349 
tical 
349] ON A CASE OF THE INVOLUTION OF CUBIC CURVES. 333 
Second terra, writing it out in full and collecting the terms which contain 
0i 4- A 
, is 
= -2 
0 1 
1 1 
+ 
0] 4" A \0 2 4" № 0 2 4" v. 
whereof the first part is 
22 
Lb V 
^ + 
8-j (0 1 + A) \0 3 + /jL 0 2 + vj ’ 
~ ^ lS ^ + A S (9 2 + A + ^0i + A 0 2 4-A’ 
= - 0i2 ~n—^~ 1 
0i + A 0.> -f- A 0 1 — 0-2 \0-2 4* A 0] A/ 
_ 2 2 _0^ /2_ 2\ __ 4 2 
xm \'e* e x -e % \e % ej’ 0 2 0* 
2 
0„ : 
and the second part is 
-l 
x s . - 2 
A 2 
0,1 0 2 + A 0 2 + A (01 + A) (0 a 4-A)[ ’ 
2 i- A «, A 1 V /_A* A 2 
= _ J“_ JV X V x _ 
0! r 01 + A 0 a 4- A 01 - 02 ~ V02 4- A 0! + a; J ’ 
and observing that 
2 = 2K<V r+x ^ = s (ft + X) - 20A + ft=S , 
= 30i 4 (A + 4* v) — 60] 4 0] 2 . '-jr, 
Vi 
— — 0i + A -T ¡jb v, 
A 2 
with the like value for 2 -a , the second part is 
0 2 + A 1 
u-^A^-ft+ft], =-|(i-i), =o. 
47. Hence the whole second term is —~w> an d combining the two terms we 
have 
coeff. XY = f- — f = 0. 
Vo if9. 
In the same manner precisely it appears that 
coeff. XZ = 
0.