228 Of the SOLIDS 



Hence this rule, multiply the fine of the greateft elevation, 

 into the line of the greateft azimuth of the folid ; the arch of 

 which this is the line, multiplied into the thicknefs of the fo- 

 lid, is equal to its attraction in the direction of the perpen- 

 dicular from the point attracted. 



The heighth and the length of the parallelepiped, are, there- 

 fore, fimilarly involved in the expreflion of the force, as they 

 ought evidently to be from the nature of the thing. 



XIX. 



■ 



This theorem leads directly to the determination of the at- 

 traction of a pyramid, having a rectangular bafe, on a particle, 

 at its vertex. For if we conlider EM (Fig. n.) as a flice of a 

 pyramid parallel to its bafe, A being the vertex, then the ilice 

 behind EM fubtending the fame angles that it does, will have its 

 force of attraction — ri <p, ri being its thicknefs, and fo of all the 

 reft ; and, therefore, the fum of all thefe attractions, if p denote 

 the whole height of the folid, or the perpendicular from A on 

 its bafe, will be p (p. But as n <p is only the attraction of the 

 part HB, it muft be doubled to give the attraction of the whole 

 folid EM, which is, therefore, 2 n <p \ and this muft again be 

 doubled, to give the attraction of the part which is on the fide 

 of AB, oppofite to EM ; thus the element of the attraction of 

 the pyramid is 4 n <p, and the whole attraction correfponding to 

 the depth p, is 4. p <p. 



If the folid is the fructum of a pyramid whofe depth is p', and 

 vertex A, the angle <p being determined as before, the attraction 

 on A is 4-p' <p- 



If 



