OP ARTS AND SCIENCES. 



225 



Fig 



(. -1 y—KA , _i y , * _i y—LB' , _, y 

 — «i fan i if _ — tjin i _£ — -f-tan ^ , — tan — ^- 



5^^ = m tan~ 



X 



-a-^^ 



X — a 



x-OB-BL 



x-OB 



= m •] tan ^ 



y.AK-KA {x-a) 



(x — ay + f — 1/. KA' — AK {x — a) 

 _i y.BL-LB' (x-OB) 



+ tan 



(x - OB)'^ ^f--y. LB' - BL{x- OB) 



-0B)\ 



If ^' be made to approach A as a limit, we have 



and, if m be made to change so that m . AA' shall always be equal to 



the constant fi, Limit (m . BB') will be equal to the constant, — . fi. 



a" 



Limit i^p = i/'o = )(^ Limit 

 AA' = AA'=0 



tan 



_i y .AK-KA (x-a) 



(x—a)'^+y^—y . KA—AK(x—a) 



+ —„ Limit 

 BB' = 



a' 



( tan-^ 



< (x-' 



AA' 



y.BL-LB' (x- 



I 



(x-OB)'+y'-y 



BB' 



B' (x-OB) \ 



TB'-BLi x-OB) > 



VOL. XXVI. (y. s. XVIII.) 



15 



