86 
subject on both the eastern and western slopes of the Pen- 
nine chain. Probably they have only to be more diligently 
sought for in order to be found in greater abundance. 
“On Convertent Functions/’ by Sir James Cockle, 
F.R.S., President of the Queensland Philosophical Society. 
Communicated by the Rev. Robert Harley, F.R.S. 
The present paper is a supplement to my paper “ On Con- 
vertent Functions,” printed in the Proceedings [supra, vol. 
VIII., pp. 2 — 3). The convertent equation (3) contains in 
substance only one disposable arbitrary, and the sign of 
summation S does not increase, and may be expunged from 
it without diminishing, its generality. Consequently the 
process would fail to convert the Boolian integral for the 
cubic and lead only to illusory results. But a recognition 
of this failure has led me to another form of convertent 
equation. And, first, if to the several dexters of (2) and (3) 
we add a term h, then the conversion will be possible, even 
though h be not a perfect differential coefficient, provided 
only that fhdu be assignable within the limits of the inte- 
gration. But the following is the mode in which I wish to 
present the process with reference to a class of integrals 
wherein all the Boolians are included. Suppose that we 
seek to convert 
fym v ) dv 
where 
<p(x, v) = XU \h[x, V) (4) 
wherein X is a function of x only, and U and V are func- 
tions of v only. Then the convertent equation is 
yT? d a< P df b 
(5) 
where 
/r = G ' W # (6) 
therein F and G are functions of x only, and the factors W 
d r \p 
