194 Mr J. Brill, On Conjugate Functions [Feb. 27, 
2 2) 2 
2 {us (~) = | i {hx (*) in (-) 
On \py/ PsP» On \p,/ — \P, 
cee 
y” = 2S Es x! a tan? 0& p Pipe 
mele)“ 
0€ \p,/  \Pp 
2 (2)- = 
By ae eo maior 
and 
4. Since logh—7S is expressible as a function of a complex 
variable, it follows that 
dlogh _ #logh 
Fete eae 
and 
oy = iy 
ae 
The first of these equations is pee to 
rele) 
Mra al sels) hai 
0& \p, on Pi Pe 
which is the form assumed by Lamé’s equation connecting the 
curvatures of the two families of a system of orthogonal curves, 
when the system is derivable from a function of a complex variable. 
It would be an interesting subject for research to discover whether 
there be an analogue to the equation 
o Ay /1\2 1\2 
AN aes 
: On ig Py Pe 
in the general theory of orthogonal curves. 
o(—3) sd logh o(—S)__dlogh 
Since aE hm aos and aera 
therefore we have 
2.e€. to 
Caper era a Ag ORE SV 
0& 7. hp, On ~ hp,” 
