352 
Monpay, May 127u, 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 Rev. John H. Jellett read a Paper, by Mr. Thomas 
J. Campbell, on the solution of cubic equations. 
‘<'To resolve the cubic equation, 
+ az?+ba+c=0, 
put x=2' + 2, and the equation becomes 
a3 4+ (3z+ a) w+ (327+ 2az+b) x x (22 + a2* + bz +c) =0, 
which may be proved by development, for 
8 = 43 + 32a"? + 3 22a' + 2° 
ax? = ax? + Qaza' + az? 
bz= ba’ + bz 
c= Cc 
08+ an?+ bz+e=0'3+ (32+a)x?+(32°+2az+b)xt+ 24+ az+bz+e. 
Call the member on the right and left of this equation fx and 
fx respectively : 
oft = 23 + (32+ a) a+ (327+ 2az+ bd) a'+ (234+ a2? 4+ bz+c)=0. 
My object is to reduce /’x to the form of 
23+ Ad’? +1 4'a' +50, 
where x” =/f"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 
