38 
A paper was read “ On Differential Equations,” by His 
Honour Chief Justice Cockle, M.A. F.R.A.S., F.C.P.S., &c., 
President of the Philosophical Society of Queensland ; com- 
municated by the Rev. Robert Harley, F.R.S., &c. 
Importing an arbitrary constant C into a result which Mr. 
Robert Rawson, an Honorary Member of the Manchester 
Literary and Philosophical Society, in a letter dated Ports- 
mouth, June 14 th, 1862, communicated to me, we may say * 
that the differential resolvent of a (trinomial) cubic, whereof 
the coefficient of the second term vanishes and that of the 
third is constant, is of the form 
Put 
<Py f"( x ) 
dsr f'(x) dx 
2 
y = 0 
/'W = ^ = X, C=K-, 
then, (1) divided by X 2 becomes 
1 _ <Fy_V_ 
X*’ dcd~ X 3 
dy 
dx 
— KV = 0 
(1) 
( 2 ) 
Now, if 
then 
L = ± K, M- :fK, 
(14 + L )(r-^ + M >=° < 3 > 
is the symbolical decomposition of (1) or (2). When L and 
M are any constants whatever, (3), when developed, gives 
rise to a linear differential equation of the second order 
reducible to an equation with constant coefficients by changing 
the independent variable from x to t, where 
