concerning the Constitution of Matter, 201 



difficulty much less if the atom consists of a vortex ring or a 

 vortex tangle, for we should then simply have to infer that 

 the existing rings or tangles are as they are because they have 

 always been so, and that an indefinite variety of rings or 

 tangles of intermediate forms and sizes would be a priori 

 perfectly possible. But if the atom consists of one or more 

 strain-figures, the question becomes : Why do the strain- 

 figures form a discrete series? Now we have conceived a 

 strain-figure to be a disturbed condition of the medium, 

 ivliich is of itself in stable equilibrium throughout, and this 

 immediately imposes an immense restriction on the possible 

 varieties ; since, also, the strains are impressed on a medium 

 which would otherwise be homogeneous and isotropic, the 

 conditions essential to stable equilibrium will be the same for 

 all strain-figures, provided, that is, that the proximity of the 

 centres of two or more does not disturb their form. But at 

 this point a further assumption will be necessary ; for if the 

 turbulent motion or other structure of the medium were abso- 

 lutely homogeneous (which implies infinite fine-grainedness), 

 and if a strain-figure defined by a distribution of displacement 

 A were a possible one, then the figure defined by the dis- 

 tribution A magnified n diameters would be equally possible. 

 Thus the possible strain-figures, though infinitely restricted 

 in variety by the conditions of equilibrium, would form not a 

 discrete but a continuous series, or possibly a discrete system 

 of continuous series. We must suppose, then, that the coarse- 

 grainedness of the medium has an influence in determining 

 the size of possible strain-figures. 



13. Physical Illustration. — A very imperfect illustration of 

 this last point may be drawn from a physical phenomenon ; 

 for consider a region free from the action of gravity and filled 

 with a saturated vapour, which by some means is maintained 

 at constant temperature and pressure. If compression takes 

 place, liquid will be formed, and will exist in equilibrium with 

 the vapour, no intermediate condition of the substance being- 

 consistent with equilibrium and stability. But, neglecting 

 surface-tension, the liquid need not be formed in masses of 

 any special size ; that is, the possible sizes of the drops of 

 liquid will form a continuous series. If, however, surface- 

 tension is taken into account, the case is different j for suppose 

 that the vapour is slightly supersaturated, and contains a 

 number of spherical drops of liquid. Very large drops will 

 continue to increase, and very small drops will diminish, 

 while drops of one particular size (if any such are present) 

 will just be in equilibrium with the vapour, although the 

 equilibrium is necessarily unstable. But notwithstanding 



Phil. Mag. S. 5. Vol. 33. No. 201. Feb. 1892. P 



