402 PEOF. A. E. FOESYTH ON THE DIFFEEENTIAL INVAEIANTS OF A SUEFACE. 
When the geometric values of the several invariants are substituted, we tind 
iv\ = BV3 ^ , 
as 
and therefore 
= BV^ 
(IK. 
dn ’ 
1 = 
which IS the geometric signijicance of the differential invaiiant of deformation of the 
third order. Its expression appears to involve association with the curve <j) = 0 ; but 
the relations in § ol shew that the association is the same for all curves, so that the 
quantity is a function solely of position on the surface, being the sum of the squares 
of the fiist derivatives of K along any two perpendicular directions along the 
surface.] 
i'KSSENTEB 
