CLASSICAL AND NEW MECHANICS 171 



of so great a velocity as that of the earth around the 

 sun. This velocity is about thirty kilometers per sec- 

 ond while V is 300,000 kilometers per second. One 

 diameter of the earth would thus, to an observer in 

 the sun, appear shortened about 7.5 centimeters, or 

 three inches. But this effect becomes quite important 

 for velocities approaching one-tenth of V. And a 

 velocity equal to that of light is absolutely unattain- 

 able because the length of the moving body would 

 then be reduced to zero. So we have the curious 

 anomaly of a finite velocity producing an infinite 

 effect. 



The same equations also show that if 1 one of two 

 clocks, which are synchronous when at rest, be moved 

 with a velocity, v, the stationary clock will run faster 

 each second than the moving one. The maximum 

 value of the difference is when one clock runs infinitely 

 faster than the other. 



We must not lose sight of the fact that this discus- 

 sion, so far as mechanical bodies and motions are con- 

 cerned, is purely academic, because for them the ratio 

 v/V is too small in any known case to have an appre- 

 ciable effect. The Principle of Relativity has its great- 

 est significance when applied to problems in electricity, 

 provided we accept the theory of electrons. // the 

 atom of matter be composed of particles of electricity, 

 if the inertia of matter be variable and due to elec- 

 trical reactions, and if the velocity of the electron 



