370 
PEOFESSOE A. E. FOESYTH ON THE DIFFEEENTIAL INVAEIANTS 
and therefore, by the relations in § 32, we have 
The result of § 24 gives 
HEuJIA 
V3 
w 
t 
T 
I) = _ i , 
and therefore, also by the relations in § 32, we have 
Also 
so that 
and 
so that 
35. Certain invariants occur as belonging to the surface, independent of all curves 
such as (f) = 0, Of these, the most important is VV“^; its value is given by 
V 4 
But, as is well known, we also have 
4K. 
so that we have 
LN - _ 1 _ 
EG — PjPo 
V = 4V^H (?Co). 
Ihis is a relation among the ditierential invariants, and it is due to the intrinsic 
nature ot the quantities E, F, G, L, M, N ; accordingly, the number of algebraically 
independent invariants up to the present order must (§ 23) be diminished by unit}’", 
on account of the preceding relation. 
It was noted, in § 21, that H and I(?Co, w'o) are alternatives in a complete 
