278 Ml". A. Cayley on the Theory of Logarithms. 



III. x=+, .r'=— , .ra' — 7/j/'= + 



e"=0 



— ^x r r 



and therefore e + e' — e" + e"' = 0. 



IV. a;= +, *■'=—, xx^ — yy'^ — 

 e =0 



e"' = 0, 



d therefore e + e' - e" + e"' = if ^, ^ (^ + ^!) , 



x' \x x'/ 



an 

 but 

 e 



V. .rE=— , a?'= +, .r,«' — ?/// = + 



■~ "^ .r \a; a;/ 



e' =0 



and therefore e + e' — e" + e'" = 0. 



VI. a;= — , J''= +, xa^ — yy'= — 



~ ^ X 



e' =0 



e"'=0, 



and therefore e + e'-e" + e"' = if ^ = (^ + ^), 



X \x xj 



bute + e'-e" + e"'= + 2=^ + ^,if^=-6^ + <). 

 ~ XXX \x X / 



