Sir William Thomson on Vortex Atoms. 17 



Diagrams and wire models were shown to the Society to illus- 

 trate knotted or knitted vortex atoms, the endless variety of 

 which is infinitely more than sufficient to explain the varieties 

 and allotropies of known simple bodies and their mutual affini- 

 ties. It is to be remarked that two ring atoms linked together, 

 or one knotted in any manner with its ends meeting, constitute 

 a system which, however it may be altered in shape, can never 

 deviate from its own peculiarity of multiple continuity, it being 

 impossible for the matter in any line of vortex motion to go 

 through the line of any other matter in such motion or any other 

 part of its own line. In fact, a closed line of vortex core is lite- 

 rally indivisible by any action resulting from vortex motion. 



The author called attention to a very important property of the 

 vortex atom, with reference to the now celebrated spectrum-ana- 

 lysis practically established by the discoveries and labours of 

 Kirchhoff and Bunsen. The dynamical theory of this subject, 

 which Professor Stokes had taught to the author of the present 

 paper before September 1852, and which he has taught in his 

 lectures in the University of Glasgow from that time forward, 

 required that the ultimate constitution of simple bodies should 

 have one or more fundamental periods of vibration, as has a 

 stringed instrument of one or more strings, or an elastic solid 

 consisting of one or more tuning-forks rigidly connected. To 

 assume such a property in the Lucretius atom, is at once to give 

 it that very flexibility and elasticity for the explanation of 

 which, as exhibited in aggregate bodies, the atomic constitution 

 was originally assumed. If, then, the hypothesis of atoms and 

 vacuum imagined by Lucretius and his followers to be necessary 

 to account for the flexibility and compressibility of tangible 

 solids and fluids were really necessaiy, it would be necessary 

 that the molecule of sodium, for instance, should be not an 

 atom, but a group of atoms with void space between them. 

 Such a molecule could not be strong and durable, and thus it 

 loses the one recommendation which has given it the degree of 

 acceptance it has had among philosophers ; but, as the experi- 

 ments shown to the Society illustrate, the vortex atom has per- 

 fectly definite fundamental modes of vibration, depending solely 

 on that motion the existence of which constitutes it. The dis- 

 covery of these fundamental modes forms an intensely interest- 

 ing problem of pure mathematics. Even for a simple Helm- 

 holtz ring, the analytical difficulties which it presents are of a 

 very formidable character, but certainly far from insuperable in 

 the present state of mathematical science. The author of the 

 present communication had not attempted, hitherto, to work it 

 out except for an infinitely long, straight, cylindrical vortex. 

 For this case he was working out solutions corresponding to every 

 Phil. Mag. S. 4. Vol. 34. No. 227. July 1867. C 



