Sir William Thomson on Vortex Atoms. 19 



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 cir- 

 cumference, 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* 1 , be practically 

 extended to any atom consisting of a single vortex ring, however 

 involved, as illustrated by those of the models shown to the So- 

 ciety, which consisted 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 vo- 

 lumes 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 funda- 

 mental modes cannot be pronounced upon without mathematical 

 investigation not hitherto executed ; and therefore we cannot 

 say that the dynamical explanation now suggested is mathema- 

 tically demonstrated so far as to include the very approximate 

 identity of the periods of the vibrating particles of the incandes- 

 cent vapour with those of their corresponding fundamental modes 

 at the lower temperature at which the vapour exhibits its re- 

 markable absorbing-power for the sodium light. 



A very remarkable discovery made by Helmholtz regarding 

 the simple vortex ring is that it always moves, relatively to the 

 distant parts of the fluid, in a direction perpendicular to its plane, 

 towards the side towards which the rotatory motion carries the 

 inner parts of the ring. The determination of the velocity of this 

 motion, even approximately, for rings of which the sectional radius 

 is small in comparison with the radius of the circular axis, has 

 presented mathematical difficulties which have not yet been over- 

 come f. In the smoke-rings which have been actually observed, 

 it seems to be always something smaller than the velocity of the 

 fluid along the straight axis through the centre of the ring ; for 

 the observer standing beside the line of motion of the ring sees, 



* [Note, April 26, 1867. — The author has seen reason for believing that 

 the sodium characteristic might be realized 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.] 



t See, however, note added to Professor Tait's translation of Helm- 

 holtz's paper (Phil. Mag. 1867, vol. xxxiii. SuppL), where the result of 

 a mathematical investigation which the author of the present communi- 

 cation has recently succeeded in executing, is given. 



C2 



