244 Mr Brill, On the Orthogonal System [May 21, 
Therefore 
soa aan oe | 
LS ere ee ES 
h, oy h, oz Cee th. sie WneZ 
and, we obtain 
eae tee Lpone, Wyes ater. lien 
Serna Ne Gh eo Soe ae ie Oe 
(le cle sib als 1 dy 1 @€ 
Oi oko) le ee 
11. Suppose that we have a second orthogonal system of 
surfaces, and let a, 8, y be the parameters of the three families 
of the system. Also let 
Ge) Ge) 2G) = 
(=) ie = i Ge) = mee 
Bnonens 
Then, if we express the equations belonging to our former system 
in terms of the elements of this system, we obtain 
a(S) +8 (Ge) +() =A 
ke (2) +h? (=) +h? (2) = h,?, 
ke (Z) +83 (a) +h () = hs 
pn oe, 
1 Oa 2B Ge "8 Gn Gy 
0g ie 2 0f 0& aS as 
2 2 
k, AnD 7 th, a8 ag t Bs pany = ()), 
4208 on nak On 
20E On _ 
Mehr an eo eo) a aa 
Treating these equations by a similar method to that adopted in 
Art. 9, we obtain 
