Particles illustrating the Line and Band Spectrum. 385 
unstable and breaks up with extreme rapidity. Nagaoka in 
his paper states that the system is unstable for some vibrations, 
but Jays little stress on that, and nowhere indicates how 
unstable the system really is. In fact, he suggests it as a 
model of the radium atom. 
Consider the following equations given by Nagaoka :— 
w?=S—pK.. . . . (11) p. 450 
This is the equation of steady motion. The sign of K is 
wrong in the text; it would correspond to an attraction 
instead of a repulsion between the electrons of the ring. 
ost Le ow? (9) p. 449 
and lastly 
© nt —{3o?—28 + u(N—L) }n? + 4auMn 
— pN(o?+ 28 + wL)—p?M?=0. (12) p. 450 
This equation is also given wrongly by Nagaoka. In 
Maxwell’s paper on Saturn’s Rings (Collected Papers, vol. i. 
p- 316, equation (22)) we have the same equation for 
attracting satellites in the ring in place of electrons. That 
case gives the one under consideration by changing the sign 
of the mass of the satellites. This change gives the equation 
written down. 
The notation in all these equations is Nagaoka’s, as given 
in his paper. 
The mistakes just alluded to arise from dropping a minus 
sign on the left-hand side of the first of equations (7) on 
p. 448. | 
Using equations (11) and (9) in (12), it becomes 
n*—{o?+ u(N—L—2K)!n?+4ouMn 
—pN{o?+2n?+ uw (23 + L)}—p?M?=0. 
Now suppose we consider a ring with an even number 
2p of electrons ; and the most influential disturbing wave, 
for which Nagaoka’s number h becomes p. His equations 
(6) p. 448 show that in this case M=0. 
By the same equations we have 
1 sin?h@ cos? 6 ~— cos? hO | 
L=%(5 6 ane ) ST isin A. 
sin? h@ sin?h@cos?@ sin? hé 
oat 5 ole S| ec a lel a te 
J= 25 a76" N=3( sin? 6 2sin 6)’ 
where a few misprints have been corrected. (Maxwell, loc. 
cit. p. 314, equations (8).) : 
