120 PHILOSOPHICAL TRANSACTIONS, [aNNO 1737. 



attracting each other in the inverse ratio of the squares of the distances, be 

 revolved about the axis xa, fig. 12, pi. 4, by which the columns ce, on, ca, in 

 that spheroid, may be in equilibrio, and so the spheroid may always have the 

 same figure, the gravity at any point of the surface n must necessarily be in- 

 versely as the radius cn. 



To know therefore whether the spheroid has this property, let us inquire what 

 attraction any corpuscle n of the whole spheroid suffers, according to the direc- 

 tion CN ; and fnjm that attraction let us deduct that part of the centrifugal force 

 which proceeds from the rotation of the spheroid acting in the direction cn; 

 and then see whether the remaining force is proportional to — . We shall first 



then investigate the following problem : and as we intend to apply our disco- 

 veries to the spheroid of the earth, which all agree to be very little different 

 from a sphere, our computations must be adapted to those spheroids which 

 have the smallest difference between the two axes. 



Prob. I. To find the attraction, which the spheroid AEae, differing very 

 little from a sphere, exercises on a corpuscle at the pole a. 



For the solution of this problem we may repeat cor. 2, prop. Ql, of the 

 Principia, by which we learn the manner of finding the attraction of any sphe- 

 roid, viz. by substituting in the general value of ce, a quantity differing infi- 

 nitely little from AC; and as in that case the problem becomes much easier, 

 we may solve it in the following manner. 



Let AMDad be a sphere, to the radius AC ; we must find the attraction of the 

 space arising from the rotation of adce, which attraction added to the attrac- 

 tion of the sphere, will give the attraction sought. 



To find the attraction of the space arising from the rotation of anegdm, call 

 AC, r; DE, ar; ap, u; then, from the nature of the ellipse, nm := a\/2ru — uu, 

 and from the nature of the circle am = ^/2ru. But the space arising from 



he produced his work on the Determination of the Terrestrial Orbit, in which are considered the 

 perturbations caused by the action of the other planets. And some time after he successfully applied 

 the same principles to the theory of the celebrated comet of 1759; the result of which calculations 

 are given in a work which appeared in 176O. And when, in 1758, the academy lost M. Bouguer, 

 a pension of 3000 livres, which he enjoyed from the Marine Board, was divided between Monnier 

 and Clairaut, which new engagement produced from his pen an excellent memoir on the maUceuvering 

 of ships. 



A considerable share of his attention was also employed on the subject of achromatic telescopes, 

 with the different kinds and combinations of glass, to render their effects colourless. These labours 

 are contained in three memoirs printed by the academy in the years 1756, 1757, and 1762. But it 

 were endless to particularise all his valuable labours. 



This last year, however, terminated the useful existence of this great man ; his death being occa- 

 sioned by a severe cold he had taken, in returning home one night after supper, at 53 years of age. 



