THE CURVE ON ONE OF THE COORDINATE PLANES. 483 



Dividing by w 2 , and ordaining according to 



JL j_ _l 



UV ' WU ' VW ' 



we get 



U 4 Mi r i +w2 §M±s^ +u «n 



L m m J 







wu L m 



+ 

 vw 



Let us bring w 4 M/ to the same stage. We get 



u^ = (uPjX^Q) - (wP 2 )(u 3 R 2 ) 



Thus 



(x x u 2 \Sj<f>k 

 \ uv *v w- 



_/^_ xrs^ 4 /_^x-| 



\WU f\_ UV \ UV/J 



, u 2 r Sj<j>k 2 ,~| 



H cci-^ - — u 2 z, 2 I 



-u/uL w- J 



x x u 2 {Sk<f>k 



4 



— =— I — ■— +u- 



wu\ m 



') 



CuyZ^Uj 



vw 

 We now recall (where n = a 2 — b 2 ) 



<f>~ 1 u> = anSaw — b 2 w 



These give 



also 



^ = b 2 d>- 1 o ) +w(a 2 +b 2 ). 



u 2 = b 2 + na^ \ (®i = na 2 a 3 

 v 2 =b 2 +na 2 > > -J y x = na % a x 

 w 2 = b 2 +na s 2 ' ^z 1 =na 1 a 2 , 



m Ji m 



+ Si * i + m2 =+L =+b 2 (a 2 +u 2 ) 



~- = a 2 ¥ 



m 



