352 
Monpay, May 127, 1856. 
JAMES HENTHORN TODD, D.D., Presipent, 
in the Chair. 
Tuomas H. Lepwicu, Esq., and John H. Otway, Esq., were 
elected Members of the Academy. 
The Rey. John H. Jellett read a Paper, by Mr. Thomas 
J. Campbell, on the solution of cubic equations. 
‘* To resolve the cubic equation, 
«+ ax?+be+c=0, 
put «=2' + 2, and the equation becomes 
a's + (32+ a) w+ (32°+ 2az+b) x x (2 +a22+ bz +c) =0, 
which may be proved by development, for 
8 = 03 4+ 32a" + 822a' + 23 
An? = ax? + 2aza' + az? 
bz= ba’ + bz 
c= Cc 
“0+ ax+ bz+e=x%+(32+a)u?+(32?+2az+b)at+ e+ az+bz+e. 
Call the member on the right and left of this equation fx and 
fx respectively : 
oft =? + (32+ a) 2? + (8274 2az + b) w+ (22+ a2?+bz+c)=0. 
My object is to reduce f’x to the form of 
234 Ad’?+1 Aa’ +c¢=0, 
where x” =/"x (or another function of f’x), and thus to find 2” 
by completing the cube, for a similar reason as we complete 
the square in equations of the second degree. 
‘* But to effect this important relation of the coefficients 
