Of GREATEST ATTRACTION. 215 



to that axis. The folution of this problem is much connected 

 with the experimental inquiries concerning the attraction of 

 mountains, and affords examples of maxima of the kind that 

 form the principal object of this paper. The following lemma 

 is neceflary to the folutiom 



Let the quadrilateral DG (Fig. 8.) be the indefinitely fmall 

 bafe of a column DH, which has everywhere the fame fection, 

 and is perpendicular to its bafe DG* 



Let A be a point at a given diftance from D, in the plane 

 DG ; it is required to find the force with which the column 

 DH attracts a particle at A, in the direction AD. 



Let the diftance ADz:r, the angle DAE =r p, DE (fuppo- 

 fed variable) —y, and let EF be a feet ion of the folid parallel, 

 and equal to the bafe DG ; and let the area of DG — m\ 



The element of the folid DF is m 2 y j and fince DE, or 



y z=.r tan <p, y ~r tan <z> — r. — £-t, fo that the element of the 



cof<p 



folid = in r. — £— .. 

 cof<p 



This quantity divided by AE 2 , that is, fince AE : AD : : 1 : 



f 



C ° f<P ' by cH^ giveS the element °f the attradion in the direc- 

 tion AE equal to ^ X *M - £& To- reduce this to the 



direction AD, it muft be multiplied into the cofine of the angle 

 DAE or <p, fo that the element of the attraction of the column 



in the direction AD is — <pcof<p, and the attraction itfelf — 



r 



m% C ' r ^ n? r 

 — ©col © zr — nn<pr 

 r j r 



When 



