722 PROCEEDINGS OF THE AMERICAN ACADEMY. 



From equations I and II we may derive one of the most interesting 

 consequences of the principle of relativity. If E is the total energy 

 (including internal energy) of a body in motion, and E is its energy 

 at rest, the kinetic energy E' is equal to E — E , and equation II may 

 be written, 



Moreover, we may write equation I in the form, 



-l\ IV 



A v i - F J 



and dividing III by IV 



m — m 



o 



In other words, when a body is in motion its energy and mass are 

 both increased, and the increase in energy is equal to the increase in 

 mass multiplied by the square of the velocity of light. From the fun- 

 damental conservation laws we know that when a body is set in motion 

 and thus gains mass and energy, these must come from the environ- 

 ment. So also when a moving body is brought to rest, it must give up 

 mass as well as energy to the environment. The mass thus acquired 

 by the environment is independent of the particular form which the 

 energy may assume, and we are thus forced to the important conclu- 

 sion that when a system acquires energy in any form it acquires mass 

 in proportion, the ratio of the energy to the mass being equal to the 

 square of the velocity of light. We might go further and assume that 

 if a system should lose all its energy it would lose all its mass. If 

 we admit this plausible although unproved assumption, then we may 

 regard the mass of every body as a measure of its total energy accord- 

 ing to the equation, 



For a body at rest, 



m = %. VI 



r 



E n 



