59 
Ordinary Meeting, January 10th, 1882. 
J. P. Joule, D.C.L., LL.D., F.R.S, &c., in the Chair. 
“On Differential Resolvents, and Partial Differential 
Resolvents,” by Robert Rawson, Esq., Assoc. I.N.A., Hon. 
Member of the Society. 
Arts. 1 to 8 contain the first and second differentia] 
resolvents of a cubic, using therein one independent vari- 
able only — and, from the second differential resolvent the 
usual root of the cubic is determined. 
In Arts. 9 to 11 there is the first partial differential 
resolvents of a general cubic, using therein two independent 
variables — and, from this partial differential resolvent the 
root of the general cubic is obtained. 
Arts. 12 to 14 contain the first partial differential re- 
solvents of a quartic, using therein three independent 
variables — and, from this resolvent the root of the quartic 
is determined. 
1. Let f + ay + m = 0 (1) 
be a cubic in which ( a ) and (m) are functions of x, a vari- 
able parameter. 
For convenience, y 1 = a 1 = ^ &c., will be used. 
ax ax 
Differentiate (1) with respect to x, then 
^=-W =p/+Qy+R (2) 
where P, Q, R are functions of (a, m) to be determined as 
follows : — 
- a l y - m 1 = 3P«/ 4 + 3Qy* 4 (3R + aV )y 2 + aQy + «R 
Proceedings— Lit. & Phil. Soc.— Vol. XXI.— No* 5. — Session 1881-2* 
