226 Of the SOLIDS 



But BC it a . tan z j and therefore KC, the fluxion of BC, is 



z 



- a , *.-■ if, then, CE = n, m = CE X CK = na . — ±_, 

 cofz col z 



and fubftituting this for m ,wegetfrznz. {me. 



Next, to exprefs lin e, in terms of z, if we make E rr BAL, 

 the angle fubtended by the vertical columns, when it is great- 

 eft, or the inclination of the plane ADM, to the plane ACN, 

 then we may confider the angle CAD, as meafured by the fide 

 of a right angled fpherical triangle, of which the other fide is 

 oo — z, and E the angle, adjacent to that fide, and therefore 

 tan e — fin (90 — 2;) . tan E — cof z . tan E. But tan E = 



tan . BAL = — r- = -, fuppofing BL, or CD = b. 

 BA a 



t 



b r m\ e b - 



Therefore tan e — — coi z, or — T zz. - . cof z. 



a coif a 



fin* 2 h % r * An/ b % /. s . 



HeNCE E3? = a* ■ C ° CZ ' ° r r=M? = a> ' C ° f * ' and 



/ 6) 



£ n ^ = fL.cofx* — fin/.— cof z 2 ; and therefore fin e = 



ii 



^ 



- . coi z 



a 



a/ 1 + — a cof 



coi z 

 a' 



If this value of fin e be fubflituted for it, we have 



b n z cof z 

 /= nyk • fin * — ^ — = . 



_ /* -*3 



a */ 1 H — - cof 2" 



Let 



