Page:Aether and Matter, 1900.djvu/225

to be involved in it. An analogy in fact suggests itself with the molecular electric theory as developed by Weber, Kirchhoff and their school, which gave a complete account of ordinary material electric phenomena, and only failed when the totally different region of radiation came into the discussion. It seems fair to conclude, in the one case as in the other, that in the constitution of the energy-relations on which the phenomena depend, a new property of the medium becomes explicitly involved in the more refined theory (not merely implicitly as in the energy-function that suffices for ordinary material electrodynamics) such for instance as the incompressibility that is utilized in the pulsatory theory or illustration of gravitation. The general reasons against the notion that the fundamental property of mass in matter is in direct connexion with the mechanism by which gravitation is transmitted have been given above (§ 116). There appears then, as yet, to be nothing to tempt us to depart from the natural prepossession, by considering the simple linear equations of the aether to be other than exact.

Dimensional Relations: in connexion with the definite scale of magnitude of Atomic Structure

122. Important considerations bearing on the question as to how far atoms of matter are constituted simply of singularities in the aether, practically point-nuclei, may be derived from the Newtonian principle of dynamical similarity, as utilized above (§ 112). Let us compare two such aethereal systems represented one by ordinary the other by subscripted variables, between which there is a correspondence given by

$(x,\ y,\ z)=k\left(x_{1},\ y_{1},\ z_{1}\right),\ t=lt_{1},$ $(a,\ b,\ c)=\vartheta \left(a_{1},\ b_{1},\ c_{1}\right),\ (f,\ g,\ h)=\phi \left(f_{1},\ g_{1},\ h_{1}\right);$

the aethereal equations for the one system will be identical with the aethereal equations for the other provided

$\vartheta /k=\phi /l,\ \phi /k=\vartheta /l,$

so that

$\vartheta =\phi$ and $k=l$.