98 Proceedings of the Royal Society 
approximately similar (and not merely different orders of different 
series chancing to concur very nearly in their periods of vibration). 
In an approximately circular and uniform disc of elastic solid the 
fundamental modes of transverse vibration, with nodal division into 
quadrants, fulfils both the conditions. In an approximately circular 
and uniform ring of elastic solid these conditions are fulfilled for 
the flexural vibrations in its plane, and also in its transverse vibra- 
tions perpendicular to its own plane. But the circular vortex ring, 
if created with one part somewhat thicker than another, would not 
remain so, but would experience longitudinal vibrations round its own 
circumference, and could not possibly have two fundamental modes 
of vibration similar in character and approximately equal in period. 
The same assertion may, it is probable,* be practically extended to 
any atom consisting of a single vortex ring, however involved, as 
illustrated by those of the models shown to the Society, which con- 
sisted of only a single wire, knotted in various ways. It seems, 
therefore, probable that the sodium atom may not consist of a single 
vortex line ; but it may very probably consist of two approximately 
equal vortex rings passing through one another, like two links of a 
chain. It is, however, quite certain that a vapour consisting of 
such atoms, with proper volumes and angular velocities in the two 
rings of each atom, would act precisely as incandescent sodium 
vapour acts; that is to say, would fulfil the “spectrum test” for 
sodium. 
The possible effect of change of temperature on the fundamental 
modes cannot be pronounced upon without mathematical inves- 
tigation not hitherto executed ; and therefore we cannot say that 
the dynamical explanation now suggested is mathematically demon- 
strated so far as to include the very approximate identity of the 
periods of the vibrating particles of the incandescent vapour with 
those of their corresponding fundamental modes, at the lower tem- 
perature, at which the vapour exhibits its remarkable absorbing 
power for the sodium light. 
A very remarkable discovery made by Helmholtz regarding the 
* [Note, April 25, 1867. — The author has recently seen reason for believing 
that the sodium characteristic might be realised by a certain configuration of 
a single line of vortex core to be described in the mathematical paper which 
he intends to communicate to the Society.] 
