Ordinary Meeting, January 22nd, 1878, 
R. Angus Smith, Pli.D., F.R.S., &c., Vice-President, in the 
Chair. 
a 
dx 
«On the Cubic Integral by 
Robert Rawson, Esq., Assoc. I.N.A., Hon. Mem. Manches- 
ter Literary and Philosophical Society; Mem. of the 
London Math. Society. 
1. As far as I know the cubic integral has received but 
little attention from mathematicians : the reason for this 
may be that it has been regarded by them as a particular 
case of the quartic integral. 
This, no doubt, is to a certain extent true; still, the 
quartic integral is readily reduced to the cubic (see Art. 13) 
and there are some advantages in considering the cubic 
integral first, in its natural order, especially so in the reduc- 
tion of it to an elementary integral of a fractional modulus 
(n) and amplitude (0). 
The quartic integral here alluded to is usually called 
elliptic integral. I cannot hope, however, to induce mathe- 
maticians to abandon this unnatural terminology, viz. ellip- 
tical integrals for the more natural one of quartic integrals, 
as suggested by Professor Cayley (see Salmon’s Higher 
Algebra, page 83). 
In this paper I have not entered into the great question 
of the comparison of cubic integrals — my effort here has 
been of a more limited kind, viz., to reduce the cubic integral 
to the elementary integral 
U dd 
u = 
Jo 
V 1 + ncos.mO 
Where (n) is a proper fraction, and (m) any positive whole 
number. I believe this elementary integral is better adapted 
Proceedings— Lit. & Phil. Soc. — Yol. XVII.— No. 7— Session 1877-8, 
