TRANSACTIONS OF SECTION A. 597 



remark Las reference to the apparent difficulty of decrease of velocity with in- 

 creased energy. 



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

 masses of the elements on the vortex a^^m hypothesis. To me it has always ap- 

 peared one of the greatest stumhling-bloclis to the acceptance of the theory. AYe 

 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. Tlie first is to cut the knot 

 by supposing that the atoms of gross matter are composed of filaments whose 

 rotating cores are of much greater density than the ether itself. The second is to 

 remember that Lord Kelvins 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 mathematical discussion ' shows that a ring 

 cannot be stable unless tlie density of the fluid outside the core is equal to, or 

 greater than, that inside. This instability also cannot be cured by supposing an 

 additional circulation 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, therefore, 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 surround- 

 ing 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 case of a vortex filament the ratio of effective 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 repugnant this may be to current ideas, we are not entitled to deny its 

 possibility, 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 effective mass — that which we can measure 

 by the mechanical effects whicli 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 vacnous cores or cores of less 

 density than the rest of the medium. If we do this then the deusity of the ether 

 itself may be greater than that of gross matter. Until, however, we meet with 

 phenomena whose explanation requires this assumption, it would seem preferable 

 to take the density everywhere the same. In this case 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 jjrobably be commensurable with the density of the matter in 

 its most compressed state, and will lie between '5 and 1 — 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 assign a 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 



' An error in the expression on p. 7G8 of ' Eesearches in the Theory of Vortex 

 Rings,' Phil. Trans., pt. ii. 1885, vitiates the conclusion there drawn. If this be 

 corrected the result mentioned above follows. See also Basset, Treatise on Hydro- 

 dynamics, § .3.38, and Amcr. Jour. Math. 



^ ' A Dynamical Theory of the Electric and Luminiferous Medium,' Phil. Trans., 

 1894, A. p. 779. 



' ' On the Propagation of Laminar Motion through a Turbulently Moving Inviscid 

 Liquid,' Phil. Mag., October 1887. 



