of Quasi-permanent Systems of Electrons. 447 
In this case the harmonic .9 = is, for each value of k, by 
far the most important (§ 4). 
The distinction drawn between relative and absolute fre- 
quencies is vital, and is particularly insisted on by Maxwell ; 
it is necessary again to insist on it since it is often overlooked. 
In fact the results of Nagaoka as to the arrangement of the 
relative frequencies of his ring in bands and series, for this 
reason do not apply to the frequencies of the waves emitted 
by his ring, and thus have no direct application to spectrum 
series. 
§ 16. We must now consider the velocity of the ring, 
remembering that the ring cannot have a determinate struc- 
ture and determinate free periods unless its velocity is 
determinate. In order to account for the determinateness of 
the wave-lengths of spectrum-lines, we must make one or 
other of two hypotheses ; either : — 
(A) Each system emitting lines has a definite structure ; or 
(B) The determinateness of wave-length is due to some 
action between the several systems, which constitute the 
radiating gas, in virtue of which only those waves which 
have definite frequencies ever become intense enough to 
produce observable lines. In this case each constituent 
system can be continually changing its structure within 
certain limits. All that is necessary is that the conditions 
for homogeneity and fineness of the lines satisfied (§ 9), so 
long as the system happens to be one of those which is 
producing a spectrum-line. 
Although for obvious reasons the first Irypothesis seems 
the more probable, the possibility that the second may be 
true cannot be left out of account entirely. All that it 
requires is that the system, during the emission of a spectrum- 
line, be not altering its velocity by more than one 10 — 12 th 
part in one second (§ 5). 
§ 17. The determinateness of structure necessary for 
hypothesis (A) can for a single ring only be obtained by 
means of expanding electrons (§1). For a system of rings 
it may be thought that the condition of permanence in spite 
of mutual perturbations of the rings, might alone suffice to 
fix the velocity of each ring within limits narrow enough 
to account for the observed fineness of spectrum-lines. But 
a closer examination of this question shows that in this way 
we can under no circumstances obtain conditions more than 
enough to fix the ratios of the velocities ; and even then it is 
doubtful whether the limits can be drawn sufficiently close 
together to give sufficiently fine lines, assuming that the 
remaining condition can be otherwise obtained. 
2H2 
