402 LECTURE XLII. 



was easily determined from the apparent change of place in a given time. 

 (Plate XXXII. Fig. 471.) 



The same astronomer also ascertained, that the squares of the times of 

 revolution of the different planets are in proportion to the cuhes of thejr 

 mean distances from the sun. For example, if one planet were four ti^iev 

 as distant as another, it would revolve in a period eight times as long, 

 since the cube of 4 is equal to the square of 8 ; thus Mars is nearly 

 four times as remote from the sun as Mercury, and the Georgian planet, 

 four times as remote as Jupiter, and their periods are nearly eight times a"s 

 long respectively. i 



It is probable that all the planets have a rotatory motion from w 

 east, either perfectly or very nearly equable.* This motion has 

 observed in Venus, the Earth, Mars, Jupiter, and Saturn : and from some 

 phenomena of the satellites of the Georgian planet, Mr. Laplace thinks that 

 it may also be assumed as nearly certain that this planet has also a rota- 

 tory motion. The figure of the planets is spheroidical ; they are more or 

 less flattened at the poles, as they revolve more or less rapidly on their 

 axes. These axes retain, with a very slight deviation, a situation always 

 parallel, in every part of the orbits. 



But, in the course of time, the gradual change of the position of the axis 

 produces a sensible effect. In the case of the earth, this effect is denomi- 

 nated the precession of the equinoxes. The equinoctial points are the 

 intersections of the apparent ecliptic, or the path of the sun in the heavens, 

 with the plane of the equinoctial, which is perpendicular to the earth's 

 axis and which passes through the equator on the earth's surface ; these 

 points of intersection have a retrograde motion, from east to west, on the 

 ecliptic. This motion was discovered by Hipparchus, in the year 128 

 before Christ, from a comparison of his own observations with those of 

 Timocharis, made 155 years before ; and since the time of Hipparchus, 

 the equinoctial points have receded about 26^. Hence it happens that 

 the constellations called the signs of the zodiac, are now at a considerable 

 distance from those divisions of the ecliptic which bear the same names. 



The earth's axis has also a small periodical change of inclination, or a 

 nutation, performed in about 19 years, and amounting in the whole to 18 

 seconds only. Its existence was determined by Newton from theory, 

 although he failed in the attempt to ascertain its quantity with accuracy ; 

 it was first actually observed by Dr. Bradley,t about the year 1747. The 

 absolute direction of the axis in the heavens is also liable to some variation, 

 in the course of many ages, but this change has not always been sufficiently 

 distinguished from the change of the position of the ecliptic. The inclina- 

 tion of the equator to the ecliptic is now very nearly 23 28*. 



In order to retain in memory a general idea of the proportional distances 

 of the primary planets from the sun, we may call that of the earth 10 and 

 that of Saturn 100 ; the distance of Mercury will then be 4, to which we 

 must add 3 for Venus, making 7 ; twice 3 or 6 for the earth, making 10 ; 

 twice 6 or 12 for Mars, making 16 ; twice 12 or 24, making 28, for the three 



* Herschelon the Rotation of the Planets, Ph. Tr. 1781, p. 115. 

 f Ph. Tr. 1748, p. 1. 



