Page:CunninghamExtension.djvu/1

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1909.]
The principle of relativity in electrodynamics.
77
THE PRINCIPLE OF RELATIVITY IN ELECTRODYNAMICS
AND AN EXTENSION THEREOF


By E. Cunningham.


[Received May 1st, 1909.][1]

Introductory.

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[2] and Einstein,[3] 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

(1)

where

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


  1. This paper contains in an abbreviated form the chief parts of the work contributed by the Author to a joint paper by Mr. Bateman and himself read at the meeting held on February 11th, 1909, and also the work of the paper by the author read at the meeting held on March 11th, 1909.
  2. Lorentz, Amsterdam Proceedings, 1903-4, p. 809.
  3. Einstein, Ann. der Physik, 17. Cf. also Larmor, Aether and Matter, Ch. xi.