CONTEMPORARY ADVANCES IN PHYSICS 169 



to be considered. Using primes to designate the values which things 

 have in the second medium, we put: 



/ = p. (9) 



The speed of the waves is the product of their wave-length by their 

 frequency : 



V = v\ v' = v'\'\ (10) 



consequently: 



v'jv = y/\. (11) 



The wave-lengths of the wave train on the two sides of the boundary 

 vary directly as the speeds. 



Return now to the last section, and introduce this result into equa- 

 tion (6) ; one gets: 



P'/P = V^' (12) 



which means: we can interpret refraction of light (or of electricity, or of 

 matter) by both the wave-theory and the corpuscle-theory, provided 

 that we make the momentum of the corpuscle vary inversely as the 

 wave-length of the waves. 

 Write accordingly, 



p\ = constant. (13) 



Now there are several remarkable experiments which show that this 

 relation actually holds, and moreover that the constant which appears 

 in it is the universal constant h of Planck: 



p = h/X. (14) 



For instance, one may pour a stream of X-rays — that is to say, 

 high-frequency light — into a gas, after having measured its wave- 

 length in the known and reliable way depending on one of the phenom- 

 ena in which X-rays behave as waves. A certain portion of the rays 

 is scattered; it is scattered as though it consisted of corpuscles, each of 

 which strikes an individual free electron and bounces off, the electron 

 meanwhile recoiling from the blow.- Further analysis of the data 

 shows that there is conservation of momentum — that the momentum 

 which the electron gains is equal to that which the corpuscle of light 

 has lost, provided that the momentum of this latter is equal to the quotient 

 of h by the wave-length of the rays. For the wave-length of the scattered 

 X-rays, measured in the same way as that of the primary rays was 

 measured, is not the same as theirs; and the difference between the 

 values of /;/X, before and after scattering, is equal to the momentum 

 which the electron received. 



- The Compton effect (cf. the seventh article of this series). 



