697] 
ON THE DOUBLE ^-FUNCTIONS. 
429 
If in these formulae w is indefinitely nearly = a, then a 3 is indefinitely small, so that 
VaabxCxd! may be neglected in comparison with Va^Cada: also w — y may be put = a 2 ; 
the formulae thus become 
A — — 
VboCod 
i 2 Va, 
-, B = (a + y) 
VbaCgda 
a x Va 3 
C = 
Vb 3 C 3 da 
where the values of A, B, C are each of them indefinitely large on account of the 
factor Va 3 in the denominator; the value of G is C = ay A, and substituting this value 
in the equation 
ay 2 w = 
C 2 — abed 
A*-l 
and then considering A as indefinitely large, the equation becomes ay 2 tu = a 2 y 2 , that is, 
w = a; so that w = a is a value of w satisfying this equation. 
Cambridge, 3 July, 1878.