). For a differential coefficient is a limit, and the limit of a function at a given value of its argument expresses a property of the aggregate of the values of the function corresponding to the aggregate of the values of the argument in the neighbourhood of the given value.
This is essentially the same argument as that expressed above in [1.2] for the particular case of motion. Namely, we cannot express the facts of nature as an aggregate of individual facts at points and at instants.
6.2 In the Lorentz-Maxwell equations [cf. [Appendix II]] there is no reference to the motion of the ether. The velocity (
) which appears in them is the velocity of the electric charge. What then are the equations of motion of the ether? Before we puzzle over this question, a preliminary doubt arises. Does the ether move?
Certainly, if science is to be based on the data included in the Lorentz-Maxwell equations, even if the equations be modified, the motion of the ether does not enter into experience. Accordingly Lorentz assumes a stagnant ether: that is to say, an ether with no motion, which is simply the ultimate entity of which the vectors (
and
