# Page:WhittakerSpaceTime.djvu/2

instant of time at some definite point of space, the disturbance will travel outwards from this point as a wave-front, which, if the space is unoccupied by matter, will be a sphere of gradually increasing size. During this process the centre of the sphere preserves its position unchanged relative to the æther; and thus it would seem as if a definite meaning could be attached to the term "absolute rest." Hopes might even be entertained of the measurement of absolute velocities relative to the æther by experimental methods.

The example which has just been given belongs to the theory of light. It is not difficult to imagine also electrical systems which might be expected to give information regarding absolute motion. For instance, two electric charges repel each other according to the law of electrostatics, but if the charges are in motion with equal and parallel velocities at right angles to the line joining them, the moving charges will be equivalent to elements of parallel currents, and the electrostatic repulsion will consequently be weakened by an electro-dynamic attraction superposed on it. Absolute rest could thus be characterised as that state in which the force between the charges has its maximum value.

Numerous optical and electrical experiments based on principles similar to these have been made at different times with the object of determining the absolute velocity of the Earth. But the expected effect has always failed to show itself; and at last physicists have been driven to the conclusion that a previously unrecognised compensatory influence must exist, which removes all effects of motion through the æther from the quantities which are measurable in the experiments.

The nature of this compensatory influence was first discovered by Fitzgerald.[1] It is, that the dimensions of material bodies are slightly altered when they are in motion relative to the æther, the linear dimensions of a body in the direction of its motion being contracted in the ratio ${\displaystyle \left(1-w^{2}/c^{2}\right)^{\frac {1}{2}}}$ : 1, where w denotes the velocity of the body and c the velocity of light. For a body moving with the speed of the Earth the ratio w/c is only 1/10,000, so the contraction is only one two-hundred—millionth.

The full significance of Fitzgerald’s hypothesis was only gradually unfolded. The first development was the discovery that if a purely electrical system is in equilibrium when at rest, the members of the same system will be in equilibrium when they have a common translatory motion, provided the system experiences an alteration of dimensions precisely the same as that which Fitzgerald attributed to material bodies. The obvious deduction from this is, that the forces of cohesion which determine the size of material bodies are really electrical in their origin: if this be accepted, the Fitzgerald contraction follows as a necessary consequence.

1. Nature, xlvi. p. 165 (June 16, 1892). The hypothesis was adopted by Lorentz in a communication made to the Amsterdam Academy on November 26 of the same year.