386 On the Line and Band Spectrum. 
We see at once that 
NL ones ncaa 
2 sin @ 
2J+L=3J—K, N=2J—K*%*, 
a) 
TT 3h : 
because 0= Bp’ h@= ry where 7 is an integer. Hence the 
equation is 
ni —f{o?+ w(J—K)}n?=p(2J — K){w? + 2n? 4+ (33 —K)}. 
2 
e 
2ma?’ 
With Nagaoka, p where e is the charge of an 
electron in electrostatic units, 1 is its mass, and a is the 
. . ad é ~ ~ 
radius of the orbit. Taking OX 10", e=34 % ee 
a=10-', all in C.G.S. units, we have ~= 10” approximately. 
I find that with sufficient accuracy for most purposes, at 
any rate for 2p=10 or more, we have 
4K =°366 x (2~) logy (2p). 
4J =*017 x (2p)?. 
For 2p=10, 4K=3°6, 4J=17. 
Suppose the period of revolution to be the period of 
sodium light ; then #?=10*. Unless the angular velocity 
be much greater, we may clearly neglect w? ; and similarly 
we shall neglect n’*. The above values give 
ni — x0 x ne = x 2500, 
n?=6lu or —37X pm, 
The moduius of the imaginary roots is about 6 x 10" or 
about 120 times the number of revolutions per second. Thus 
these disturbances would increase 2°7 times during 73,5 of 
a revolution. It is difficult to see how such a system could 
represent even so unstable a thing:as the radium atom; 
nor do I think that Nagaoka is justified in speaking of his 
system as “ generally stable.” 
* Note (June 9th).—These values are only approximate: strictly 
N—L—2K lies between J and J—K, 2J-+L between 3J-—K and 
3J—2K, and N between 2J and 2J—K; the order of n” is not materially 
altered. 
If the velocity of the corpuscles were as great as that of light, the 
stability would be about 1400 times greater, that is, the same disturbance 
would only be produced after about 12 revolutions. 7 
