178 
MR. W. M. HICKS OK THE STEADY MOTION AND 
R„ . 4/t 2 — 1 
HK=I S { 
p ow a 
2^/CC-c) 1 4 
f — 7 — P /iV /(C—c) l A,, cos wv 
Therefore 
C^*=! 2 {-i E »QV 2 -^rx}A„ 
= -V ss ( Q “t- p »f) A " 
= [T.F., 24] 
a L J 
=/* ( b y 4 ) 
Hence energy = n[xxfj Q , as is right, or 
7T 7T& 
a: 
/W^o 4l /V _i r o_|_ 2 ^r 
1 T„ 
Rr 
4?i 2 — 1 R„ 
(3. Here if/ along the tore is (p 3 —\a 2 ), and denoting the general value of if/ by 
^i+xrjj 3 
1 bifr. 2 
10 - ■ p 
/3xfj 0 W=i TX ^ dv 
[2*1 fok. 
Now j - dv is proportional to the flow round the ring due to translation alone, 
0 p 
and is therefore zero. 
Hence 
p = r, (%«•* 
a~Yo J 0 ou 
But 
V(C-c) 
2\fr 0 \/2 
7T\/(C—C) 
-^|„+ as i 1 +sb) T '« I 
cos nv 
Therefore 
cos nv (say) 
wi^ dv 
a J 0 0 —c ou 
Hence by 7 
^ =4§ wfd(c^)-l-* A » p >- |A ‘ p ‘ +iA « p » cos V+S ' B - cos nv]dv 
Now 
„ f* cos nvdv 
0*^=1.-^r 
Therefore 
