230 Of the SOLIDS 



by hypothefis; and, confequently, its cube, or 64 m* <p l X 



3 {1 — - m _£j or om ittiriQ; the conft ant multipliers, <p 3 . ^T" ?? 

 4 fin <p - ° r r fin <p 



mull be a maximum. 



If we take the fluxion of each of thefe multipliers, and di- 

 vide it by the multiplier itfelf, and put the fum equal to no- 



• • • 



thins;, we fhall have, -3_r — ftco ft — <pco <p = or 3 _. 

 <p 1 — nn<p fin <p <p 



cofp 1 cof<p cof<p . fin<p -f- cofip — cof<p . fin <p 



1 — fin<p fin<p fin<p(i — fin<p) 



, , C ° ^ r, and inverting; thefe fractions ? =r 



fin <p (1 — fin <py ° 3 



fin(p(i— fi n rt = tany ( I — flavor » = 3tan» (1— fin f ). 

 cof 9 



The folution of this tranfcendental equation may eafily be 

 obtained, by approximation, from the trigonometric tables, if we 

 confider that 1 — fin 9 is the coverfed fine of 9. Thus taking 

 the logarithms, we have L 9 ~ L . 3 -j- L . tan 9 -{- L . coverf. 9, 

 From which, by trial, it will foon be difcovered, that 9 is 

 nearly equal to an arch of 48 °. To obtain a more exact va- 

 }ue of 9, let 9 = arc (48 ° -f /3), /3 being a number of mi- 

 nutes to be determined. Becaufe arc. 48 ° =: .8377580, 

 and arc(48°+/3) = .8377580 + .0002909/3, therefore log. 

 arc (4.8? + /3) = 9.9231186 + .0001506 (B. 



In 



