170 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1757. 



LI J I. The Resolution of a General Proposition Jor Determining the Horary AU 

 teration of the Position of the Terrestrial Equator ^ from the Attraction of the 

 Sufi and Moon : with some Remarks on the Solutions given by Other Authors to 

 that Difficult and Important Problem. By Mr. Tho. Simpson, F.R.S. p. 41 6. 



Since the time that Dr. Bradley published his observations and discoveries 

 concerning the inequalities of the precession of the equinox, and of the obliquity 

 of the ecliptic, depending on the position of the lunar nodes, mathematicians in 

 different parts of Europe have set themselves diligently to compute, from physical 

 principles, the effects produced by the sun and moon, in the position of the ter- 

 restrial equator ; and to examine whether these effects do really correspond with 

 the observations. Two papers on this subject have already appeared in the Phil. 

 Trans. ; in which the authors have shown evident marks of skill and penetration. 

 There is nevertheless one part of the subject that seems to have been passed over 

 without a due degree of attention, as well by both those gentlemen, as by Sir 

 Isaac Newton himself. This part, which on account of physical difficulties, is 

 indeed somewhat slippery and peq^lexing, is the principal subject of this essay. 



General Prop. Supposing a homogeneous sphere oabcd (fig. l) revolving 

 uniformly about its centre, to be acted on at the extremity a of the radius oa, in 

 a direction al perpendicular to the plane of the equator abcd, and parallel to the 

 axis of rotation ?p, by a given force, tending to generate a new motion of rota 

 tion at right angles to the former : it is proposed to determine the change that 

 will arise in the direction of the rotation, in consequence of the said force. 



Let F denote the given force, by which the motion about 

 the axis pp is disturbed, supposing /to represent the cen- 

 trifugal force of a small particle of matter in the circum- 

 ference of the equator, arising from the sphere's rotation ; 

 and let the whole number of such particles, or the content 

 of the sphere, be denoted by c : let also the momentum of 



