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 In a similar manner we derive from the continuity of $$\mathfrak{H}{}_{n},\ \mathfrak{E}_{h}$$ and $$\mathfrak{E}_{k}$$, by means of the relation to be derived from ($$VI_c$$)

the continuity of $$\mathfrak{H}'_{n}$$.

If we also notice the other equations ($$VIII_c$$), then it is clear, that all limiting conditions are contained in the formulas

in which h can be now any arbitrary direction in the border surface.

§ 59. The equations $$(I_d) - (V_d)$$ and ($$VIII_d$$) differ from the equations which apply to stationary bodies by § 52, only by the fact that

has taken the place of

This coincidence opens for as a way, to treat problems regarding the influence of Earth's motion on optical phenomena, in a very simple way.

Namely, if a state of motion for a system of stationary bodies is known, where 

are certain functions of x, y, z and t, then in the same system, if it is displaced by the velocity $$\mathfrak{p}$$, there can exist a state of motion, where

are exactly the same functions of x, y, z and t' [that is, $$t-\frac{1}{V^{2}}\left(\mathfrak{p}_{x}x+\mathfrak{p}_{y}y+\mathfrak{p}_{z}z\right)$$].

Although we have given (in the previous consideration) to the coordinate axes the directions of the symmetry axis, the derived theorem applies to any right-angled coordinate system. We can easily recognize this, when we consider, that for local time $$t'$$ it can also be written

where r is the line drawn from the coordinate origin to the point (x, y, z), and $$t'$$ is independent of the direction of the coordinate axes.