356 RADIATION OF ENERGY. 



the Principles of the Conservation of Momentum, and the Conservation of 

 Energy to be always true for material bodies, when we make measurements of th 

 physical state of a moving body, the units of length, time and mass are not 

 stant but vary with its speed. 



The principle 1 shows that a second measured by a stationary clock bears to 

 a second measured by a clock moving with a velocity v, the ratio 



con- 



!-•:-:- 



where c is the velocity of light. 



The unit of length in a moving system is shortened in the ratio 



1 — 1^1: 1. 



Consequently any moving body, to a stationary observer, appears to be shortened 

 in the direction of its motion. 



If m is the mass of a body in motion and m is its mass at rest, the mass of 

 the moving body will be apparently greater than that of the body at rest in the 

 ratio 



1 





The experiments of Kauffmann 2 and Bucherer 3 on the mass of charged particles 

 moving in a vacuum tube seem to confirm this increase of mass with velocity 

 although as More 4 has pointed out all that was really determined in these experi- 

 ments was the decrease of the ratio e/m as the velocity increased and the results 

 might be explained by assuming that e, the charge, was not constant as is usually 

 assumed but decreased with the velocity. 



The kinetic energy, E, of a moving mass, ra , is equal to \m$ % according to 

 the Newtonian mechanics : according to the principle of relativity it appears to be 

 greater than this and is given by 



E = woe 2 L /V\-l 



c 2 



According to this theory, therefore, if the velocity of a body could be made equal 

 to that of light its kinetic energy would appear to be infinite. 



It is, I think, evident that the principle of relativity occupies an important 

 place in the theory of radiation. In the first place it discards the ether, and in 



1 For a clear statement of this principle see Lewis and Tolman, Phil. Mag., October, 1909. 



! AnnaUn der Physik, 19, p. 487, 1906. 



9 Phys. Zeitschr., 9, p. 755, 1908; Ber. d. deutsch. Phys. Ges., 6, p. 688, 1908. 



• Phil. Mag., February, 191 1 , p. 216. 



