Page:Zur Elektrodynamik bewegter Systeme II.djvu/8

 the direction of velocity is changing with time is without observable influence. The proof shall be neglected here. Thus, we practically are allowed to consider the diurnal motion as pure translation as well, which superimposes the motion in the annual path, at every place of Earth's surface in every moment.

§ 4. Relative motions.

Now we consider the general case of relative motions, but we presuppose that the product of common translation velocity and relative velocity is a vanishing magnitude with respect to the square of the speed of light. This condition, which is formulated in (9), has led us to equations from I'a to IVa. They are formally in agreement with I' to IV. The difference only lies in the fact, that in place of the "absolutely resting" spatial reference system, we use a "relatively resting" one, and in place of the "general time" we use "local time". Thus this means when applied to Earth: as far as the product of Earth's velocity assumed by us, and the actually given relative velocity with respect to Earth can be neglected with respect to the square of the speed of light, it is irrelevant as to whether we relate our equations to a coordinate system at rest with respect to Earth and to "terrestrial time" $$t$$, – or to another arbitrary coordinate system, which has the uniform velocity ($$-p$$) against Earth and a time $$t$$ defined by (6).

What was spoken out as a condition here, is actually valid for all observations, when we understand under $$p$$ the velocity of Earth against the fixed stars (ca. $$10^{-4}$$).

We can distinguish two fields of application:

1. Astrophysics. Here, it is either $$v=-p$$ (fixed stars), or it is at most of the order of magnitude $$p$$. Thus, the neglectable magnitudes are at most of order $$10^{-8}$$, while the measurement of the aberration angle and the corresponding change of wave lengths not nearly reach this precision.

2. Motions of extended bodies at Earth's surface. Here, $$v$$ remains small compared with $$p$$, and $$p\cdot v$$ is neglectable for any observation.

Thus everything strictly derived in §3 for relatively resting systems, applies with practically sufficient precision also to relatively moving systems.

Summarized: the (thus far) known facts of electrodynamics give us the choice for the representation: using the stationary Earth and