Ordinary Meeting, December 24th, 1867. 
E. W. BinNey, F.RS., F.G.S., Vice-President, in the Chair. 
“ Memorandum on the Evaluation of Integrals,” by the 
Hon. Chief Justice Cockle, F.R.S., &c., of Queensland. 
Communicated by the Rev. Professor Harley, F.R.S. 
The processes indicated in my paper “ On the Conversion 
of Integrals”* admit of direct application to certain results 
which Boole attained by a contemplation of the researches 
of Mr. Harley*)” and of Mr. Cayley. The object of this 
memorandum is to give a more general form and perhaps a 
more convenient expression to a portion of the processes of 
that paper. Thus we may generalise and restate (7) by 
saying that if 
* d 3 d) d 2 (b n d 2 (h 
+ a -=-£ + fiv r 
d(f> 
dvdx ^ dx 
ev~- + 
dx r 
dvdx 2 dx 2 
wherein A, «, /3, . . £ are functions of x only and free from 
v, be, when v is treated as the only independent variable, a 
perfect differential coefficient with respect to v of a function 
/ 2 , then /(pdv, which for the sake of brevity we may replace 
by y, satisfies the linear differential equation of the second 
order 
+ <^>! + + + *2 + ** + x - (i > 
where f % is obtained, where obtainable, by properly assigning 
* Phil. Mag. Suppl., July, 1867, p. 537. Art. 9 may be expunged as in- 
volving an error of computation, and Art. 10 is susceptible of a perhaps more 
general expression. 
t Mr. Harley and I have since been conducted independently to a generali- 
zation of one of Boole’s results, which consists in applying Boole’s process to 
forms of trinomial equations other than that discussed by him. I think it 
right to say that Mr, Harley’s communication to me on the subject included 
his demonstration of his generalization, mine to him a verification (or perhaps 
two) only. 
Peoceedings — Lit. & Phil. Society — Yol. YII. — No. 6. — Session, 1867-8. 
