Page:CunninghamExtension.djvu/1



[Received May 1st, 1909.]

1. The absence, as far as experiment can detect, of any phenomenon arising from the Earth's motion relative to the electromagnetic æther has been fully accounted for by Lorentz and Einstein, provided the hypothesis of electromagnetism as the ultimate basis of matter be accepted, so that the only available means of estimating the distance between two points is the measuring of the time of propagation of effects between the bodies, such propagation taking place in accordance with the equations of the electron theory. It has been proved not only within the limits of experimental accuracy, but exactly, that any actual effect is completely obscured by the fact that the observer necessarily shares in the motion of the earth, and has therefore different measures of time and space from those which he would have if he did not do so. The foundation of this theory of relativity is the set of relations subsisting between the space and time measures of two observers having a uniform relative velocity. If this is v and the axis of x is taken in the direction of v, these relations are

where

$$\beta=\left(1-v^{2}/c^{2}\right)^{-\frac{1}{2}}.$$

The analytical result obtained is that, if e, h, u are vectors and &rho; a scalar satisfying the equations

$$\begin{array}{rl} \frac{1}{c}\left(\frac{\partial e}{\partial t}+\rho u\right)= & \mathsf{curl}\ h,\\ \\-\frac{1}{c}\frac{\partial h}{\partial t}= & \mathsf{curl}\ e,\\ \\\mathsf{div}\ e= & \rho,\\ \\\mathsf{div}\ h= & 0,\end{array}$$