[800 
800] OF A SYSTEM OF LINEAR EQUATIONS. 21 
may in any 
As is known, there is no irreducible solution, but only the composite forms 
x, yY, to find 
ciing for the 
rn coefficients 
I = a (ace — ad 2 — b 2 e + 2bed — c 3 ), 
II = (ac — b 2 ) (ae — 4bd + 3c 2 ), 
the developed values of which are given above: II (as a form beginning A — 1 and 
with B = 0) can be nothing else than, and is in fact = Q: and so I (as a form 
beginning with A — 1, B= — 1) can be nothing else than, and is in fact =Q — P; that 
egree 4 and 
is, we have 
P = - I + II, or I = -P + Q, 
Q= II, 11= Q; 
and so, in general, we have a standard set of values for the asyzygetic seminvariants 
of a given degree and weight; or, what is the same thing, for the covariants of a 
given deg-order.