506 LECTURE XLII. 



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 2(5^°. 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, al- 

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

 was first actually observed by Dr. Bradley, about the year 1747. The abso- 

 lute 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 dis- 

 tinguished from the change of the position of the ecliptic. The inclination 

 ot* 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 small planets, Juno, Pallas, and Ceres; twice 24 or 48, making 52, for 

 Jupiter; twice 48 or 96 for Saturn, making 100 ; and twice 96 or 162, 

 making I96, for the Georgian planet; and these sums will represent 

 the distances, without any material exception, in the nearest integer num- 

 bers. \ 



The planet Mercury is little more than one third as large as the earth in 

 diameter. He performs his revolution in somewhat less than three months, 

 at about two fifths of the distance of the earth. His orbit is more eccentric, 

 and more inclined to the ecliptic, than those of any of the planets ex- 



