598 REPORT — 1895. 



velocity of tlie intrinsic motion of the medium. Tliis gives for the mean square 

 velocitv 6-3 >^ 10"* cm. per second. If we follow Lord Kelvin and use for com- 

 parison the energy of radiation per c.c. near the sun, or say TS erg per c.c, the 

 resulting density will be lO"-'. The energy per c.c. in a magnetic field of 

 15,000 c.g.s. units is about 1 joule. If we take this for comparison we get a 

 density of 10-^^. But 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 10"® — 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 1. This gives the enormous energy of 10^* 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 1 metre high against its weight. Thus the diiR- 

 culty 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. Larmor refers to the 

 large forcives which would be called into play by hydrodynamical motions. Per- 

 haps an answer to this may be found in the remark that where all the matter is of 

 the same density the motions are kineuiatically deducible from the configuration 

 at the instant, and are independent of the density. It is only where other causes 

 act, such, e.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 measur- 

 able forcives. 



Ever since Professor 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 in- 

 creases with rise 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 madium surrounding 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, comparable with its own diameter, wotdd pass 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 comparatively easy, and little attention has 

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

 velocity and energy of a vortex ring. We start with the energj^ large ; the ring 

 now has a very large aperture, and has a very thin filament. As the energy de- 

 creases the aperture becomes smaller, the filament thicker, and the velocity of 

 translation greater. We can trace quantitatively the whole of this part of its 

 history until the thickness of the ring has increased to about four times the diameter 

 of the aperture, or perhaps a little further. Then the mathematical treatment em- 

 ployed fails us or becomes very laborious to apply. Till eighteen months ago, this 

 was the only portion of its history we could trace. Then Professor M. J. M. Hill ' 

 published his beautiful discovery of the existence of a spherical vortex. This con- 

 sists of a spherical mass of fluid in vortical motion and moving bodily through the 

 surrounding fluid, precisely as if 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 

 energy and increased velocity. AVe then lose sight of it again, but it now lengthens 



' ' On a Spherical Yortex,' PMl. Trans., 1894. 



