768 
MR. J. 0. MALET ON A CLASS OE INVARIANTS. 
Now let 
from which 
Ql-6, 3Q2- u, Qg — v 
P 1 = g, u=v=F a ^ 
from which equations two distinct invariants, of the second kind, of the cubic may be 
found, thus 
|= f ^+3f ¥ T 3 =^(f+3PiP 8 ) 
therefore 
Hence 
f+ 3P i P a _l * 
Pg 1 V * <U 
dP. 
^f+ 3P 1 P 3 
is an invariant which I shall call I x . 
Again 
or 
Hence we have 
dP x _ 2cf)" 2 <f>" 
dx ~ + (f)' 3 
<df+ 2P 1 3 -3 P 4=-“ 
dl\ 
dx 
+2P i 3 —3P 2 
and we have another invariant 
f+ 2p 1 3 - 3p a 
u 
v * 
which I shall call L. 
dP x 
We have also, calling '"“■^jf“2P 1 s +3P 2 , L, 
therefore 
from which 
and we have the invariant 
<f/ Z Jj = U 
.,jdL 0 // iz/T 
^+ 2 ^ L= rf7 
^ +2PlL = I„^ 
u* dt 
dL 
dx 
L* 
+ 2P X L 
I 3 say. 
