448: Prof. H. Nagaoka: Kinetics of a System of 
Suppose that the disturbances are propagated round the 
nail 
ring in waves with velocity - for p, o, and _ for ¢, and there- 
fore given by ‘ : 
pi =Acos (nt +a+hs) po =Acos (nt +a+2hO+hs) 
o,=B sin (nt +a+hs) o.=B sin (nt +a+2h0+hs) 
€ =Ccos (n/t +y+hs) €,=C cos (n't +74 2h6 + hs) 
where h=1, 2, 3,:. ; . 
Putting for simplicity w=nt+aths, u'=n/t+y+hs, we 
have 
Pt —P2 = —2A cos uw sin? hO— A sin u sin 2h0, 
O,—0,= 2Bsin usin? hO—B cos u sin 2h0. 
Denoting the number of particles in a ring by », let 




pea 2. om (v—1)7 
Goll ah ee 
lL snh@cos@ cos? hOé 
RG ae | | 
sin 2h0@ cos 0 | 
M= aie sin? @ 
Neos sin? /@ cos? 6 1sin* hé | 
on ( sin? 0 2 sin 0 a (6) 
sin” hé | 
Jo 3 sin’ @ | 
] 
K=> 2 sin 0 | 
where the summation extends to all possible values of 0. 
Suppressing the suffix in 7,, $,, 2;, we find 
| 
eM a ee = 5.. (K+ (LA—MB) cos 1} 
1 

ove OVie eee e . 
aS apie Fa (MA + NB) sin uw 
OF 2 OV & 
Oz air OF 5 
(7) 

5, —§ —_— — 
e 
an J cos wu’ 
2a 
