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, 186£, 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 
d‘y f"(x) dy pfyvMlVo 
/'(*)=¥ =x > c=K ’> 
(i) 
then, (1) divided by X 2 becomes 
_ 1 _ dy_ 
X 2 ’ da* X 3 ’ dx 
K 2 y = 0 
( 2 ) 
Now, if 
L = ±K, M=:qFK, 
then 
(t4 +l )(t 4 + m > =0 < 3 > 
is the symbolical decomposition of (1) or (£). 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 
