system of measurement furnished by the transformed axes, with reference to which the particles are at rest. But according to FitzGerald's hypothesis of contraction, when a material body is in motion relative to the aether, in a direction parallel to the axis of x, its dimensions parallel to this direction contract in precisely this ratio; so that the equation of the body, in terms of the coordinates x1, y1, z1, which move with it, is unaltered. Thus the hypothesis of FitzGerald may be expressed by the statement that the equations of the figures of ponderable bodies are covariant with respect to those transformations for which the fundamental equations of the aether are covariant.
The covariance holds with respect to all linear homogeneous transformations in the variables (x, y, z, t), of determinant unity, which transform the expression (x2 + y2 + z2 - c2t2) into itself. This group comprises an infinite number of transformations; so that there are an infinite number of sets of variables resembling (x1, y1, z1, t1), of which any one set (xr, yr, zr, tr) can be derived from any other set (xs, ys, zs, ts) by a transformation of the group; among the sets wo must of course include the original set of coordinates (x, y, z, t). But hitherto we have proceeded on the assumption that the original set (x, y, z, t) is entitled to a primacy among all the other sets, since the axes (x, y, z, t) have been supposed to possess the special property of having no motion relative to the aether, and the time represented by the variable t has been understood to be a definite physical quantity. The other sets of variables (xr, yr, zr, tr) have been regarded merely as symbols convenient for use in problems relating to moving bodies, but not as corresponding to physical entities in the same degree as (x, y, z, ct). We must now inquire whether this view is justified.
The question amounts to asking whether absolute position in space, or at any rate absolute fixity relative to the aether, is something which can be brought within the bounds of human knowledge.
It is well known that the science of dynamics, as founded
