of Edinburgh, Session 1876-77. 
389 
that is, 
1- 
2x 2x^ | x 2 , 1 
(1 - x) 3 + (1 - #) 3 (1 + x) J (1 — x) 2U 1 - X 2 ' 
This equation may be simplified : write 
then 
and the equation is 
! 
1 - x 2 2 1 +x 2 
x 4 Jr x 3 (l-x) 2 - x) 2 
A 1 2 
X 3 (1 - x) 2 #(1 - x) 2 
+ 
1 + x ry — 1 
(i -x)x 2H -r=^2 ; 
that is, 
{ 
I 1 _ 2 2 
X 4 + x 2 x 3 (l — x) 2 x 2 (l - x) 2 
2 _ 
x(l — x) 2 
1 + X 
( 1 - x)x 2 
2 
( 1 — x) 2 
Q 
i 
viz., this is 
J ( 1-x) 2 (1-x) 2 2 2 2 n} j-x 2 !-x 
( X 4 X 2 X 3 X 2 X J ^ X 2 1 + X ’ 
that is 
giving 
