kept in view it is quite in~possible that the student can make topsy-turvydom of either mundane or zodiacal Directions. I use this latter term with all reserve, see- ing that they are not formed in the plane of the Ecliptic, as are Secondary or Progressive Directions, but to zodiacal places in the circle of observation, and that they are as much mundane as the others so named.

The use of logarithms of sines, tangents, etc., may a t first come awkwardly to the hand of the novice, but they are of such help to the mathematician in the construc- tion of a speculum from the Ephemeris, and in the pre- paration of astronomical tables, as to be practically in* dispensable. This boon we owe to Baron Napier of Murchiston, who constructed them for the purpose of astrological calculations, and in the same way we owe the comparative accuracy of our Ephemerides to the researches of Sir Isaac Newton, who, when a mere boy, picked up a second-hand work on Astrology and was so fascinated thereby that he commenced the study of Astronomy the better to master the book of Destiny. H e delivered much prophetic writing which the learned men of the University have thought it expedient to shelve ! The world has barely seen that other Sir Isaac, the prophet and interpreter of stellar influence.

Kepler, who demonstrated the Law of Areas, that of

Elliptic orbits, and the law of periodic squares, confesses that constant observation-'' An unfailing experience," ,hesays-of mundane eventsin harmony with the changes occurring in the heavens, had "instructed and compelled .his unwilling belief." Here is a master-mind, used t o the observation. of natural phenomena, and competent in every way to form an unbiassed opinion in a matter 'of this nature, compelled against his inclination to a belief in Astrology !

He calculated horoscopes for many illustrious con- temporaries. *So also did Tycho Brahe, the famous [Danish Astronomer, whose Rudolphine Tables are the model of those used by advanced astronomers to-day. H e invited Kepler to assist him in his great work, and died while it was yet unfinished. For many years he subsisted solely upon the proceeds of his horoscopical work. Seeing then. that the reader is in such honour- able company, let him persevere in his studies, and having convinced himself of the truth of the Science, let him not be ashamed to declare it. The contents of the following chapters form no part of the original plan of this work upon Prognostic Astronomy, which aims solely. at a clear exposition of the true method of calcu- lating arcs of direction. But I have too much respect for the critic not to lay my finger upon possible points of debate before handing my work over to his tender mercies. The student may concern himself, with them or not as he pleases.

CHAPTER XIV.

THE Part of Fortune or Lunar point is an ancient Egyptian symbol @I used as a hieroglyphic t o express 4' propertyy' or "'territory," and is so preserved in use by astrologers at the present day, though by astronomers it is sometimes used to signify the Earth.

In Astrology it is held to denote property of all kinds, but chiefly goods and chattels, land and house property.

The method of computing its position in the horo- scope is a matter of discussion. Some authors take its Ecliptic position and this would be correct if directions are made i n the plane of the Ecliptic as are Progressive or Secondary directions. The rule for finding its Ecliptic position is as follows :

Rule-Add together the longitude of the Ascendant and the longitude of the Moon, and subtract from their sum the longitude of the Sun.

Thus in the Royal Horoscope : s. 0 '

Long. Asc. 8 27 37 Long. D 5 29 27

14 27 4 Long. 0 7 16 54 -- Long. @ 7 -10 io=in.roO~o' --

But in Primary-Direction we are not concerned with any measures made in tire plane of the Elliptic, but solely with those made in the circle of observation, i.e., the prime vertical.

The rule is therefore as follows :

As the Moon's position is to the Sun's, so is that of the Part of Fortune to the Eastern horizon, measured in the circle of observation.

W e have therefore to find what space intervenes between the Sun and Moon as seen from the place of birth.

Bring the Moon in the Royal Horoscope to con- junction with Sun in mundo.

Semi-arc 0 6 7 31 log. - .42586

(a.c.) 9.57414 Mer. Dist. 0 1 3 58 - 1.11018 Semi-arc 3 8 5 28 ,* - - -32348

Prop. Dist D 1 7 ' 41 ,. . I -00780 1st Dist. D 32 37 - Arc of Direction 50 18 D d 0 m. con. -

If the Moon were in conjunction with the Sun in mundo, the @ would be exactly on the Ascendant. If the Moon were in opposition to Sun then @ would be on the west horizon. From the conjunction to opposi- tion of the luminaries the @ is under the horizon, and from the opposition to the conjunction, it is above the horizon. Hence, as the Moon is going to the conjunc- tion, the above distance 50~18' will be that of @ above the horizon.

Hence we have Horizontal Arc @ 50°18' Now the semi-arc of the Part of Fortune is always that of the Moon, diurnal if @ be above the horizon, and nocturnal if below it. In this case the @ is above the horizon and therefore has the Moon's semi-arc diurnal, viz., 85'28'. Then

0 I

Semi-arc - - @ 85 .28 Hor. Arc - - @ 50 18

Mer. Dist. - - R.A. of KC.-

@ 35 19 - 210 27

R.A. of @ 245 37

As the @ has the same semi-arc as the D, it must also have the same declination, viz., 3OS.36', and we are therefore able to obtain its longitude, if required. But as all directions to the Par t of Fortune must, on this basis, be mundane, the longitude is not required. T h e following are the requisite elements of the

PART OF FORTUNE

K . A . 1 Mtr. Dill. 1 Semi-Arc \ Hor. A n \ Cvf Dill.

The. @ is therefore in the eleventh house, 6'41' from i t s cusp.

I may now give one or two instances of directions to @ .

EXAMPLES

I. Bring q to conjunction @ in mundo.

Semi-arc @85 28 log. -32348

(ax.) 9'67652 Mer. Dist. @35 10 11 *70914 Semi-arc ' V.57 44 8 1 ,49385

Prop. Dist. 323 45 1 1 .87951 1st Dist. 3 5 0 16

Arc of Direction 26 31 ~ f . d @ --

2. Bring the Moon to the square aspect of a. This aspect will fall in the eighth house, being the

space of these houses measured on the semi-arc of the Moon. But as the semi-arc of the Moon and are the same we merely take the cuspal distance of the @ from the D'S distanceto the eighth cusp.

0

Semi-arc - - D56 59 Mer. Dist. - D32 57

D from 8th cusp - 24 22 @ from n t h cusp - 6 41

Arc of Direction I7 41 D a@

3. Bring Uranus to the square of @ in mundo. The aspect falls in the second house, from the cusp of which Uranus is situate 24O58', on a semi-arc of 95O37'.

0 .' Semi-arc @85 28 log. -32348

(a.c.) 9.67652 Cusp. Dist. @ 6 41 I, 1-43028 Semi-arc g 9 5 37 9 1 "27474

Prop. Dist. -

3 7 29 Ã 1.38154, 1st Dist. M24 58

Arc of Direction 17 29 M a @

I believe that the above method of computing the place of @ is the only true method, as being strictly in harmony with the basic principles of Primary Directions. I n any system in which. difference of longitude is the basis of measurement, I should simply take the longi- tude of the Part of Fortune, and in regard to transits, lunations and eclipses, I am sure that this is the correct point to observe.

Here, however, in the mundane system of directions, the basis is entirely different. I t is no longer mere longitude, but position of longitude in the prime vertical.

I t seems to me to be utterly beside the mark to regard the Part of Fortune as a ? myth" because it has no tangible existence, unless by the word we under-

stand a veil " hiding some great truth, as the ancient mythos and symbol always did. For what, after all, is the Mid-heaven or Ascendant but a particular degree of the Ecliptic which at the moment of birth happens t o be upon the meridian or horizon. And what is this " degree " ifknot an intangible point, a mathema- tical unit of space in an imaginary circle ? Yet what observer would deny the influence of these particular degrees or their specific signification ? I am afraid that, under the pretext of building up the science, there has been considerable tearing down and throwing about of good material by certain writers on this subject.

C H A P T E R XV.

THE apparent places of the planets given in the Ephemeris are computed from the standpoint of an observer supposed to be situated at the centre of the Earth. But the place o f observation being on the surface of the Earth and not at its centre, will affect the observed position of the various bodies.

&n the case. of the Sun and planets, their distances from the Earth are so great as to render this difference between their geocentric and observed positions of practically no account. But in regard to the Moon, i ts

A . EarWs centre. B. Place on Earth's surface. C. Moon's Geocentric long. D, Moon's Observed long.

nearness to the Earth renders the parallax of impor- tance, if we are to regard the Moon as effecting its influence by direct rays from its observed position t o the place of observation. The above sketch will show how the semi-diameter of the Earth effects the apparent position of the Moon. The effect is exagger- ated for the purpose of illustration. The Moon is, of course, proportionately much further from the Earth than the sketch indicates.

The Horizontal Parallax of the Moon is given in the Nautical Almanac each day for noonand midnight. The Parallax depends on the Moon's place in its orbit,, and consequently on its distance from the Earth, and it has to be corrected to the hour angle of the Moon at any moment. Supposing, for instance, that the Hori- zontal Parallax I) is given as 54' at noon on a particular day of the year. This means that at Greenwich noon the position of the T) in its orbit is such that wherever it may be on the horizon at that time, its observed posi- tion will differ from its geocentric position by 54'.

The Parallax is of course greatest when the Moon is in Perigee, i.e., nearest the Earth, and least when in Apogee, or farthest from Earth.

The longitude at which the Moon is farthest from the Earth is known as its Apogee, and from this point to its longitude at any date, measured on the Ecliptic, is the Moon's Anomaly. This Anomaly is increased daily by 13~4' nearly, while the Moon's mean longitude is in- creased daily by I 3O10'35". consequently, the Apogee of the Moon is moving forward at 6'35'' per day, and in the course of a year the Apogee of the Moon is actually advanced in the zodiac by 40~53'45". Hence, the Hori- zontal Parallax of the Moon is an irregular quantity so far as the Calendar is concerned. As, however, all respectable Almanacs give the dates in eachmonth when the I) is in Perigee and Apogee, an approximation to within a minute of space can be made in regard to the- 1)'s Parallax at any date. For at the Apogee the mean Parallax is 54'4" and does not vary more than a few seconds; while a t Perigee the mean Parallax is 60'19" and varies but little more than 1'.

The following Anomalistic Table will render the cal- culation of the place of the Moon's Apogee a matter of simple addition and subtraction.

ANOMALISTIC TABLES.

Epoch = o Jan. od. oh. om. 1800-Anomaly's gs. 20' 20'

Years add -

s. 0 I

2 28 43 5 27 27 8 26 10

0 7 57 3 6 40 6 5 24 9 4 7 0 15 54 3 I4 38 6 . 13 21

1 9 46 7 23 7 2 19 32 9 2 53 1 2 9 18

I0 12 39 5 9 , 3

11 22 24

Months add

Jan. Feb. March April May June July ' Aug. Sept. Oct. Nov. Dec.

Days add

W e may take an example of the use of these Tables. I t is stated in the Almanac for 1901 that the Moon is in Apogee on the 15th October. Let us test the Tables by this statement.

ANOMALY s. 0 r

Epoch 1800 - Add go - -

I, 10 - 11 I - , October , 15th - -

Anom. 15th October, 1901 Moon's long. -

Place of Apogee 7 13 22

Here we find by the Anomaly that the Moon is just past its Apogee at noon on the 15th October, 1901, the longitude of the Apogee being 1 ~ 1 3 ~ . : Recollecting then that the Anomaly of a body is i ts distance in longitude from its Apogee, we may at ones find the Horizontal Parallax for this Anomaly by means of the following Chord of Parallax, which I have invented for the purposes of this treatise.

As in this place we are concerned specially with the Royal Horoscope, let us find the Parallax for the 9th 'November, 1841.

Epoch 1800 - - 9 20 20 Add 40 - - 2 19 32 .

I I I - - 2 28 43 - 1841 3 8 35

,, November 0 ?I 45 ' 9th - - 3 27 35

Anomaly = 7 17 '55

W e find. by reference t o the Chord of Parallax that the D'S Horizontal Parallax with this Anomaly is 59'.

The Moon is not, on the horizon. I t is just below the cusp of the ninth house, with an hour-angle of - 32'37' W.

This, then, will be the second part of our problem, to find the Parallax due to the Moon's position a t the Royal Nativity.

The latitude of the place of observation is 51~32' N., to which we add the Moon's declination S. 3O26', which gives the Moon's Zenith distance a t southing as 55O8'.

This will form the base of a right-angled triangle, whose base will be the Moon's meridian distance 3 ~ ~ 3 7 ' . W e have to find the length of the hypotenuse in degrees and minutes of a circle, and this will give us the Moon's Zenith distance at the moment of birth.

Log. COS. 32'37' 9.92546 + Log. cos. 55O8' 9-75714

= Log. cos. 6i013' 9.68260 .- The horizon being at all points goo from the zenith,

a t which distance we have found the Parallax to be 5g1, we must find by proportion the Parallax due to the Moon at a zenith distance of 61~13'.

As go0 : 59' : : 61~13' ; 40'

The Moon will therefore be depressed by Parallax toward the S.W. horizon to the extent of 4or, making its zenith distance by observation 6i053', and its altitude .go0- 61~53'=28~7',

The Moon's true zenith-distance at southing was

5s08' and by adding the proportion of Parallax due to this distance, viz., 36', we have its observed zenith dis- tance at southing 55O44'. Then to obtain its observed meridian distance or hour-angle :

Log. cos. 6i053' - 9.67327 - Log. cos. 55O44' 9-75054

This observed meridian distance, 33Oi1' less 32O37' its true meridian distance, shows a difference of 34' between a calculation of the Moon's Right Ascension from a geocentric position and its Right Ascension taken from ,observation on the surface of the earth. If we admit Parallax as a factor in Primary Directions, taking the direct rays of the body to the place of birth as operative, instead of the influence being via the Earth's centre, then the observed place of the Moon must be the point dealt with in calculating the arcs oi direction. But this part of the enquiry I must leave to those who have time and inclination to pursue it, and having shown the method of calculating the parallactic angle, I leave it an open question.

SEMI-DIAMETERS

The Moon's apparent semi-diameter, i.e., the distance between its limb or outer edge and the centre of its disc, is controlled by its distance from the Earth, just as is Parallax. I t varies from 14'44" to 16'45" and hence its apparent diameter will be between 29'28" and 33'30".

As all directions are made to the centre of a body, it may reasonably be allowed in practice to take 15' to 17' from the Arc of Direction to obtain the first contact, and to add the same quantity to the arc to obtain the last contact. Thus in the Direction Asc. 8 T) 5g019', this would be extended from first to last contact thus :

Asc. 8 T> first contact 5g0 3' Asc. 8 D zod. 5919' Asc. 8 I) last contact 5g035'

The following Table may be useful :

I) Semi-diameter = Parallax x ,2729

Similarly the Sun's disc has an apparent semi-diameter, varying from 15'46" at Apogee to I 6'1 8" at' Perigee, and in this case it will be sufficient if we apply only its mean semi-diameter 16' to the Arc of Direction.

The semi-diameters of the planets are inconsiderable,, as are also their parallaxes.

Parallax - Semi-diameter -

54'

14'44"

55'

15'1"

58'

15'50''

1

56'

15'17"

59'

16'6~~

57' ------- 15'33"

60'

16'22'~

CHAPTER XVI.

ALTHOUGH it is the custom to account one-third of a planet's semi-arc as its house-space, yet in effect it is not actually so; and by employing this uniform division of the semi-arc, we undoubtedly sacrifice a moiety of truth upon the altar of convention. ' That the time taken by a planet to pass from the

cusp of one house to that of the next is not uniformly one-third of its semi-arc is evident from the fact that the semi-arc of a planet, being parallel to the Equator, does not lie in the same plane as the Circle of Observa-

tion (or Prime Vertical) which cuts the Equator at an angle equal to the latitude of the place of observation. Hence an equal division of the Circle of Observation, such as is effected to produce the " Houses," will not effect an equal division of any concentric circle except such as lie in the same plane, or such as lie in planes that are parallel to it.

The foregoing diagram represents one hemisphere of the heavens reduced to the Earth's circumference. The Circle M.C.-I.C., of which one half only is shown, is the Circle of Observation in Latitude ~ 2 ~ 2 8 ' N. I t cuts the Equator at that angle, and is divided into twelve equal parts (six only are shown) by circles which converge and intersect at points ~ 7 ~ 3 2 ' N. and S. of the Equator. These divisions are the houses numbered 10, 9, 8, 7, 6, 5, and 4.

The Moon's place is shown near the cusp of the eighth house on a semi-arc MD that is g08' N. of the Equator, and 102'5' from M to D, that is from the meridian to the point where the Moon sets on the W. horizon H-H. The Moon's Meridian Distance M-T) is 65'25'. The rotation of the Earth on its axis from W. to E. makes the Moon appear to pass from the Meridian at M to the Horizon at D along the arc M T) D, which is its diurnal semi-arc. I ts nocturnal arc 77O54' extends from D to C. This semi-arc, like that of Uranus above it and of Mars below it, is parallel to the Equator. That portion of its arc between the axis N.S. and the point D is the Moon's ascensional difference due to its declination North. Had the Moon been on the Equator its diurnal and nocturnal semi-arcs would have been equal, as is the case with the Sun at the Equinoxes.

Now it will be quite clear that as the D'S semi-arc is not in the same plane as the Circle of Observation, M.C. -I.C., nor in a plane that is parallel to it, the circles representing the cusps of the houses ( H g H, H 8 H, etc.) cannot cut it into equal parts, being themselves a t equal distance from one another. Hence, although the whole semi-arc of the T) 102~5' is equivalent to the space of three houses or go0 of the Circle of Observa-

tion, yet each house will not comprise 34O2', or one- third of the T)'S semi-arc, since the T) cuts into the cusp of each house at a different obliquity.

In order, therefore, to find the point at which the Moon cuts into the cusp of each house successively, and the space of its semi-arc intercepted, we must calculate the obliquity of the Moon's arc under the polar elevation of each cusp.

The formula and calculation are as follows :-

Log. tang. Ecliptic Obliquity 23'28' = 9-63761 + Log. tang. Lat. of Place 5z028' - 10-11450

= Log. sine Asc. Diff. of Tropics 34'24' 9.75211

Log. sine (& of 34O24'=) 11~28' - g'zgS41 + Log. cotang. E.O. 23'28' - - 10-36239

= Log. tang. Pole of 3rd, 5th, gth, 11th' 24O36' 9.66080

Log. sine (3 of 34'24'=) 22'56' - 9'59069 + Log. cot. E.O. 23'28' - 10.36239

= Log. tang. Pole of 2nd, 6th, 8th, n t h , 41'55' 9.95308

The meridian (tenth and fourth) has no obliquity, and the pole of the first and seventh is that of the latitude of place of observation, 52O28'.

W e now determine the D'S house-space, i.e., the amount of its semi-arc intercepted by the cusps, by taking its ascensional difference under the polar elevation of the ninth and eighth, and add it to 30° just as, in order to find its whole semi-arc, we take the Moon's Ascensional Difference under the pole of the first or seventh and add it to go0.

The I> is moving in an arc g08' N. of the Equator.

Then : 0 I

Log. tang. Pole 9th 24 36 + Log. tang. Declin. J) g 8

= Log. sine Asc. Diff. 4 13 Add I House 30 0

D Arc in 9th House = 34 13 -

Log. tang. Pole 8th 41 55 + Log. tang. Declin. J) g 8

= Log. sine Asc. Diff. 8 18 Add 2 Houses 60 o

Arc in 9th and 8th = 68 18 Arc in 9th 34 I3

Arc in 8th House 34 5

Log. tang. Pole 7th 52 28 + Log. tang. Declin. J) g 8

= Log. sine Asc. Diff. 12 5 Add 3 Houses go o

102 5 Arc in 8th and 9th 68 18

Arc in 7th House . 33 47

W e now have the true arc of the Moon in each of the three houses, ninth, eighth and seventh. In ninth 34'13'~ in eighth 34O5I9 in seventh 33O47', and these, added together, give the whole semi-arc 102'5'. .Therefore, instead of a uniform space of 34O2' we have a different space of the Moon's arc in each house. In order to find the Moon's position, to which all mundane directions will be made, we take

T) Space in 8th and 9th 68 18 Less Mer. Dist. J) - 65 25

J) 's Dist. from 8th cusp 2 53

There is here a difference of 14' from the distance as usually calculated, viz., 2O39' which represents a period of three months.

This true computation of the house-space does not affect the meridian distance or semi-arc of the D. It only affects its cuspal distance, and will throw out all mundane directions made to the Moon's place, as well as those of the Moon to the mundane sextile Mid-heaven and mundane trine Ascendant. But inasmuch as all the planets are similarly affected in proportion to the obliquity of their semi-arcs to the Circle of Observation, the whole basis of mundane directions is in need of a revision. I might have taken any other planet, Uranus, for example, moving on an arc 23O1g' N., and its position and house-space would be found to be similarly incorrect as calculated by the method of Placidus.

Note.-In the preceding diagram, the reader is sup- posed to be looking at the spherical body of the Earth from a position in space outside of it. Consequently the curved arc of the Moon between the ninth cusp and the meridian appears shorter than that between the cusp of the eighth and point D on the horizon, while in reality it is longer.

Now let us prove this unequal division of the semi- arc to be a fact. This will entail disproving the ordinary equal division of the semi-arc.

Postulate: When the body of a planet is on the cusp of a house it must have the same oblique ascension or descension as that cusp.

Take the ordinary method first. The T) has Right Ascension 1 4 3 ~ 2 0 ~ ~ Semi-arc 102'5'~

and Meridian Distance 65O25'. Its distance from the cusp of eighth is (8 Semi-arc 68O4' - Meridian Distance 65O25') = 203g1.

The Oblique Descension of the eighth house cusp is Right Ascension of Mid-heaven 208~45'- 60° 148'45'.

Add z03g' to bring the J) to a conjunction with the eighth cusp and obtain

0 I

Obi. Desc. of 8th at Direction = 151 24 Obi. Desc. of D under Pole of 8th = 151 38

Diff. - 14

This is exactly the same as we found before when calculating the true house-space of Moon.

Now take the method of unequal division, which is undoubtedly the true method.

0 I

D 's Dist. from cusp of 8th - 2 53 Add this to R.A. of M.C. - - 208 45

R.A. of Mid-heaven when I) is on cusp of the 8th - 211 38

Take 60' for Obi. Desc. of 8th - 60 o

Obi. Desc. of 8th at Direction - 151 38 Obi. Desc. of T) under Pole of 8th - 151 38

- -

Take another example. When the T) was on the cusp of the ninth, its

meridian distance must have been the same as its house-space, which we have found to be 3 4 O 1 3 ' , while the ordinary method gives 3 4 O 2 ' .

0 I

I) 's House-space in 8th - - 34 5 Distance from cusp . - 2 53

Dist. below 9th 31 12

From R.A. of M.C. - 208 45 Take (as above) - - 31 12

R.A of M.C. when JI was on the 9th cusp - I77 33

R.A. of Moon - - 143 20

Dist. required 34 13

No further proof is needed. I t will be well, however, that the student should take

out the distances of the planets under the pole of those houses to the cusps of which they are applying at birth.

A table of the Poles of the houses for every even degree of latitude between 45' and 55O is here annexed. The elevation due to the fractional parts can be found by proportion.

POLAR ELEVATION

1 3rd 5thl 1 2nd. 6th N. Lat. 9th 11th 8th 1 2 t h

Obi. of Ecliptic = 23'27'

Having obtained the arc of a planet in the ninth its arc in the tenth will be the same, and by subtracting this arc from 60° its arc in the third and fourth houses will be found.

Having also its arc in the eighth, that in the eleventh will be the same, and the arc for the second and fifth will be found by taking it from 60'.

The arc for the twelfth and seventh is the same, and. by taking it from 60' we have the arc for the .first and sixth.

There can be little doubt 'that a true system of Primary Directions can only be evolved from a close adherence to astronomical principles of calculation, and anything like loose figuring in a system which is

purely mathematical, will only end in dissatisfaction. Fortunately for the science, the Zodiacal Directions which belong to this system do not come under the same imputation of inaccuracy and are far more numerous than those in mundo. Consequently a very good show has always been possible with expert know- ledge of the system. But when, as is frequently the case, an event of great importance has been signified chiefly by a mundane arc of Direction, rectification from that event by the old method of equal house-space could only make doubt more doubtful still. And per- haps this accounts for the general experience, that when a nativity has been rectified so as to make an appropriate arc of direction coincide with a specific event, other arcs do not synchronise with the events they are held to signify.

I trust that in the hands of experienced and patient workers, these suggestions will bear fruit such as one may conscientiously dedicate to the cause of Truth.

CHAPTER XVII.

ALTHOUGH it is certainly a fact that the influence of a planet or luminary is perpetually vested in the place (mundane or zodiacal) originally held by that body, yet, as the influence of these bodies is continuous after the moment of birth as before it, attention should be given to their actual positions at the time they form a con- junction or aspect by direction.

Within the space of six hours, or an arc of go0, the Right Ascensions of the major bodies will not have materially altered, nor will their semi-arcs have under- gone any appreciable change by difference of declination. This will apply also to the minor planets when retrograde.

In the case of the Moon, however, a material altera- tion of Right Ascension will be effected in even the space of half-an-hour.

Let us take an illustration of the second distance of the Moon in the royal horoscope. W e have already directed the Moon's longitude to the western horizon (Chap. X., ex. 4) where we found the arc of direction to be 5g0ig'. The speculum shows us that the direction of the Moon's body in mundo to the same point measures an arc of 5~~51'.

During the time taken in the formation of these arcs the Moon will be moving forward in the zodiac, increas- ing its Right Ascension, and its declination south. The ecliptic longitude and the Right Ascension of the Moon at the time of its setting have to be found.

Take the mundane arc 52'51' first, and convert it into time =3h. 3103. 24s. Rule: Divide the degrees by

15 and call the result hours. Multiply the remainder by 4 and call them minutes. Then divide the minutes of space by 15 and call them minutes of time. Multiply the remainder by 4 and call them seconds of time. Thus :

The Nautical Almanac, Whitaker's Almanack and some other publications give a Table for converting Time into Equatorial Degrees and the reverse of this.

W e must now find the increase of the Moon's longi- tude and declination for 3h. 31m. by means of the Ephemeris ; and thence take its corrected Right Ascen- sion and semi-arc. .

The Moon's diurnal motion is 13~49'. Using diurnal proportional logarithms we have :

Diurnal motion 13 49 log. - 3398 Time 3h.31m. ,, -8341

Acceleration 2 I ., 1.0739 1st Long. DV29 27

2nd .? D A I 28

The Moon's Declination increases 0 I

5 58 in 24 hrs. - - log. 3h. 31m. (as before) - .Go45

,, .8341

o 52 increment - 1-4386 3 36 1st Declin.

4 28 2nd log. tang. 8-89274 51 32 Latit. * I I S 10-09991

5 39 Asc. Diff. - ,, sine 8-99265 90 0

84 21 Semi-arc T), at setting.

Now for the Right

Cos. Declin.

Ascension : 0 I

4 28 log. 9.998679

(a.c.) 0.001321 Cos. Lat. (2nd) 4 16 ,, 9'998795 Cos. Long. A I 28 ,, 9.999858

Cos. R.A. 0 38 9.999974 Libra = 180 o

R.A. ~ 1 8 0 38 Q.E.F. R.A. of M.C. 210 27

Mer. Dist. D 29 49 Semi-arc D 84 21

Hor. Arc = 54 32 1) 8 Asc. (2nd position) Hor. Arc = 52 51 D 8 Asc. (1st position)

1 41 --

W e have therefore an arc of i04i' (corresponding to an interval of one year and eight months), between the opposition of the Moon's radical place in mundo and the opposition of 1)'s body, or in other words: an interval of 6m. 44s. of time elapses between the setting of the Moon's place as seen from London at 10.48 a.m., 9th November, 1841, and the actual setting of the Moon's centre on the same date. This observation institutes a series of double directions in the case of the Moon, and smaller differences will be due on the same account to Mercury, Venus, Sun and Mars. No doubt they play some part in the general imputation of fickle- ness levelled against '' fair Cynthia " by astute observers of her influence. I t may help, along with parallax, to explain why the directions of the Moon to important places in the horoscope are sometimes void of any apparent effect at the ascribed time, and why some directions continue so long in effect.

Let us now take the direction of the Moon in the zodiac, for the second distance.

W e have already found the arc of the Moon to opposition Ascendant in zodiac to be 59' 19'. This

corresponds to 3h. 57m. 16s. and we now find the Moon's increase of longitude for this interval.

0 I

Diurnal motion 13 49 log. -2398 Time 3h.57m. , , - .7836

Acceleration 2 16 1st Long. D"W9 27

2nd Long. D + 1 43

The Obi. Desc. of this point Obi. Desc. of 7th House

Arc of D long. to W. horizon = 60 16

Collating all these arcs :

T ) 's place Radix oppos. Ascdt. m. - 52 51 5)'s body to oppos. Ascdt. m. - - 54 32 T> 's long. Radix oppos. Ascdt. zod. - 59 I9 7)'s long. a t setting oppos. Ascdt. zod. - 60 16

Mean Arc 1) 8 Asc. 56 44& Total Range of Arc 7) 8 Asc. - - 7 25

Mean mundane Arc 7) 8 Asc. - - 53 41& Range of ,, fl 2 I 1 41

Mean zodiacal , , s t - 59 474 Range of ,, 8 1 .* - - 0 57

W e have here a total arc of 7'25' ranging from September, 1894, to February, 1902, during which the Moon can legitimately be said to affect the fortunes by its opposition to the Ascendant.

If the true arc for the Moon's setting be reduced by parallax, we have a still further range of influence, thus,:-

0 I

T) 8 Asc. mundo, Arc - 52 51 Parallax - 40

D 's place sets by observation 52 11

T) 's true setting, Arc - 54 32 Horizon Parallax 59

D'S body sets by observation 53 33

The question involved is of extreme interest, but it cannot possibly be answered from a single instance. A large number of cases would have to be taken, the mundane directional arcs reduced by Parallax, and in- creased by Right Ascension, and the zodiacal increased by Oblique Descension. A survey of the six resulting arcs in reference to the events of life would certainly afford some evidence in favour of one method or another, and so render "the frequently observed disparity between the Moon's arcs of direction and the corre- sponding events" a thing of the past.

RIGHT ASCENSION AND

DECLINATION

FOR EVERY DEGREE OF T H E ZODIAC

AND THE

ASCENSIONAL DIFFERENCE

OF EVERY DEGREE IN LAT.

Declin. Rt. Ascen. London Birming'm I . I I

VS' For the R.A. of Libra add 180' to the same degree of Aries. The Declin. and Asc. Diff. are the same for both.

Deg. - 0

0 1 2 3 4 5

-..- 6 7 8 9

10

London Birming'm Liverpool , l o ! I O I Declin.

0 I

11 29 11 50 12 10 12 31 12 51 13 12

t . Ascen.

KS' For R.A. of Scorpio add 180' to the same degree of Taurus. The Declin. and Asc. Diff. are the same for both.

Declin.

0 I

20 10 20 22 20 35 20 46 20 57 21 8 -- 21 19 21 29 21 39 21 49 21 58

Rt. Ascen. London - -- 0 1 0 1

67 49 27 31 58 52 27 52 59 54 28 12 60 57 28 31 62 0 28 49 63 3 29 8 -- 64 7 29 25 65 10 29 42 66 14 29 59 67 18 30 15 68 22 30 30

Birming'm Liverpool

0 I

29 39 30 1 30 23 30 44 31 4 31 24

fSS" For the R.A. of Sagittarius add 180°t the . same degree of Gemini. The Declin. and

Asc. Diff. are the same for both.

Declin. Rt. Ascen.

0 I

90 0 91 5 92 11 93 16 94 22 95 27

96 32 97 38 98 48 9 9 48

100 53 . - --

101 58 103 3 104 8 105 12 106 17

107 21 108 26 109 30 110 34 Ill 38 -- 112 42 113 46 114 50 115 53 116 57

London Liverpool

0 I

35 46 35 45 35 44 35 42 35 39 35 35

35 30 35 24 85 17 35 10 35 1

34 52 34 42 34 31 34 20 34 7 -- 38 54 33 40 33 26 33 10 32 54

32 37 32 20 32 2 31 43 31 24

KS" For the R.A. of Capricornus add 180Â to the. same degree of Cancer. The Declin. a n d Asc. Diff. are the same for both.

Liverpool

- 0 I

29 89 29 16 28 53 28 29 28 5 27 41

27 16 26 61 26 25 25 69 25 33

2S3 For the R.A. of Aquarius add 180Q to the same degree of Leo. The Declin. and Asc. Diff. are the same for both.

Deg. Declin. London Rt. Ascen. Liverpool

VS' For the R.A. of Pisces add 180Â to the same degree of Virgo. The Declin. and Asc. Diff. are the same for both.

TERNARY PROPORTIONAL

LOGARITHMS

o0 lo 2 O

Infinite. 2-25527 1.95424 4-03342 2.24809 1.95064 3'73239 2-24103 1.94706 3-55630 2-23408 1-94352 3'43136 2'22724 1'94000 3'33445 2-22051 1-93651

London 1 ~ i r m i n ~ ' m Liverpool - ' Deg. Declin. It. Ascen.

tSS' For the R.A. of Libra add 180' to the same degree of Aries. The Declin. and Asc. Diff. are the same for both.