Page:The principle of relativity (1920).djvu/40

 which have a uniform translators motion relative to each other.

2. Every ray of light moves in the "stationary co-ordinate system" with the same velocity c, the velocity being independent of the condition whether this ray of light is emitted by a body at rest or in motion. Therefore

velocity = Path of Light/Interval of time,

where, by 'interval of time' we mean time as defined in §1.

Let us have a rigid rod at rest; this has a length l, when measured by a measuring rod at rest; we suppose that the axis of the rod is laid along the X-axis of the system at rest, and then a uniform velocity v, parallel to the axis of X, is imparted to it. Let us now enquire about the length of the moving rod; this can be obtained by either of these operations.—

(a) The observer provided with the measuring rod moves along with the rod to be measured, and measures by direct superposition the length of the rod:—just as if the observer, the measuring rod, and the rod to be measured were at rest.

(b) The observer finds out, by means of clocks placed in a system at rest (the clocks being synchronous as defined in §1), the points of this system where the ends of the rod to be measured occur at a particular time t. The distance between these two points, measured by the previously used measuring rod, this time it being at rest, is a length, which we may call the "length of the rod."

According to the Principle of Relativity, the length found out by the operation a), which we may call "the