CHAPTER VI

PLANETARY PERIODS, ETC. We now come to the point where it will be necessary to explain more fully the various elements with which so far the reader has only been dealing in a more or less mechanical way. It is, of course, of first importance that the student of Astrology should have a correct method, and this has been given as fully as space will permit in the preceding pages. But it is also necessary that one should know why he is doing a thing, as well as how to do it. Henry Ward Beecher once said that if a man turned soil with a spade knowing why he did it, the work was more effectively done than if he did not know. For this reason it will be convenient for the student to have a general view of the cosmical elements that he employs in his calculations and of the factors that enter into his consideration when studying a horoscope. For purposes of calculation, the astronomer regards the planets as moving around the Sun in circular orbits at a uniform rate, and the positions thus obtained are called the mean longitudes of the planets. But it is known that the orbit of a planet answers to the functions of an ellipse, of which the Sun is presumed to occupy one of the foci. Then it becomes necessary to correct the Mean Longitude of the planet by an equation which is called the Centre equation. Let us make this quite clear. The circular orbit supposed in the first instance is what may be called the Mean Orbit of the planet, as compared with its true orbit, which is elliptical. Similarly, the motion of the planet in the circular orbit is called the Mean Motion, as compared with the true motion, which is variable, being quickest at the perihelion and slowest at the aphelion. The difference between the Mean longitude and the True longitude is determined by the Anomaly, which is the distance of the planet from its Aphelion, or farthest distance from the Sun. The anomaly is thus L-A, i. e., longitude minus aphelion. But it will be seen that ellipses may be of greater or less eccentricity, and the equation to centre depends on the eccentricity. This may need a word of explanation. Suppose a circular orbit. Draw the two diameters at right angles to one another; they are of equal length. Now suppose another figure in which the one diameter is longer than the other. The circumference of this figure will be an ellipse. The greater diameter is called the Major Axis, and the diameter at right angles to it is the Minor Axis. The proportion of one to the other axis determines the amount of eccentricity. Twice the eccentricity gives the equation to centre, and to reduce this to degrees and minutes of a circle it has to be multiplied by the chord of 60 degrees, which is 57°·29578. This gives the maximum equation to centre when the planet is 3 signs or 90 degrees from its aphelion, and therefore on the Minor Axis. The eccentricity of the various planets may be here stated: Mercury, 0.2055; Mars, 0.0931; Jupiter, 0.0482; Saturn, 0.9562; Uranus, 0.9467; Earth, 0.0168; Venus, 0.0068. These quantities undergo a gradual change. Thus it is found that Jupiter, Mars, and Mercury are increasing the eccentricity of their orbits, while Venus, the Earth, and Saturn are reducing it. The orbit of Venus is now almost circular, and it affords an example of the perfect astronomical paradigm. Thus by the mean motions and the equation to centre the true longitudes of the planets in their heliocentric orbits are obtained. But inasmuch as the orbits of the planets do not lie in the same plane as the Sun, but cross its apparent path at various angles of inclination, a further equation is due to reduce the orbital longitudes of the planets to the ecliptic. To further reduce these true longitudes into their geocentric equivalents, i. e., as seen from the Earth’s centre, we have to employ the angle of Parallax, which is the angle of difference as seen from two different points in space. This will vary according to the relative distances of the bodies from one another. The Moon’s longitude is always taken geocentrically. When approximate longitudes are required, the employment of a mean vector, which is equal to half the minor axis of the planet, is found convenient. For the convenience of astronomical students I may here give the constant logarithms of the values of the tangent, which, being added to the logarithm of the tangent of half the distance of the planet from the Sun in longitude, will give the tangent of the complement. LOGARITHMS Neptune, 9.97107; Uranus, 9.95479; Saturn, 9.90858; Jupiter, 9.83114; Mars, 9.32457; Venus, 9.20812; Mercury, 9.63210. To these add the bog, tangent of half the angle between the planet and Sun, taken by heliocentric longitude, which call A. Call the result B. For major planets add A and B, and for minor planets subtract B from A. In either case the result will be the angle of longitude between the planet and the Sun as seen from the Earth, and hence its geocentric longitude may be known. But a more convenient method of obtaining the approximate longitudes of the planets geocentrically is by means of the Planetary Geocentric periods. Thus Uranus has a period of 84 years, after which it returns to the same longitude on the same day of the year and will be further advanced in its orbit by 1° 5′. Saturn has a period of 59 years, after which it comes to the same place in the zodiac and will be further advanced by 1° 53′. Jupiter has a period of 83 years, when it is found to be only 4′ advanced upon its former longitude. Mars’ period is 79 years plus an advance of 2° 4′. Mercury’s period is also 79 years, and its advance is 5° 32′. Venus has a period of 8 years, when it is further advanced in the zodiac by 1° 32′. For the calculation of the approximate geocentric longitude of the major planets these periods are very useful, but are of less value in regard to the minor planets Venus and Mercury. Suppose I want the longitude of Uranus in the year A. D. 827. I have its longitude on the first of January, 1912, in Capricorn 28° 17′. Then 1912-827 gives 1,085 years, which being divided by the period of Uranus (84 years), yields 12 periods and 77 years. The increment for 1 period being 1° 5′, that for 12 will be 13°, and 77-84ths of 1° 5′ will be another degree, making 14 degrees. As the date is anterior, this amount must be subtracted from its longitude on the first of January, A. D. 827, and in effect we obtain Capricorn 14 degs. 17 mins. as the longitude of Uranus on the first of January, 827, as seen from the Earth. For the purpose of determining the effects, if any, due to the presence of a planet in its Aphelion, Perihelion, or Node, the following values are given for the year 1800 A. D.: Planet.   Aphelion. Perihelion. Node. S. ° ′ S. ° ′ S. ° ′ Mercury 8 14 21 2 14 21 1 15 57 Venus 10 8 36 4 8 36 2 14 52 Mars 5 2 23 11 2 23 1 18 1 Jupiter 6 11 8 0 11 8 3 8 24 Saturn 8 29 4 2 29 4 3 21 57 Uranus 11 17 21 5 17 21 2 12 51 Neptune 7 12 22 2 12 22 4 9 35 The longitudes of the Aphelia are increased in 100 years by the following quantities: Neptune, 1° 25′; Uranus, 1° 28′; Saturn, 1° 50′; Jupiter, 1° 35′; Mars, 1° 52′; Venus, 1° 43′; Mercury, 1° 34′. These quantities are additive for years after 1800, and subtractive for years before that epoch. In the present state of astronomical science it is not certain that these values are absolutely correct. Calculated from the Tables of Kepler, the differences are only slight, but still sufficient to make considerable error in testing for exact conjunctions or ingresses. Lilly, who predicted the Great Plague and Fire of London some years previous to the event from the ingress of the Aphelion of Mars to the sign Virgo, evidently made use of the Rudolphine Tables constructed by Tycho and Kepler, and according to these the ingress took place in 1654, while according to more modern Tables it did not take place until 1672. It is probable, however, that the positions of the Aphelia here given will be sufficiently close for all practical purposes. A word or two may now be said regarding the periodic conjunctions of the planets. As will be seen from the periods given, five periods of Jupiter are nearly equal to two of Saturn. It is found that the two planets form their conjunctions every 20 years. Thus there was a conjunction in Virgo in 1861, another in Taurus in 1881, and another in Capricornus in 1901. The next will be in Virgo in 1921. The two planets are thus now forming their successive conjunctions in the Earthly Tripicity; but in 1981 will make their mutation conjunction by falling together in the Airy sign Libra. Uranus and Jupiter form their conjunctions every 14 years. Thus there was a conjunction in Sagittarius in 1900, and there will be another in Aquarius in 1914, another in Aries in 1928, and so on. The conjunctions of Neptune with the other major planets are necessarily in terms of the periods of the latter, those of Neptune and Uranus being very infrequent, while those with Jupiter will be proportionately more frequent. For the period of Jupiter is only 12 years, while Neptune remains in the same sign for 15 years. The conjunction of Jupiter and Neptune in Cancer in 1907 will be followed by another in Leo in 1919, and this again by another in Virgo in 1932. Obviously, if the planets by their transits effect anything whatsoever, the double transit of major planets must have a correspondingly greater effect. The careful student of Astrology will institute a number of tests in order to find what effects are due to the combined action of the planets when in conjunction at transit, and also when in opposition or quadrature. The chief points to be noticed in connection with the transits of the planets are the Midheaven, Ascendant, and the places of the Sun and Moon, as already mentioned in Chapter II of this section. The ancients also included the places of the Moon’s Nodes, and it is usually found that the transit of the South Node over any of the Significators is attended by unfortunate results. With these observations as a general guide to the cosmical factors involved in the planetary motions, the reader will be able to take a more intelligent interest in the foundations of his study than is the usual case from the pursuit of the subject by rule-of-thumb methods. When we come to the consideration of the Moon as a cosmical factor we are face to face with one of the most difficult and evasive problems. For many centuries astronomers grappled with this inconstant factor with small success, and at the present day the problems attaching to the vagaries of lunar motion are in anything but a satisfactory condition. Prior to the time of Ptolemy nothing was known of the Moon except that it had a certain mean motion and formed its syzygies at definite periods, the mean values of which were very closely known. But certainly nothing was known regarding the inequalities of motion which are found to exist. Ptolemy discovered the equation due to the action of the Sun upon the Moon in its orbit. This is called the Evection. Tycho later discovered that a further equation was due to the disturbance caused by the Sun along the vector. Both these equations were employed by Kepler. But of these, later astronomers have added one after another equation, going so far as to employ the action due to Venus and Jupiter, while ignoring that due to the action of the other planets upon the Moon. Buckhardt, whose formulae were used in the calculation of the Nautical Almanac for many years, employs no less than 37 equations of the Moon’s mean longitude. Indeed, the whole business has become farcical. The fact is that only three of these equations are necessary in order to obtain the Moon’s true place in the ecliptic at any time, and for the syzygy only one equation is necessary. The trouble has arisen from the fact that the eccentricity of the Moon’s orbit has been wrongly estimated, and most of these equations now employed by astronomers are effectual only in correcting this false estimate. Kepler gives the maximum equation to centre as 4° 59′ 59″, while modern astronomers have given it as 6° 18′ 28″. Neither of these is quite correct, though Kepler is much nearer the truth. Another problem in connection with the Moon that has puzzled astronomers for a long time and is still in the region of experimental science is what is known as the Secular equation. It is found that by taking the present mean motion of the Moon and applying the various equations, found necessary to bring the calculations into line with observations of the Moon’s position in the zodiac, a considerable difference is found to exist between the calculated place of the Moon and its recorded position at the time of ancient eclipses. According to our modern Tables, ancient eclipses happened sooner than they should have done, or, in other words, the Moon was more advanced in its orbit than our Tables require. The inference is that the Moon was formerly moving quicker in a smaller orbit than now, or conversely, the Moon is now receding and getting farther from the Earth. Consequently its action on the tides must be diminishing, and also its action on the equatorial mass of the Earth, which is considered to be the chief factor in the production of what is called the Precession of the Equinoxes. Yet whereas by one statement the disturbance due to the Moon is diminishing, another statement shows that the Precession of the Equinoxes is increasing! =Voila le debacle.= All these anomalies and contradictions are due, as I shall show in my new Tables and Thesis, to the importation of false factors into the problem of the Moon’s motion, which, in fact, is extremely simple, perfectly regular, and affected only by its anomaly or distance from the aphelion and, where the time equation is employed, by the increase of radius. Jupiter and Venus have no more action on the Moon than have Mars and Saturn, in fact none at all, and the only body that has any action upon the lunar orb is the Sun, which it exerts indirectly through its action on the Earth. These problems need not, however, vex the minds of the student of Astrology. It is sufficient for him that he has the place of the Moon calculated for him in the ephemeris reduced from the Nautical or other official Almanac. It is important, however, that he should know that such problems exist. Sir Isaac Newton was first led to the subject of Astronomy by his thoroughness and scientific propensity. He studied Astrology, and proceeded to the study of Astronomy the better to understand and deal with the problems that the predictive science presented. For it is to be observed that Astrology in his day was entirely in the hands of astronomers, who calculated their own ephemerides and pursued the higher methods of astrological calculation as presented in my “Profnostic Astronomy.” Kepler avowed himself to be convinced of the truth of the science of Astrology, and showed himself to be a competent critic as much by his understanding of the astronomical problems involved as by his marvellous forecast of the rise and fall of Wallenstein. Tycho, his colleague and collaborator, also a great astronomical discoverer, was a professed Astrologer, and added to his stipend by the calculation of horoscopes. Astrology is quite a reputable study, and needs but to be emancipated from the service of a horde of half-educated plagiarists and parasites in order to take its place once more among subjects of serious consideration by the learned. Astronomy is interesting, but to be made useful it must find interpretation in terms of our daily life and common needs. It is in this connection that Astrology has played Cinderella since the days of official science. The day is not far off when it will come into its own.