September 12, 1895] 



NA rURE 



47, 



attempted. Lord Kehin ("Vortex Atoins," Proc. Roy. Soc, 

 Edin., vi. 94; Phil. Ma^. (4), 34) had proposed his theory of 

 vortex atoms. The permanence of a vortex filament with its in- 

 finite flexibility, its fundamental simplicity with its potential 

 capacity for complexity, struck the scientific imagination as the 

 thing which was wanted. Unfortunately the mathematical 

 difficulties connected with the discussion of these motions, espe- 

 cially the reactions of one on another, have retarded the full de- 

 velopment of the theory. Two objections in chief have been 

 raised against it, viz. the difficulty of accounting for the densities 

 of various kinds of matter, and the fact that in a vortex ring the 

 velocity of translation decreases as the energy increases. There 

 are two ways of dealing with a difficulty occurring in a general 

 theory — one is to give up the theory, the other is to try and see 

 if it can be modified to get over the difficulty. Such difficulties 

 are to be welcomed as means of help in arriving at greater 

 exactness in details. It is a mistake to .submit too readily to 

 crucial experiments. The very valid crucial objection of Stokes 

 to MacCuUagh's ether is a ca.se in point. It drew away atten- 

 tion from a theory which, in the light of later developments, 

 gives great hope of leading us to correct ideas. .As Larnior has 

 pointed out, this objection vanishes when we have intrinsic rota- 

 tions in the ether itself. \ special danger to guard against is 

 the importation into one theory of ideas which have grown out 

 <if one es.sentially different. This remark has reference to the 

 apparent difficulty of decrease of velocity with increased energy. 



.Maxwell was, I believe, the first to point out the difficulty of 

 explaining the masses of the elements on the vortex atom hypo- 

 thesis. To me it has always appeared one of the greatest 

 stumbling-blocks to the acceptance of the theory. We have 

 always been accustomed to regard the ether as of extreme 

 tenuity, as of a density extremely though not infinitely .smaller 

 than that of gross matter, and we carry in our minds that Lord 

 Kelvin has given an inferior limit of about lo"''''. There are 

 two directions in which to seek a solution. The first is to cut 

 the knot by supposing that the atoms gf gross matter are com- 

 posed of filaments whose rotating cores are of much greater 

 density than the ether itself. The second is to remember that 

 Lord Kelvin's number was obtained on the supposition of elastic 

 solid ether, and does not necessarily apply to the vortex sponge. 

 Unfortunately, however, for the first explanation, the mathe- 

 matical discussion ' shows that a ring cannot be stable unless 

 the density of the fluid outside the core is equal to, or greater 

 than, that inside. This instaljility also cannot be cured by sup- 

 posing an additional circulatir)n added outside the core. Unless, 

 therefore, .some modification of the theory can be made to secure 

 stability this idea of dense fluid cores must be given up. 



We seem, then, forced back to the conclusion that the 

 density of the ether must be comparable with that of ordinary 

 matter. The effective mass of any atom is not composed of that 

 of its core alone, but also of that portion of the .surrounding 

 ether which is carried along with it as it moves through the 

 medium. Thus a rigid sphere moving in a liquid behaves as if 

 its mass were increased by half that of the displaced liquid. In 

 the ca.se of a vortex filament the ratio of efl'ective to actual mass 

 may be much larger. In this explanation the density of the 

 matter composing an atom is the same for all, whilst their masses 

 depend on their volumes and configurations combined. Now 

 the configuration alters with the energy, and this would make 

 the mass depend to some extent at least on the temperature. 

 However repugn.ant this m.ay be to current ideas, we are not 

 entitled to deny its pos.sibility, although such an effect must be 

 small or it would have been detected. Such a variation, if it 

 exists, is not to be looked for by means of the ordinary gravi- 

 tation balance, but by the inertia or ballistic balance. The mass 

 of the core itself remains, of course, constant, but the efl^ectivc 

 mass — that which we can measure by the mechanical efliects 

 which the moving vortex produces — is a much more complicated 

 matter, and requires much fuller consideration than has been 

 given to it. 



The conditions of stability allow us to assume vacuous cores 

 or cores of less density than the rest of the medium. If we do 

 this, then the density of the ether itself may be greater than that 

 of gro.ss matter. Until, however, we meet with phenontena 

 whose explanation requires this assumjition, it would seem pre- 

 ferable to take the density everywhere the same. In this case 



t .\n error in tlic expression on p. 768 of " Researcfies in the Theory of 

 ir"^u^^i *^^' ''"'■ ''■'"'•«•?'• 'i' 1885. vitiates iheconclu.siontliercdr.iwn. 

 J r this I)e corrected the result mentioned above follows 

 -' Treatise on Hydrodynamics," § 338. and Aim-r. Jour 



See also B.-Lsset, 

 .1/WM. 



NO. 1350, VOL. 52] 



the density of the ether must be rather less than the apparent 

 density of the lightest of any of the elements, taking the apparent 

 density to mean the effective mass of a vortex atom per its 

 volume. This will probably be commensurable with the density 

 of the matter in its most compressed state, and will lie between 

 •5 and I — comparable, that is to say, with the density of water. 

 Larmor,' from a special form of hypothesis for a magnetic field 

 in the rotationally elastic ether, is led to a.ssigna density of the 

 same order of magnitude. If the density be given it is easy to 

 calculate the intrinsic energy per c.c. in the medium. The 

 velocity of propagation of light in a vortex sponge ether, as 

 deduced by Lord Kelvin,^ is '47 times the mean square velocity 

 of the intrinsic motion of the medium. This gives for the 

 mean square velocity 6 '3 x 10'" cm. per second. If we follow 

 Lord Kelvin and use for comparison the energy of radiation per 

 c.c. near the sun, or say I '8 erg per c.c, the resulting density 

 will be lo'-'. The energ)' per c.c. in a magnetic field of 15,000 

 c.g.s. units is about i joule. If we take this for comparison we 

 get a density of lo"'-". liut the intrinsic energy of the fluid must 

 be extremely great compared with the energy it has to transmit. 

 If it were a million times greater the density would still only 

 amount to lO'* — comparable with the density of the residual 

 gas in our highest vacua. To account for the density of gross 

 matter on the supposition that it is built up out of the same 

 material as the ether leads to a density between -5 and i. This 

 gives the enormous energy of to" joules per c.c. In other 

 words, the energy contained in one cubic centimetre of the ether 

 is sufficient to raise a kilometre cube of lead i metre high 

 against its weight. Thus the difficulty in explaining the mass 

 of ordinary matter seems to reduce itself to a difficulty in 

 believing that the ether possesses such an enormous store of 

 energy. It may be that there are special reasons against .such a 

 large density. Larraor refers to the large forcives which would 

 be called into play by hydrodynamical motions. Perhaps an 

 answer to this may be found in the remark that where all the 

 matter is of the same density the motions are kinematically de- 

 ducible from the configuration at the instant, and are indepen- 

 dent of the density. It is only where other causes act, such. 

 f.g., as indirectly depend on the mean pressure of the fluid or 

 where vacuous spaces occur, that the actual value of the density 

 may modify the measurable forcives. 



Ever since Prof. J. J. Thomson proved that a vortex atom 

 theory of matter is competent to serve as a basis of a kinetic 

 theory of gases, it has been urged by various persons as a fatal 

 objection that the translation velocity of the atoms falls off as 

 the temperature rises. I must confess this objection has never 

 appealed to me. Why should not the velocity fall off? The 

 velocity of gaseous molecules has never been directly observed, 

 nor has it been experimentally proved that it increases with ri,se 

 of temperature. We have no right to import ideas based on the 

 kinetic theory of hard discrete atoms into the totally distinct 

 theory of mobile atoms in continuity with the medium surround- 

 ing them. Doubtless the molecules of a gas effuse through a 

 small orifice more quickly as the temperature rises, but it is 

 natural to suppose that a vortex ring would do the same as its 

 energy increases. To make the objection valid, it is necessary 

 to show that a vortex ring passing through a small tube, com- 

 parable with its own diameter, would ]iass through more slowly 

 the greater its energy. It is not, however, necessarily the case 

 that in every vortex aggregate the velocity decreases as the 

 energy increases. The mathematical treatment of thin vortex 

 filaments is com])aratively easy, and little attention h.as been 

 paid to other cases. Let us attempt lo trace the life history as 

 to translation velocity and energy of a vortex ring. W'e start 

 with the energy large ; the ring now has a very large aperture, 

 and has a very thin filament. .\s the energy decreases the aper- 

 ture becomes smaller, the filament thicker, and the velocity of 

 translation greater. We can trace quantitatively the whole of 

 this jiart of its history until the thickness of the ring has in- 

 creased to about four times the diameter of the aperture, or 

 perhaps a little further. Then the mathematical treatment em- 

 pl(.)yed fails us or bec(nnes very laborious to apply. Till eighteen 

 months ago, this was the only portion of its history we could 

 trace. Then Prof. M. J. M. Hill (" On a Spherical Vortex," 

 Phil. Trans., 1894) published his beautiful discovery of the 

 existence of a spherical vortex. This consists of a spherical 



1 " .\ Dynamical Theory of the Electric and Luminifcrous Medium," 

 Phil. Trans.. 1894, \. p. 779. 



- " On the Prop.agation of Laminar Motion through a Turhulently Moving 

 Inviscid Liquid,' P/iil. Mag.^ October 1887. 



