SOME CONTE.\fPOR.IRy .'tnr.tXCRS IN PItVSICS-ril 315 



The relation between X' and X, the wavelengths of the primary 

 l>eani and of the scattered beam, is still simpler, heiii^ 



X'-X=-^(l-cose). (10) 



mc 



• 



The intrusion of this anijle 6 into the final equation may seem to 

 contradict my earlier statement that the results of the impact are 

 calculable; for it is true that there are not equations enough to elimi- 

 nate 6. and yet I have offered no additional means of calculating it. 

 In fact it cannot be calculated with the data at our command. All 

 that we are able to say is that if the resulting quantum goes ofT in 

 the direction 6, then its frequency is given b>- (9). What deter- 

 mines 6 in any particular case? Re\ erting to the image of the billiard- 

 balls, it is easy to see that the direction in which the rebounding ball 

 rolls away depends on whether it gave a central blow, or a glancing 

 blow, or something in between, to the initially stationary ball. If 

 we knew just which sort of a blow was going to be giv-en, we could 

 calculate B; otherwise we can only apply our conditions of conservation 

 of energ^y and conservation of momentum to ascertain just how much 

 of its energ>- the rebounding ball retains when 8 has some particular 

 value, and then produce — or, if we cannot produce at will, await — a 

 collision which results in that value, and make our comparison of 

 experiment with theory. So it is in this case of the rebounding quan- 

 tum. When a beam of primary electrons is scattered by encountering 

 a piece of matter, some quanta rebound in each direction, and all the 

 values of 9 are represented. We cannot know what determines the 

 particular value of 6 in any case; but we can at least select any direc- 

 tion we desire, measure the frequency of the quanta which have 

 rebounded in that direction, and compare it with the formula. Fig. 6 

 is a diagram illustrating these relations." 



The comparison, which has now been made repealedU' b\- Compton, 

 repeatedly by P. A. Ross, and once or oftener by each of several other 

 physicists — notably de Broglie in Paris — is highly gratifying. The 

 value of the frequency-difference between the primar\- X-rays and 

 the scattered X-rays, that is to say, between the impinging quanta 

 and the rebounding quanta, is in excellent accord with the formula, 

 whether the measurements be made on the quanta recoiling at 45°, 

 at 90° or at 135°, or at intermediate values of the angle 6. The 

 method consists in receiving the beam of scattered X-rays into an 

 X-ray spectroscope, whereby it is deflected against an ionization- 

 chamber or a photographic plate at a particular point, of which the 



