;!()() 
ME. E. AV. BAEXES OX THE THEORY OF THE 
1 
Now l)y § o‘J M = 0, unless the axes of y tuid include the axis of — 1, in 
which case 
1\1 = d" 1 l(wi + con) is positive or negative. 
Therefore 0, unle.ss the axes of r and (qcoi + ^<^- 2 ) include the axis of — 1, 
ill which e.cse 
M;,„ = =F 1, as is positive or negative. 
Again, by § 14, 
CO, CO., 
p-lq-1 
, ,, = h+ 7 + 7A 7 A) • 
We therefore have 
fo (a 
loo' 
CO, CO.-, 
p~\ v-1 
7 '7 
P-2 
CO.,\ 
r=:0 r=0 
p2 (^1’ ^"* 2 ) 
\P 
7 / 
+ 
2y<hl\{oj„ OJ.) - 2 B 1 ( ^ , ^j I (7)1 + m') 271) + ,S'i( 0 j ^ 277) - M) 
Wl CO.P 
277) [ 
p ’ '1' 
But from the values which have just been given, it is clear that 
log r.T (a 
"1 "3\ A fo 1 
— , - ) = X X loc 
1' C] / ,.= o s=0 
rco^ ^ SCO. 
P 7 
+ Pi < 7^ ^ ~ Pi ("n "i) 
F I / 
OJ s. 
~lp2), 22^0 
Hi; 
■p / *^1 
~2JJl 1 “ 
PP 
5)1 
7/J 
[ill ill') 277) 
-D /"l "-A O 
This result agrees with that of § 67, and on comparison of the absolute term we 
see that 
p-\ 2-1 
log n Il'r.c ( — + = pcj (log p., (ajj, w.,) — ())) + ill') 277) ..Bj (wj, CO.,)] 
r = 0 s = 0 P ‘1 
CO 
— I ^'\g P-2 + Pp’>/) ^ -.'Bi ^ 
.A1 
