vacuous cores; the same system can equally exist with linear dimensions k times as great when all the time constants will be diminished k² times.
124. The definiteness of scale of the molecules of material systems thus precludes the possibility of their being constituted of singularities of a uniform continuum, of either of these kinds with nuclei undistinguishable from mathematical points. The constancy of inertia and gravity throughout all chemical transformations forms practically sufficient evidence for the physicist that all matter is built up out of the same primordial stuff: this stuff, if it is constituted of intrinsic singularities in a uniform aethereal continuum with relations exactly linear, must thus be made up of elements of type rather more complex than simple positional and motional singularities with nuclei devoid of sensible volume. Another element apart from finiteness of dimensions of nuclear structure that could enter, on the theory of an aether exactly linear in its relations, is that of time: for example it has been seen how the gravitation of atoms can be imitated by supposing a definite periodic time of pulsation to be associated with each electron. A change of scale such as that above discussed would then change the forces of gravitation, unless possibly the time of pulsation could be suitably altered and the change thus counteracted.
125. In the above considerations there is strong evidence that gravitation is not to be expected to be appreciably involved within the scheme which suffices to cover the phenomena of electrodynamics and optics. The introduction of the time-relation inherent in pulsating nuclei seems still to be the only obvious way of representing it, in default of its arising from second-order terms in the dynamical relations of the aether. The permanence of scale of magnitude of the material atoms of various types involves the presence of actions depending on the magnitude and structure of the electric nuclei, which though they may be purely aethereal are local, and thus not pertinent to general electrical and optical theory: the existence
