378 A CENTURY OF SCIENCE 



So even the measurement of the length of a moving body 

 depends upon the condition of synchronism at different 

 points in space. 



The principle of relativity requires that the velocity 

 of light shall be the same in one system as in another 

 relative to which the first is in motion. Hence the 

 definition of synchronism makes it possible to obtain a 

 set of transformations connecting space and time meas- 

 urement on one system with those on another. This 

 group of transformations is exactly that which Lorentz 

 had found would transform the electrodynamic equations 

 into themselves. But Einstein's point of view brought 

 out a remarkable reciprocity which Lorentz had missed. 

 If two parallel rods MN and OP are in motion relative to 

 each other in the direction of their lengths, not only does 

 OP appear shortened to an observer at rest with respect 

 to MN, but MN appears shorter than normal in the 

 same ratio to an observer who is moving along with the 

 rod OP. 



Einstein's theory makes the velocity of light the maxi- 

 mum speed with which a signal can be transmitted. This 

 leads to his celebrated addition theorem. Consider three 

 observers A, B and C. Let B be moving relative to A 

 with a velocity of nine-tenths the velocity of light, and C 

 in the same direction with an equal velocity relative to B. 

 In terms of old-fashioned notions of time and space, the 

 velocity of C relative to A would be computed as one and 

 eight-tenths the velocity of light. But the relativity 

 theory gives it as ninety-nine hundredths the velocity of 

 light. For the velocity of light can never be surpassed 

 by that of any material object. This deduction from 

 theory is most strikingly confirmed by the fact that 

 although beta particles have been observed with velocities 

 as high as ninety-nine hundredths that of light, the 

 velocity of light is never quite equalled. It may be 

 remarked in passing that the principle of relativity 

 requires that the masses of all material bodies shall vary 

 with the velocity in the same manner as Lorentz found 

 to be the case for the electromagnetic mass of the def orm- 

 able electron. In this connection Bumstead (26, 498, 

 1908) has devised an elegant method of deducing the 

 ratio of longitudinal to transverse mass. 



