324 
MR. G. T. WALKER ON REPULSION AND ROTATION 
Then, with the same notation as before, the magnetic potential due to the single 
pole will be, on the a, b shell, 
H cos pt 
= 
[/r + a 2 + 2 pa sin 9 cos 0 + 7 ]* 
H cos pt T_ a . 
P 
1-sin 9 cos y -j- (b -j~ second harmonics 
P 
The equations (xiii.) now give 
Ha 
'A =-v c°s y -|- fourth powers of a 
P~ 
v Ha . 
B = — sin y + . . . 
P“ 
_ _ 2aa ' 2 tv 
d? 
'E = + ~ E' 
• . (xv.), 
and since in fi 0 there was no term cos 0, the coefficients 'C, 'F will be zero. 
Also 
D = [3<x. 'A] + fourth powers, 
E = -^p[3o- ,'B] . . . 
Therefore 
rv ^irpa , 
U = -77- ocr . 
Ai 
Jjy - 7T P a C) )( j' 
- A\ 
' Ha' 
-7- COS y 
P 
.Ha' . / 
+ sm y 
p 
The couple on the a, b shell has been proved to be (xiv.) 
This is equal to 
^(WE - ‘B'D). 
~^ < ^ 3 ['A.E' + 2 'B.D'], 
or 
or 
Qirpcda aa ' 2 Ha Girpa'cr' Ha' r . , n 
^ AT J- L- cosy sin y -2smycosy], 
- h 2 3 !slTr % AJ' d + 26 ')- 
p s p' 3 A l A\ cP 
