394 -^ 7iew Solution of two Fluxions proposed ly Simpson. 



I. Given the fluxion ^ f!r^» ^^ ¥^^r~y^'^ ^ V ^'- 



to find its fluent. 



r 



% -5 -1 



Here g' -^ ]/' ' X 7/ y = g' + y\ y y y - 



s- y +i'^y y- 



Put g"- y " 4- 1 = X ; 



. -2 z-1 



then y = -^ - ; 



and y = -;,— : 



to 



and -4y y = = j. 



and 



y y 





Therefore ^^y -+j2 ^ y = z"" x —x^r- - 



-^4 — , and Its flut-nt is - — --- — 



6 ■is 



5z^ — 3xj^ 



lis* 



2" X 5 — 35 





g + f 



A^ 





was to be found 



2. Given the fluxion a — fz"^^ z ^" », required it3 

 fluent. 



Here a-//|^;«-^"- 



1 . -, 'i,-| — |k-1 —in . 



Z=z a —jx I * Z z:^ 



— 3 }i— 1 , 



az —J I « 



Put az " ~f=y; 



then.~-'^= ^+/; 

 a 



also z = -=^— ,— ' : 



