PROCEEDINGS 
OF 
THE LITERARY AND PHILOSOPHICAL 
SOCIETY. 
Ordinary Meeting, October 4th, 1870. 
Rev. Wm. Gaskell, M.A., Vice-President, in the Chair. 
“On Convertent Functions,” by Sir James Cockle, F.R.S., 
Corresponding Member of the Society. 
It was only after some rather intricate and laborious cal- 
culations that the possibility, which ought to have presented 
itself to my mind earlier, of illusory results stealing in and 
interrupting the processes, occurred to me. And even then 
I did not at first realize the full extent of such results, or 
sufficiently explain and illustrate the means which I sug- 
gested for escaping them. Perhaps those means may be in 
some measure inapplicable or impracticable, and the impor- 
tance and interest which, as I conceive, attach to the subject 
induce me to enter upon it more elaborately. To do it full 
justice would require opportunities that I camiot promise 
myself at present, but I propose, in this necessarily short 
paper, to show how to obtain convertent functions in certain 
marked cases. The results here indicated seem to show (1) 
a correlation between the theory of coresolvents and that of 
convertent functions, (2) the possibility of arriving at an 
organized theory of conjugate definite integrals, and (3) the 
Proceedings— Lit. & Phil. Society. — Yox. X. — No. 1— Session 1870-71. 
