VOL. XLIX.] PHILOSOPHICAL TRANSACTIONS. IQ 



orbit, with respect to its own, by making their common intersection recede, in 

 the same manner as the sun's action operates on the lunar orbit, an aUeration in 

 the obliquity of the ecliptic would necessarily follow, and on closer examination 

 it appeared, that Jupiter really caused the earth to deviate in its course, and gave 

 a retrograde motion to the line of intersection of their orbits ; and further, that 

 according to the present situation of that line, its regress was such, as to have 

 occasioned a gradual diminution in the obliquity of the ecliptic for many ages 

 past : by which means that question seems decided. The reason why the astro- 

 nomers have not hitherto been able to settle that point is, because this variation 

 proceeds at so slow a rate, that the observations of the ancients are not suffi- 

 ciently exact to ascertain the small diminution, that has happened since their 

 time. I have endeavoured to fix the laws, the quantity, and the period of this 

 variation. From the same cause are also computed a progressive motion occa- 

 sioned in the earth's aphelion, and a small regressive one in the equinoctial 

 points : in all which is added the small share of influence that belongs to Saturn. 

 In the last proposition are deduced some inequalities that occur in certain ele- 

 ments of the earth's theory, that have hitherto been supposed invariable. These 

 as they are very small, I have only added in that view, that you, who know the 

 best what degree of precision may be expected from astronomical observations, 

 may judge whether they are worth notice or not. 



I must observe, that some of the points of these two treatises have been con- 

 sidered by others ; and if my conclusions any where diff^er from them, I leave it 

 to other geometricians to decide which are right. All I shall say on that head 

 is, that my result agrees with the computation of the great Sir Isaac Newton. 

 As to the method, I have rather chosen to deduce the propositions by geometri- 

 cal reasoning, after the manner of Sir Isaac Newton, which in researches of this 

 kind always appeared to me much more simple, more rational, and more elegant, 

 than the long calculus of an intricate analysis. Besides, if in the application 

 there slips any error, it is more easily discovered in the former method. 



On the Precession of the Equinoxes and Nutation of the Eartfis Axis. 

 Lemma 1. To find the Sun's Force on the Equatorial Parts of the Earth. 

 Let T (fig 1 pi 2) be the earth's centre, b the pole, at the right line joining 

 the centres of the earth and sun, Asa a circle described from the centre t, and 

 perpendicular to the equator ts, and Ta the intersection of the circle TAsa, 

 and of the plane perpendicular to the plane of the ecliptic : then from the point s 

 of the equator draw sm parallel to at, meeting Ta in m, and produce it to p, so 

 that it may be sp = 3sm, and from p make pn perpendicular to the plane 

 of the equator ts. Then by the similar triangles stm, spn, it will be st : 



3sM X TM 



INC 



D 2 



TM :: sp or 3sm : pn = -^-^ — . Now, if the earth's radius st denote the force 



ST 



