Page:Elektrische und Optische Erscheinungen (Lorentz) 097.jpg

 in the direction ($$b'_{x}, b'_{y}, b'_{z}$$) within the moving body.

From (81) we find

and for that we can write, neglecting magnitudes of second order,

Here, $$\mathfrak{p}_{n}$$ is the component of velocity into the direction of the wave normal, with which $$W'$$ is related. Eventually

§ 69. Up to now, the investigation was general. Now it shall be assumed, that the body be isotropic. The velocity W is thus independent of the direction of the waves, and also the ratio

the absolute refraction index of the stationary body, only depends on T.

When interpreting formula (82), which now passes to

we have to remember, that we have used a coordinate system for the description of the phenomena, that moves together with ponderable matter. Thus (83) is the velocity of the light waves relative to that matter. If we wish it know the relative velocity $$W$$ with respect to the aether'', we have to compose the velocity (83), which has the direction of the wave normal, with the component $$\mathfrak{p}_{n}$$ of the translation velocity (that exactly falls in that direction). By that we obtain

which is in agreement with the known assumption of.