Consider the following:
On the one hand, the principle of relativity, by Galileo, (totally applied to the Newtonian mechanics) says:
There is no mechanical experiment that you could perform to measure the difference between inertial frames of reference.
On the other hand, Maxwell's equations (or the laws of electrodynamics; laws of motion) under the principle of relativity, by Galileo, yield a non-equivalence of inertial frames of reference.
My question is: From Maxwell's equations we get an electromagnetic wave. By asking which frame of reference the wave has the velocity of $c$ we then realize that the aether is this reference. We all know that this is wrong today, but, from the perspective of a physicist of XIX century, when we try to measure the velocity of $c$ in a moving frame (with respect to the aether frame) with the Galileo's relativity principle, we then realize that the speed $c$ is different, say: $\displaystyle c' = v_{s} + c$ (*)
Is this formula $\displaystyle c' = v_{s} + c\,$ another way to verify that Maxwell's equations are different in different frames? (**)
(*) where $c$ is the speed of light with respect to the rest frame of reference with respect to the aether, $v_{s}$ is a velocity of a moving frame $S$ with respect to the aether and $c'$ is the speed of light with respect to the S reference frame.
(**) and then there is no equivalence of inertial frames for electromagnetism; and then the physics is different in one reference at rest with respect to the aether compared to a moving one, also with respect to the ether; and then there is one "absolute" frame where Maxwell's equations hold: the aether frame; and then there exists a type of an experiment that could mesure the absolute motion; and then this contradicts the principle of relativity for electromagnetism.