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