CONTEMPORARY ADVANCES IN PHYSICS 167 



Comparing the equations (5) and (3) to which the two conceptions 

 lead, one sees that far from contradicting one another, they are both 

 acceptable, provided that : 



PIP' = v'lv. (6) 



We may hold both the theories simultaneously, we may interchange 

 the two at will, provided we assume that the momentum of the cor- 

 puscles varies inversely as the speed of the wavefronts. In spite of 

 the outcome of Foucault's experiment, we may adopt either the wave- 

 theory or the corpuscle-theory or both at once to describe refraction, 

 provided we assume that when a beam of light is refracted toward the 

 normal, the speed of the wavefronts diminishes but the momentum of 

 the corpuscles grows greater. 



Why then did everyone concede that the corpuscular theory of light 

 was killed by the experiment of Foucault? Because everyone was 

 making two assumptions which seemed so obvious as to be hardly worth 

 the stating, and so certain that it would have been regarded as absurd 

 to call either into question: 



(A) It was being assumed, that the momentum of a corpuscle must 

 always be strictly proportional to its velocity; in other words, that the 

 mass of a corpuscle must be invariant. 



(B) It was being taken for granted that in a wave-theory of light 

 the speed of the waves, and in a corpuscle-theory of light the speed of 

 the corpuscles, must be identified with the actual speed of light as 

 measured in any actual experiment. 



When these assumptions are made, equation (5) goes over into the 

 form, 



sin e/sln d' = p'/p = v'/v, (7) 



which is contradictory to equation (3) and disproved by the experiment 

 of Foucault. 



But it no longer seems radical to change the first of these assump- 

 tions, for it is known from observation that there are particles — elec- 

 trons, for example — of which the mass is not invariant, but depends 

 upon the speed. For such a particle the momentum is not exactly 

 proportional to the velocity. It is then not quite so revolutionary to 

 go further, and suppose that the corpuscle of light is of so strange a 

 nature that its velocity and its momentum are in magnitude inversely 

 proportional to one another. If one made this supposition then one 

 could accept the second assumption, and still explain the refraction 

 of light by the corpuscle-theory. 



Even the second assumption, however, is not sacred. It may seem 

 absurd to set up a wave-theory of light, and then say that the speed of 



