600 REPORT— 1895. 



into one another but close together, and all engaged in the operation of threading 

 each other. The conditions for permanence are : (1st) the strength of each ring must 

 he the same, (•2nd) the number must be less than 6. Now apply this. H and CI hare 

 equal linMngs, therefore equal strength. Consequently we can have molecules of 

 HCl, or any combinations up to 6 atoms per molecule, although the simpler one is 

 the most likely. has twice the linking, therefore the strength double. Hence one 

 of H and one of O cannot revolve in permanent connection. We require first to 

 arrange two of H together to form one system. This system has the same strength as 

 O, they can therefore revolve in permanent connection, and we get the water mole- 

 cule. Or we may take two of the O atoms and one of the double H molecule, and 

 they can form a triple system of three rings threading one another in permanent 

 connection, and we get the molecule HoOj. This short example will be sufficient 

 to indicate how the theory gives a complete accoimt of valency. 



The energy of rings thus combined is less than when free ; consequently they 

 are stable, and the act of combination sets free energy. Further, Thomson points 

 out that for two rings to combine their sizes must be about the same when they 

 come into proximity ; consequently combination can only occur between two limits 

 of temperature corresponding to the energies within which the radii of both kinds 

 of rings are near an equality. 



We can easily extend Thomson's reasoning to explain the combination of two 

 elements by the presence of a third neutral substance. Call the two elements 

 which are to combine A and B, and the neutral substance C. The radii of A and 

 ±J are to be supposed too unequal to allow them to come close enough together to 

 combine. If now at the given temperature the C atom has a radius intermediate 

 to those of A and B, it is more nearly equal to each than they are to one another ; 

 C picks up one of A, and after a short time drops it ; A will leave C with its 

 radius brought up (say) to closer equality with it. The same thing happens with 

 the B atoms, and they leave C with their radii brought down to closer equality 

 with it. The result is that A and B are brought into closer equality with one 

 another, and if this is of sufficient amount, they can combine and do so, while C 

 remains as before and apparently inert. 



Thomson's theory of chemical combination applies only to thin rings. Some- 

 thing analogous may hold also for thick rings, but it is clearly inapplicable to 

 vortex aggregates similar to that of Hill's. We are not confined, however, to this 

 particular kind of association of vortex atoms in a molecule. For instance, I have 

 recently found' that one of Hill's vortices can swallow up another and retain it 

 inside in relative equilibrium. The matter requires fuller discussion, but it seems 

 to open up another mode of chemical combination. 



A most important matter which has not yet been discussed at all is the relation 

 between the mean energy of the vortex cores, and the energy of the medium itself 

 when the atoms are close enough to afl'ect each other's motions (as in a gas). The 

 fundamental ideas are quite difi'erent from those underlying the well-known 

 kinetic theory of gases of hard atoms. Nevertheless, many of the results must b»- 

 very similar, based as both are on dynamical ideas. Whether it will avoid certain 

 difficulties of the latter, especially those connected with the ratio of the specifie 

 heats, remains to be seen. The first desideratum is the determination of the 

 equilibrium of energy between vortices and medium, and before this is done it is 

 useless to speculate further in this region. 



A vortex atom theory of matter carries with it the necessity of a fluid ether. 

 If such a fluid is to transmit transversal radiations, some kind of quasi-elasticity 

 must be produced in it. This can be done by supposing it to possess energetic 

 rotational motions whose mean velocity is zero, within a volume whose linear 

 dimension is small compared with the wave length of light, but whose velocity of 

 mean square is considerable. That an ether thus constituted is capable of trans- 

 mitting transverse vibrations I showed before this Section at the Aberdeen meeting 

 of the Association,^ by considering a medium composed of closely packed discrete 



' Not yet published. 



^ ' On the Constitution of the Luminiferous Ether on the Vortez Atom Theory,' 

 £rit. Assoc. Bejjorts, 1885, p. 930. 



