WILSON AND LEWIS. — RELATIVITY. 



425 



Figure 19. 



has zero magnitude we can ascribe to the Hght no finite vahie of Mq 

 or w. In this case, as in the case of inelastic impact between material 

 particles, the total values of ?/io does not remain constant, but is larger 

 after impact. In all cases we obtain the same results from the law 

 of the constancy of extended momen- 

 tum as those obtained by tlie appli- 

 cation of the ordinary laws for the 

 conservation of energy, mass, and mo- 

 mentum, whatever axes be arbitrarily 

 chosen. 



Another simple illustration of these 

 laws is furnished (Figure 19) in the 

 case where the material particle does 

 not absorb the light, but acts as a 

 perfect reflector, which corresponds 

 closely to elastic impact between 

 particles. Here a' antl b' are the 

 vectors of the light-particle and the 

 material particle after impact; and 



these vectors are readily shown to be determined either by the condi- 

 tion that the magnitude of b is equal to the magnitude of b', that is 

 that the value of viq for the material particle undergoes no change, or 

 from the condition that the angle between b and a + b is the same 

 as the angle between b' and a' + b'. This latter condition may in 

 fact be regarded as necessary a -priori, since it is the only construction 

 which can be, in the nature of the case, uniquely determined. 



Let us now consider light traveling back and forth in a single line 

 between two mirrors whose positions are fixed relative to one another. 



If the mirrors are very close to one another, 

 we may as before consider the whole system 

 as concentrated at a point. This gives us 

 a new kind of particle, an infinitesimal 

 one-dimensional Ilohlraum. Since how- 

 ever the energy contained within the par- 

 ticle is in part moving with the velocity 

 of light in one direction and in part with 

 the velocity of light in the other direction, 

 we may draw two singular vectors (Figure 

 20) to represent the extended momenta in 

 the two directions. Now these vectors added together give a (5)-vector 

 which will behave in every way like the extended momentum niQW of 



Figure 20. 



