232 Mr Brill, On Orthogonal Systems [May 21, 
2. If we separate the equation 
OE Gh, 
aa th, 5g + abe iF} =o 
into its real and imaginary parts, we obtain 
op 0g oh, _ Oh, 
h, peaches loa +q 1% 
og Op Ol, eh, 
and haa ge to, ae. 
From these we easily deduce 
0 0 7) 7) ol 
hag t Cag * Pag Tael # (B+) Ze =O 
=0 
0. 
Cpe og op 2 
and =h, ae path + hp get andl + (p peg) Ge=0 
which may be written in the form 
h 0 logk 0 ad, Oh, _ 
2 07 woe a p 1 Be 
0 19, 0logk ch, 
and h, an tan is h, aE 3E 
Thus we have the two equations 
0 (h, Ologk 1 oh,) | 0 fh, Ologk 1 Oh.) _ 
ei Ge Th oe Taya on |e eee 
= 0. 
de, Oa ene x at ple ag i a 
aie ae jo Ue an aan h, aan 5h fe = 0. 
3. From the equations of Art. 1, we deduce 
fa Ss a (2) a al ee ea =a (ee) 
'? 0a oy @ Oy Oa Ce 
Thus we have hh, me n= hoh; 
and therefore 0 (E, » =h,h,. 
O(a, y 
