240 Mr Brill, On the Orthogonal System [May 21, 
9. Let & 7, € be the parameters of the three families of 
surfaces forming our orthogonal system. We have the equations 
(a) + Gy) + (Ge) = 
(az) + Ge) + (GE) =e 
GI (OS\ 4 (OS) ne 
CG te =e 
an at On OE | On OE _ 
once oyney a702  ~ 
ob OF , 0b 0& 0b 0 4 
On Oi Gy Oz0% > * 
0€ On  0€ On _ OE On | 
Anon Onan oe ie 
which may also be written in the form 
GEN GaN? hog 
lo. () % lbs (=) The = 
BL CEN (Cp ane alan OG eae 
nalde) + nz lay) tne lg) =) 
00) eae a) a) 
0 
hXoz) he \z 
1 0G 0G | 1 On on 1 a€ 
le OF OZ Ii OH OZ © li Cy O72 
10£0E& 1 Ondn 1 OF 0¢ 
ae at ipo hee” 
1 og 0F | 1 On On as Os 
lo Ceoy lo Ceoy lo Ge Oy 
From the last three equations of the first group we obtain 
0& 0& 0& 
Oe 5 ON) 02 i 
1B) TEA ta 9 a 
OO, 2) OABex) Ole, 9) 
On On On 
Oar fs Oy i Oz yah 
0 ( “a .) 4 
