474 



NATURE 



[September 12, 1895 



mass of fluid in vortical motion and moving bodily through the 

 surrounding fluid, precisely as it it were a rigid sphere. This 

 enables us to catch a momentary glimpse, as it were, of our 

 vortex ring some little time after it has passed out of our ken. 

 The aperture has gone on contracting, the ring thickening, and 

 altering the shape of its cross section in a manner whose 

 exact details have not yet been calculated. At last we just 

 catch sight of it again as the aperture closes up. We 

 find the ring has changed into a spherical ball, with 

 still further diminished energ)- and increased velocity. We 

 then lose sight of it again, but it now lengthens out, 

 and towards the end of its course approximates to the form 

 of a rod moN-ing parallel to its length through the fluid with 

 energy and velocity which again can be approximately deter- 

 mined. In this part of its life the velocity of translation decreases 

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

 iheor)' 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 

 recognLsed. WTien 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 

 20° C, the vortex was in the spherical shape, then at 3000° C. 

 its velocity of translation would only have been reduced to four- 

 fifths its value at the lower temperature, whilst the aperture of 

 the ring » ould have a radius about I 4 times that of the sphere. 

 At 2000' C. the velocity would not difter 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 mo<lifications 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, jxjstulate 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 

 l)cen fully investigated, but there can be little doubt that by 

 diminishing the energy of a completely hollow vortex we can 

 cause it to disappear. We can certainly create one in a perfect 

 fluid. Secondly, J. J. Thomson has shown that if a molecule 

 be composed of linked filaments, the energy increases as the 

 components move further a|)art. In such a case an extra supply 

 of energy goes to exjMnding the molecule, and less, if any, 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 rotation of the plane of [Kilarisation 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 explanation of physical and chemical proiierties 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 I'rof J. J.Thomson (" A Treatise on the Motion of 

 Vortex Rings,'' Macmillan, 1883), which obtained the .\dams' 

 Prize in 1S82. This, however, is confined to the treatment of 

 thin vortex rings, still leaving a wide field for fiiture investiga- 

 tions in connection with thick rings and with vortex aggregates 

 which produce no cyclosis in the surrounding medium. His 

 wf)rk is an extremely suggestive one. lie shows that such a 

 theory is capable not only of explaining the gaseous lawsof a 

 so-called jwrfect gas, but possibly also the slight deviations there- 

 fr'iiii. <Juite as striking is his explanation of chemical com- 

 binaiion — an explanation which flows ijuite naturally from the 

 theory. A vortex filament can be linked on itself: two or more 

 can tic linked together, like helices drawn on an anchor ring ; 

 ■Iv, several can l>c arranged together like parallel rings 

 ■• Iv threading one another. In the latter case, fir such 



■ 'i be permanent, the strengths of each ring 



1! and further, not more than six can thus be 



I r. The linked virtices will \k in permanent 



combmntion nn account of their linkedncss ; the other arrange- 

 ment mny \<r p'Tmanent if subject to no external .-ictinns. If, 

 I dislurl)cd by the presence of other vortices 



I When alr>ms are thus combined to form n 



• iml>er of molecules will always be dis- 



I will lie permanent when the ratio of 

 r ■ r, , ^' ^o the un]>;nr(<l (inie 'if any atnni is 



NO. 1350, VOL. 52] 



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 theor)' chemical compounds 

 are to be regarded as systems of rings, not linked into one 

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

 threading each other. The conditions for permanence xie : ( 1 ) 

 the strength of each ring must be the same, (2) the number 

 must be less than 6. Now apply this. H and CI have equal 

 linkings, therefore equal strength. Consequently we can have 

 molecules of MCI. or any combinations up to 6 atoms per 

 molecule, although the simpler one is the most likely. O has 

 twice the linking, therefore the strength double. Hence one 

 of M 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 jwrmanent connection, and we get the water 

 molecule. Or we may lake 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 IIoO„. This short example will be sufliciont 

 to indicate how the theory gives a complete account 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 jioints out that for two rings to 

 combine their sizes must Ix? 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 e.tsily extend Thomson's reasoning to explain the 

 combination of two elements by the presence of a third neutral 

 substance. Call the two elements wliich are to combine A and 

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

 be supposed too unequal to allow them to cume 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 K. and after a short time drops it ; A will leave C with 

 its radius brought up (.s.iy) to closer equality with it. The siime 

 thing hapjiens with the B atoms, and they leave C with their 

 radii brought down to closer equality « ith it. The result is that 

 .'\ 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. Something 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. Kor instance, I 

 have recently found (not yet published) 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 

 enuugh to aflect each other's motions (as in a gas). The fun- 

 damental ideas are quite different from those underlying the well- 

 known kinetic theory of g.ases of har<l atoms. Nevertheless, 

 many of the results must be very similar, based as liolh are on 

 tlynamical ideas.. Whether it will avoid certain dilficidties of 

 the latter, especially those connected with the ratio of the 

 specific heats, remains tn 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. 



.\ vortex atom theory of matter carries with it the necessity 

 of a fluid ether. If such a fluid is to transmit transversal radia- 

 tions, some kind of quasi-elasticily must be |)roduced in it. This 

 can lie 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 consideralile. That an 

 ether thus constituted is capable of transmitting transverse vibra- 

 tions I showed before this Section at the Aberdeen meeting of 

 the .Association ( " ( )n the Constitution of the Luniiniferous Ether 

 on the \'ortex .\tom Theory," liril. Assoc. Kf ports, 1S85. ji. 930), 

 by considering a medium composed of closely |iacUe(l discrete 

 small vnrtex rings. Lord Kelvin (" On the '\'ortex Theory of 

 the Luminileriius Kther,'' lirit. Assoc. A'(/n,rts, 1SS7, p. 486, aLsi:» 



