Page:CunninghamPrinciple.djvu/2

Rh of light. The present paper reconsiders Abraham's discussion and comes to the conclusion that the objection is not valid. The discussion was suggested by the fact that it has been proved that Maxwell's equations represent equally well the sequence of electromagnetic phenomena relative to a set of axes moving relative to the aether, as relative to a set of axes fixed in the aether. More explicitly this is stated as follows : —

If there are two sets of rectangular axes (A, A') coinciding at a certain instant, of which A' is moving relative to A with velocity v in the direction of the axis of x, which is conceived as at rest, and if x, y, z, t be space and time variables associated with A, and x', y' z', t' similar variables associated with A', then the equations

transform identically into the equations

the accented and unaccented magnitudes being connected by the relations

$\begin{array}{ll} x'=\beta(x-vt], \\y'=y, \\z'=z, & \beta=\left(1-v^{2}/c^{2}\right)^{-\frac{1}{2}} \\t'=\beta\left(t-\frac{vx}{c^{2}}\right),\end{array}$|undefined

$$\begin{array}{l} E'=\beta\left(\frac{E_{x}}{\beta},\ E_{y}-vH_{z},\ E_{z}+vH_{y}\right),\\ \\H'=\beta\left(\frac{H_{x}}{\beta},\ H_{y}-vE_{z},\ H_{z}+vE_{y}\right)\end{array}$$

Further, if $$\rho=\tfrac{1}{4\pi}div\ E$$, and $$\rho'=\tfrac{1}{4\pi}div\ E'$$, the volume integrals taken through corresponding regions $$\tau,\ \tau',\ \int_{\tau}\rho d\tau$$ and $$\int_{\tau'}\rho'd\tau'\!$$ are identically equal, giving an exact correspondence as regards distribution of electric charge.

Thus the above transformation renders the electromagnetic equations of a system independent of a uniform translation of the whole system through the aether.