Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/467

 would have the great advantage of explaining the contraction postulated by Fitz Gerald, since it would represent the contraction as actually produced by the notion. But if this assumption be correct, the theory of electricity and aether is without doubt the fundamental theory of Natural Philosophy, and the framework of space and time should be chosen with a view chiefly to the expression of electrical phenomena. This may most naturally be done by stipulating that the wave-fronts of disturbances generated in free aether shall, in the system of length and time adopted, be accounted spheres whose centres are at the origins of disturbance and whose radii are proportional to the times elapsed since their initiation. Referred to axes of which satisfy these conditions, the fundamental equations of the electric field assume the form which has been taken as the basis of all our theoretical investigations.

Imagine now a distant star which is moving with a uniform velocity w or o tanh a relative to this framework. The theorem of transformation shows that there exists another framework, with respect to which the star is at rest, and in which moreover the condition laid down regarding the wave-surface is satisfied. This framework is peculiarly fitted for the representation of the phenomena which happen on the star; whose inhabitants would therefore naturally adopt it as their system of space and time. Beings, on the other hand, who dwell on a body which is at rest with respect to the axes would prefer to use the latter system, and from the point of view of the universe at large, either of these systems is as good as the other. The equations of motion of the aether are the same with respect to both sets of coordinates, and therefore neither can claim to possess the only property which could confer a primacy—namely, an absolute relation to the aether.

To sum up, we may say that the phenomena whose study is the object of Natural Philosophy take place each at a definite