5.2 The assumption of the existence of an ether at once raises the question as to its laws of motion. Thus in addition to the hierarchy of macroscopic and microscopic equations, there are the equations of motion for ether in otherwise empty space. The à priori reasons for believing that Newton's laws of motion apply to the ether are very weak, being in fact nothing more than the inductive extension of laws to cases widely dissimilar from those for which they have been verified. It is however a sound scientific procedure to investigate whether the assumed properties of ether are explicable on the assumption that it is behaving like ordinary matter, if only to obtain suggestions by contrast for the formulation of the laws which do express its physical changes.
The best method of procedure is to assume certain large principles deducible from Newton's laws and to interpret certain electromagnetic vectors as displacements and velocities of the ether. In this way Larmor has been successful in deducing Maxwell's equations from the principle of least action after making the necessary assumptions. In this he is only following a long series of previous scientists who during the nineteenth century devoted themselves to the explanation of optical and electromagnetic phenomena. His work completes a century of very notable achievement in this field.
5.3 But it may be doubted whether this procedure is not an inversion of the more fundamental line of thought. It will have been noted that Newton's equations, or any equivalent principles which are substituted for them, are in a sense merely blank forms. They require to be supplemented by hypotheses respecting the nature of the stresses, of the masses, and of the motions, before there can be any possibility of their application. Thus by the time that Newton's equations of motion are applied to the explication of etherial events there is a large accumulation of hypotheses respecting things of which we know very little. What in fact we do know about the ether is summed up in Maxwell's equations, or in recent adaptations of his equations such as those due to Lorentz. The discovery of electromagnetic mass and electromagnetic momentum suggests that, for the ether at least, we gain simpler conceptions of the facts by taking Maxwell's equations, or the Lorentz-Maxwell equations, as fundamental. Such equations would then be the ultimate microscopic equations, at least in the present stage of science, and Newton's equations become macroscopic equations which apply in certain definite circumstances to etherial aggregates. Such a procedure does not prejudge the debated theory of the purely electromagnetic origin of mass.
5.4 The modern theory of the molecule is destructive of the obviousness of the prejudgment in favour of the traditional concepts of ultimate material at an instant. Consider a molecule of iron. It is composed of a central core of positive electricity surrounded by annular clusters of electrons, composed of negative electricity and rotating round the core. No single characteristic property of iron as such can be manifested at an instant. Instantaneously there is simply a distribution of electricity and Maxwell's equations to express our expectations. But iron is not an expectation or even a recollection. It is a fact; and this fact, which is iron, is what happens during a period of time. Iron and a biological organism are on a level in requiring time for functioning. There is no such thing as iron at an instant; to be iron is a character of an event. Every physical constant respecting iron which appears in scientific tables is the register of such a character. What is ultimate in iron, according to the traditional theory, is instantaneous distributions of electricity; and this ultimateness is simply ascribed by reason of a metaphysical theory, and by no reason of observation.
5.5 In truth, when we have once admitted the hierarchy of macroscopic and microscopic equations, the traditional concept is lost. For it is the macroscopic equations which express the facts of immediate observation, and these equations essentially express the integral characters of events. But this hierarchy is necessitated by every concept of modern physics—the molecular theory of matter, the dynamical theory of heat, the wave theory of light, the electromagnetic theory of molecules, the electromagnetic theory of mass.
[6. Maxwell's Equations][4]. [6.1] A discussion of Maxwell's equations would constitute a treatise on electromagnetism. But they exemplify some general considerations on physical laws.
These equations (expressed for an axis-system
involve for each point of space and each instant of time the vector quantities (
