Page:Eddington A. Space Time and Gravitation. 1920.djvu/75

III] quickly, and in the initial adjustment described above the clock must be set back a little. The clock-reading of the event is thus smaller. There are other small corrections arising from the FitzGerald contraction, etc.; and the net result is that, it does not matter what uniform motion is given to the scale, the final result for $$s$$ is always the same.

In elementary mechanics we are taught that velocities can be compounded by adding. If $$B$$'s velocity relative to $$A$$ (as observed by either of them) is 100 km. per sec., and $$C$$'s velocity relative to $$B$$ is 100 km. per sec. in the same direction, then $$C$$'s velocity relative to $$A$$ should be 200 km. per sec. This is not quite accurate; the true answer is 199.999978 km. per sec. The discrepancy is not difficult to explain. The two velocities and their resultant are not all reckoned with respect to the same partitions of space and time. When $$B$$ measures $$C$$'s velocity relative to him he uses his own space and time, and it must be corrected to reduce to $$A$$'s space and time units, before it can be added on to a velocity measured by $$A$$. If we continue the chain, introducing $$D$$ whose velocity relative to $$C$$, and measured by $$C$$, is 100 km. per sec., and so on ad infinitum, we never obtain an infinite velocity with respect to $$A$$, but gradually approach the limiting velocity of 300,000 km. per sec., the speed of light. This speed has the remarkable property of being absolute, whereas every other speed is relative. If a speed of 100 km. per sec. or of 100,000 km. per sec. is mentioned, we have to ask—speed relative to what? But if a speed of 300,000 km. per sec. is mentioned, there is no need to ask the question; the answer is relative to any and every piece of matter. A β particle shot off from radium can move at more than 200,000 km. per sec.; but the speed of light relative to an observer travelling with it is still 300,000 km. per sec. It reminds us of the mathematicians transfinite number Aleph; you can subtract any number you like from it, and it still remains the same.

The velocity of light plays a conspicuous part in the relativity theory, and it is of importance to understand what is the property associated with it which makes it fundamental. The fact that the velocity of light is the same for all observers is a consequence rather than a cause of its pre-eminent character.