10 
Thus the proposed (b) is not integrable, neither is it satisfied 
on therein substituting the value of ^ given by the equation (c) ; 
but if we cut off from this value the constant term, the remaining 
equation z — x^y satisfies the proposed.” 
We may apply to solutions obtained as suggested in the 
above article the term “ discriminoidal.” But there exist 
unintegrable equations having single solutions not to be so 
obtained. Solutions of the latter class may be called ultra- 
dis criminoidal. ” 
The equation (7) given by Mr. Eobert Eawson at page 
117 of his interesting communication ^^On Tertiary DifFer- 
ential Equations '' {ante, vol. xvi., pp. 1 1 4-8) is very remark- 
able as Avell as very general. It belongs to a distinct species 
of discriminoidal solution. The reciprocal of the first factor 
of the dexter of Mr. EaAvson’s (8) is an integrating factor of 
his (7), provided that w is the product of a function of x 
into a function of y. An analogous property is possessed 
by every equation of the species to which Mr. Eawson’s 
equation (7) belongs. 
2, Sandringham Gardens, Ealing, 
October 10, 1879. 
