TRANSACTIONS OF SECTION A. 599 



out, and towards tlie end of its course approximates to the form of a rod moving 

 parallel to its length through the fluid with energy and velocity which again can 

 be approximately determined. In this part of its life the velocity of translation 

 decreases with decrease of energy. I believe it will be found, when the theory is 

 completely worked out, that the spherical atom is the stage where this reversal of 

 property takes place. 



Even in the ring state, however, the change of velocity with energy is very 

 small ; much smaller, I think, than is generally recognised. When the energy 

 is increased to twenty times that of the spherical vortex, the velocity is only 

 diminished to two-thirds its previous value. If at ordinary temperatures, say 27° C, 

 the vortex was in the spherical shape, then at 3,000° G. its velocity of translation 

 would only have been reduced to four-lifths its value at the lower temperature, 

 whilst the aperture of the ring would have a radius about 1'4 time that of the 

 sphere. At 2,000° C. the velocity would not differ by much more than one- 

 twentieth from its original value. In fact, near the spherical state the alteration 

 in velocity of translation is very slow. It is therefore possible, that if the atoms 

 of matter be vortex aggregates, the state in which we can experimentally test our 

 theory is just that in which the mathematical discussion fails us. Other modifica- 

 tions tend to diminish this change of velocity. I will refer here to three only. The 

 first is that of hollow vortices. We must not, however, postulate vacuous atoms 

 without any rotational core at all ; for in this case we should probably lose the 

 essential property of permanence. The question has not been fully investigated, 

 but there can be little doubt but that by diminishing the energy of a completely 

 hollow vortex we can cause it to disappear. We can certainly create one in a per- 

 fect fluid. Secondly, J. J. Thomson has shown that if a molecule be composed of 

 linked filaments, the energy increases as the components move further apart. In 

 such a case an extra supply of energy goes to expanding the molecule, and less, if 

 i,ny, to increasing the aperture. Lastly, a modification of the atomic motion to 

 which I shall refer later, and which seems called for to explain the magnetic rota- 

 tion of the plane of polarisation of light, will also tend to lessen the change of size, 

 and therefore change of velocity with change of energy, even if it does not reverse 

 the property. 



If we pass on to consider how a vortex atom theory lends itself to the explana- 

 tion of physical and chemical properties of matter independently of what may be 

 called ether relations, we find that we owe almost all our knowledge on this point 

 to the work of Professor J. J. Thomson, ^ which obtained the Adams' Prize in 

 1882. This, however, is confined to the treatment of thin vortex rings, still leaving 

 a wide field for future investigation in connection with thick rings and with vortex 

 aggregates which produce no cyclosis in the surrounding medium. His work is an 

 extremely suggestive one. He shows that such a theory is capable not only of 

 explaining the gaseous laws of a so-called perfect gas, but possibly also the slight 

 deviations therefrom. Quite as striking is his explanation of chemical combina- 

 tion — an explanation which flows quite naturally from the theoiy. A vortex fila- 

 ment can be linked on itself: two or more can be linked together, like helices 

 drawn on an anchor rins: ; or, lastly, several can be arranged together like parallel 

 rings successively threading one another. In the latter case, for such an arrange- 

 ment to be permanent, the strengths of each ring must be the same, and further, 

 not more than six can thus be combined together. The linked vortices will be in 

 permanent combination on account of their liukedness ; the other arrangement may 

 be permanent if subject to no external actions. If, however, they are disturbed by 

 the presence of other vortices they may break up. When atoms are thus combined 

 to form a compound, a certain number of molecules will always be dissociated ; 

 the compound will be permanent when the ratio of the average paired time to the 

 unpaired time of any atom is large. Thomson considers every filament to be of the 

 same strength. Then an atom consisting of two links will behave like a ring of 

 twice the strength, one of three links, of three times the strength, and so on. On 

 this theory chemical compounds are to be regarded as systems of rings, not linked 



■ 'A Treatise on the Motion of Vortex Rings.' Macmillan, 1883. 



