Page:Aether and Matter, 1900.djvu/204

 that only the vectors denoted by accented symbols shall remain, by substituting from these latter formulae: thus

$$g=g'+\frac{v}{4\pi c^{2}}(c'+4\pi vg),$$

so that

$$\epsilon^{-1}g=g'+\frac{v}{4\pi c^{2}}c',$$

where &epsilon; is equal to $$\left(1-v^{2}/c^{2}\right)^{-1}$$, and exceeds unity;

and

$$b=b'-4\pi v\left(h'-\frac{v}{4\pi c^{2}}b\right)$$

so that

$$\epsilon^{-1}b=b'-4\pi vh';$$

giving the general relations

Hence

Now change the time-variable from t' to t", equal to $$t'-\frac{v}{c^{2}}\epsilon x'$$; this will involve that $$\frac{d}{dx'}+\frac{v}{c^{2}}\epsilon\frac{d}{dt'}$$ is replaced by $$\frac{d}{dx'}$$, while the other differential operators remain unmodified; thus the scheme of equations reverts to the same type as when it was referred to axes at rest, except as regards the factors &epsilon; on the left-hand sides.