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.