Appendix I.
If in place of the law of transmission of light we had taken as our
basis the tacit assumptions of the older mechanics as to the absolute
character of times and lengths, then instead of the above we should
have obtained the following equations:
_x _ = _x_ _vt_
_y _ = _y_
_z _ = _z_
_t _ = _t_
This system of equations is often termed the Galilei transformation.
The Galilei transformation can be obtained from the Lorentz
transformation by substituting an infinitely large value for the
velocity of light _c_ in the latter transformation.
Aided by the following illustration, we can readily see that, in
accordance with the Lorentz transformation, the law of the transmission
of light _in vacuo_ is satisfied both for the reference-body _K_ and
for the reference-body _K _. A light-signal is sent along the positive
_x_-axis, and this light-stimulus advances in accordance with the
equation
_x_ = _ct_,
_i.e._ with the velocity _c_. According to the equations of the Lorentz
transformation, this simple relation between _x_ and _t_ involves a
relation between _x _ and _t _. In point of fact, if we substitute for
_x_ the value _ct_ in the first and fourth equations of the Lorentz
transformation, we obtain:
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