Page:Zur Elektrodynamik bewegter Systeme I.djvu/9

 equation 16); thus in a medium as air, for which it is notably $$\eta=0$$:

However, in vacuum it must necessarily be $$V_0 =1$$. The influence of the medium thus doesn't vanish only by the fact, that its electromagnetic constants are passing into that of vacuum, but only by the fact, that its velocity $$w$$ simultaneously takes the value which we have assumed in the vacuum once and for all time: the value 0. That there is a finite difference between $$V$$ and $$V_0$$, which doesn't depend on the density of the gas anymore, appears to as an inadmissible consequence of my equations.

In opposition to that I want you to consider: imagine that Maxwell would have carried out his observations on the friction of gases before his theoretical investigation. As an experimental result, he had to say that the coefficient of friction $$\varkappa$$ is independent of density $$\rho$$. He presumably would have added, that this law of course cannot be valid up to the most extended rarefactions, yet that the last part of curve $$\varkappa=f(\rho)$$ which must be directed from the constant finite value to the point $$\rho=0$$, is unknown in terms of form and extension.

We are in a similar position with respect to function $$V=f(\rho)$$. A theory, which represents the properties of a continuum, must necessarily have a gap at the place, where the concept of the continuum fails. By that, however, also the limit for the applicability of equation (5) is given: when we think of a gas as rarefied to an extent, at which it cannot be spoken about the velocity of gas as a steady function of space anymore (which is a constant in our case), then the symbol $$w$$ has no meaning anymore. Then the ideas by which we have operated, vanish; in this field only an atomistic theory can try to represent the phenomena.

The dilemma is: Either the equation (5) actually is the case, so that the difference $$V-V_0$$ is caused by air (C). Or in reality it is $$V=V_0$$, so that the value of (5) is feigned by the deformation of the stone console (L) in the Michelson experiment. None of both assumptions may (in my view) be rejected by us for reasons of physical experience. The decision between the theories cannot be found here.