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 folution. 
Ler 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. 
Ler 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 AD =7, the angle DAE = 9, DE (fuppo- 
fed variable) =y, and let EF be a fection of the folid parallel, 
and equal to the bafe DG; and let the area of DG = m’. 
Tue element of the folid DF is m’¥; and fince DE, or 
yr tang, j=ortan ? —r.—®_., fo that the element of the 
cof@ 
folid = m?r. —2_.. 
col@ 
Tus quantity divided by AE’, that is, fince AE: AD:: 1: 
cof, by ae gives the element of the attraction in the direc- 
; mre cole °9 
tion AE equal reir 4 eae = “*. To: reduce this to the 
direction AD, it muft be multiplied-into the cofine of the angle 
- DAE or ¢; fothat the element of the attra@tion of the column. 
in the: direCtion. AD. is = 9 cof g, and the attraction itfelf — 
6 3 (2 yt? ] 
~ {¢cofe=" fing 
WHEN. 
