229 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
entiation and the multiplication by a constant in the same manner, regarding both 
the one and the other as an operation. A similar process has been employed for 
the solution of ordinary simultaneous equations by Mr Grecory in the Cambridge 
Mathematical Journal, i. 1738. 
1p. Syed 
° : . 2 
By taking the 4 differential of the first equation, we get - +a vt =0; which, 
by virtue of the second, gives 
of _abe= 0; ora=Ac** oy=—A [Pore 
dt at 
‘ KA , 
Ex. 2. Te +ay +b6x=0, at + dy + bax 0. 
These equations may be written 
sabi of ey Pee 
(, +)e+ay= (+) y+la=0; 
whence, by eliminating y, we obtain 
{ (Fa+4) Gat) -av} 20 
Let a?, G2, be the roots of the equation 
(e+a’) (¢+6)—av’=0 
then i= — a’) - 6") x=0; which gives 
a=A e*'+ Bet 
and fae ee er 
dt x 
Ex. 3. es 

{ Gat?) Gat?)—o¥} == Gare) 10-9 
= (4) 
This coincides with Ex. 4, Class 1, and the solution is 
1 1 
Lay Ab ace Bt, pee, Be Oe No 
ee ge -- a) $i ote 6) b (0) 
