222 Of ths SOLIDS' 



felf, the fum of the quotients is equal to nothing. Therefore 



* — i -A --U-. -4 



coiV~" , 5 cof<p 3 . cof> 3 fin p. Imp 



-r + i ~ == o, or 



tan*-? 3 cofV fm«T* 



i (i — cof?') 5 <p fin (p 3 <pcof<p 



cof <p 2 (tan p — ?) 3 cof <p fin <p 



= °, 



and fin <P 8 __ 5 fin <P _ 3Cof<p _ . 



cof <p z (tan <p — <p) 3 cof <p ~ fin <p ' 



fin? _ 5 3 £^, and «»C 



cof cp (tan <p — <p) 3 fin <p 2 tan<p — <p 



4 -f- 3 cot <p\ 

 3 



tt % tan a , 



Hence — ^ r — • = tan <p — «, and <p n tan <p — 



5 -f- 9 cot <p* y y 



3 tan (p 5 tan <p + 9 tan <p . cot <p * — 3 tan<p __ 



5 -f- 9 . cot <p* "" 5 + 9 cot <p 2 



2 tan <p -{- 9 cot <p 

 5 + 9 cot <p 4 



Let tan (pzzt, then 9 zz 



2/ + 2 



> _ 2 t* + 9 t 



5 + 9 ? 5 '' + 9 



^ , — J-; which, therefore, is the value of <p when F is a 

 9 + 5' 



maximum* 



The 



