Of GREATEST ATTRACTION. 239 



fin <f = - cof ( n " — n") — - cof ( ," + *'") 

 2 2 



fin <p'" = - cof („'"— , ) — I cof (,'"-1- 1 )• 



2 '2 



By either of thefe methods, the determination of the attrac- 

 tion is reduced to a very fimple trigonometrical calculation. 



XXII. 



The preceding theorems will alfo ferve to determine the at- 

 traction of a parallelepiped, of any given dimenfions, in the di- 

 rection perpendicular to its fides. 



Let BF (Fig. 16.) be a parallelepiped, and A, a point in BK, 

 the interferon of two of its fides, where a particle of matter is, 

 fuppofed to be placed ; it is required to find the attraction in 

 the direction AB. 



Though the placing of A in one of the interfections of the. 

 planes, feems to limit the inquiry, it has in reality no fuch ef- 

 fect \ for wherever A be with refpect to the parallelepiped, by 

 drawing from it a perpendicular to the oppofite plane of the fo- 

 lid, and making planes to pafs through this perpendicular, the 

 whole may be divided into four parallelepipeds, each having 

 AB for an interfection of two of its planes ; and being, there- 

 fore, related to the given particle, in the fame way that the. 

 parallelepiped BF is to A. 



Let GH be any fection of the folid parallel to EC, and let it 

 reprefent a plate of indefinitely fmall thicknefs. 



Let AB' = x, B'b, the thicknefs of the plate — x. Then <p 

 being fo determined, that fin <p — fin B'AH X fin BAG, the at- 

 traction of the plate GH is <p x } which, therefore, is the ele- 

 ment 



