OF A SURFACE, AND THEIR C4EOMETRIC SIGNIFICANCE. 
3G!) 
tangent to (f), we take tlie direction determined by clx/chi and di//chi as beino- 
perpendicular to the direction determined by x' and y '; hence 
Moreover 
and therefore 
(In ~ ~Y y ^'I’m + 
Ih = V (E4l - 
the quantities in the brackets in the last expressions being the quantities r and s of 
§ 15 . 
Identijication of the Simplest Invariants, 
34. Using these results, w^e can at once obtain the interpretation of several of the 
invariants. We have 
and therefore 
B = ~ ^ 
dn 
f dx . j d'l/ 
\/ 
~ V^’ 
Again, 
-p2 
A = (L. M, NI,r, 2/Y 
= i (n M, 
— . 
5 
v\. 
and therefore by tlie relations in § 32, we I 
Also 
w'. B- 
- p' • 
W = ^{(EiM-FL)a3'^+.. .} 
_ J {up w'o). 
Vu’., 
VOL. cci. — A. 3 g 
