296 
MR. G. T. WALKER ON REPULSION AND ROTATION 
Consider 
H 0 = e ln9 sin pt 
at the surface of the shell, and let the induced currents give rise to momentum at the 
surface of 
H = e ine [B sin pt -f- C cos pt\. 
Since H is the potential of a distribution on the cylinder of imaginary matter of 
surface density w , we have 
7b 
w — -—- e ine [B sin pt + C cos pt]. 
On substituting in (iv.) we see that 
an 
'lira 
[B sin pt -b C cos pi] — — p [B cos pt — C sin pt] — pA cos pt. 
Therefore 
Therefore 
Hence 
an -r-» ™ „ | 
2^ B -^ C=0 [_ 
•* >a + ^ b + £ c = °-J 
— 2napA B C 
4:7T 2 ay 2 + <x 2 /i 2 'In a/p an 
A np ( 2nap sin pt + ancospt) in$ 
-A- . o o o o o ^ 
corresponding to a term 
H 0 = Ae ine sin pt. 
On differentiating with respect to t, we see that if 
H 0 = A'e in0 cos pt, 
then 
w 
A , np ( 273 -ap cos pt — an sin pt) in9 
= ~ A 4t r*a*p* + 0*1# ' ' 
On separating real and imaginary parts, it is clear that when 
H 0 = [M cos nO -f- N sin n0] sin pt 
+ [Q cos nO -+■ It sin nff] cos pt, 
