1904-5.] Prof. Metzler on Axisymmetrie Determinants. 71 9’ 
( ' \( '' ) 
Vs'+/C/ V K /s—s' — l 
c= 2 ,: 2* 
1 1 1 
Similarly, 
2 
where 
/2r | + 
t + if | S | k\ f 2 
v 1 1' + s | s | s' + K \ 
V a i j 
\ 
a l <VA 
a l a 2 1 / 
1 50 
+ 
'so 
lil^ 
\{2r\t' + s\s\ 
S+K\ 
\ “i 
<*2 .// 
\ a l a 2 
* ) 
(2r j t + s 
S |r\ 
V «, 
a 2 V 
f2r\t' + s 
I s V2'-|r + s|s|r\ 
V «i 
a 2 / \ a x a 2 i J 
= B + D + E 
D =2< 
B = same as in I., 
2r | t' + s j s \/2 r 1 1' 
u-1 u 2 
f2r\t + s | .s ^ 2 r \t + s 1 1 
\ a l a 2 
C)( I ) 
E= 2 i 2 i 2* 
(2 r 1 1' + s | s | k\/ 2r 1 1' + s \ t - k\ 
\ a i hJK a i 0 
. IT. 
2r\t + s | s \/2r 1 1 + s \ s | /c\/2r 1 1' + s 1 1 — k 
a l a 2/\ a l a 2JJ\ 
3. Let E = Ej + E 2 + E 3 4- . . . -4- E / _ 1 
where 
2' 2 / 
{ 2v 1 1 + s 
|s|k 
V2r j + s | i — k\ 
V -1 
“2./ 
A «-i * / 
(2r 1 1' 4- s 
I*v 
'2r if' + s s k\ / 2r \t' + s 1 1 - A 
\ a i 
a 2 /\ 
a i a 2 j)\ a i i ) 
then if A is axisymmetrie it is easily seen that 
+ E^ = 0 
Qd + 0!-1)E 1 + E 2 = O 
Qd + 1 )e i + (t - 2)E, + E 3 = 0 
£D + (t — 1)E^ 4- {t — 2)E 2 + ...... + 2E/_ + E^_j = 0 o. 
Solving for E x , E 2 , etc. in terms of D we have 
