Of GREATEST ATTRACTION. 229 



If we fuppofe BC and BL to be equal, and therefore the 

 angle BAL 2: the angle BAC, calling either of them n, then 

 fin <p =z fin n 2 , by what has been already fhewn ; and from this 

 equation, as ?? is fuppofed to be given, <p is determined. 



This expreflion for the attraction of an ifofceles pyramid, 

 having a rectangular bafe, may be of ufe in many computations 

 concerning the attraction of bodies. 



If the folidity of the pyramid be given, from the equations 

 f=z 4 p <p, and fin <p zz fin J, we may determine q, and p, that is, 

 the form of the pyramid when /is a maximum. 



Let the folidity of the pyramid —m*, then p, being the al- 

 titude of the pyramid, and jj half the angle at the vertex 

 p tan v\ — half the fide of the bafe, (which is a fquare), and 

 therefore the area of the bafe = 4 p 1 tan ?j% and the folidity of 



the pyramid ^ p 3 tan % 5 fo that ^ p 3 tan % — m, J . 

 3 3 



c % 

 Now tan y? = — A, and fin <p = fin J, alfo 1 — fin <p — 



1 — fin &■ = cof ^ 2 , therefore tan ?j 2 — — 1 -^£- — : fo that m 3 = 



1 — fin <p 



* p 3 . _iHL£_, and ^ - 3 m , . *-W or . = 

 3 r 1 — fin ^ r 4 fin <p ' ^ 



z» / 3 U— ■ m <P) . we jj^^ therefore, /, that is 4/><p = 



4-mcp U3jA—- — HL£/. This laft is, therefore, a maximum 

 Y 4 fin <p 



Ff 2 by 



