1888.] of Curves and of Surfaces. 233 
We also have 
ve 78 _ 3 { Bi a (h, ut 
Oa dy® dx {h, dy) dy lh, Ox 
mg ale h, On -—(R) g-# oot 
~ Ba (i dy th, dady dy \h,/ dx h, dwdy 
O(h,/hes 1) _ 7 2 O(h,/hos 9) _ aE 
Be eS yi oe i 
JEG a Cea hee (i 
Similarly we should obtain 
oi cL a : (7). 
0a? By : 2 On \A 
Thus we have 
aa a TE (00) + (Gy) } + Papen le By Fe 
E)-8EE SB B 
“hewn 20)+8 20 
4. Ifin the equation 
0” logh ee logh _ 
Ox" oy” 
we substitute for h the value found in Art. 1, and utilize the 
transformation of the preceding article, we have 
=0 
0° Pos 
\h 3E +h, = log h, hk 
oe & Fe ag (oshhh) += (; -- = 5, (oslih mh =) 
By means of the first of the two equations at the end of Art. 2 
we have 
> 
h? 
0” logk 20 logk 0 (h,\0 logk | d (h,\ 0 logk 
ae tag Tih wb) aE tay Rt) a | 
—hjh 
~~ Wh lies, a8} tan te Bel) 
