362 BELL SYSTEM TECIIMCAL JOURNAL 



of particles should conform to the laws of classical mechanics. As just noted, 

 it should conform much more closely to those of relativistic mechanics. 

 Also, to the extent that the flow of energy follows the laws of wave mechan- 

 ics, as suggested below, the behavior of the particles will also conform to 

 those laws. Similar considerations apply to the mass of radiation as derived 

 from its energy. 



Another experiment which helps to fix the required properties of the 

 patterns is that of Davisson and Germer, in which it is shown that a particle 

 moving with velocity V is diffracted as if it had a wave length X such that 



A= ' 



(^mo V ' 



where h is Planck's constant and mo is the rest mass. 



If, in (7) with a unity, we assume the energy frequency ratio to be equal 

 to //, the wavelength associated with the first factor reduces to the value 

 given by experiment. This does not mean that an ordinary physical wave of 

 this length is present in the pattern. It does mean that, at any instant, the 

 amplitude of the sinusoidal variation of displacement with distance, as 

 given by the remaining factors, varies sinusoidally with the wave length X, 



and is zero as points separated by - . Hence, when the presence of equally 



spaced obstacles calls for zero values of displacement at equally spaced 

 intervals, the distorted wave should be capable of forming a stable dif- 

 fraction pattern when the translational velocity of the pattern is such that 

 the interval between points of zero displacement has the value required by 

 the spacing of the obstacles. 



Thus the wave pattern will conform to this experiment provided, first, 

 that it is characterized by a particular wave length, and second, that the 

 factor of proportionality between its energy and frequency is equal to //. 

 The first requirement implies that the wave pattern when at rest has 

 practically all of its energy associated with components which are all of the 

 same frequency, or else are confined to a narrow band near the characteristic 

 frequency. 



At this point let us pause for a short review and discussion. Brieily, we 

 have replaced the "rigid body" of special relativity by an oscillatory motion 

 of the ether, the envelope of which is analogous with the configuration of the 

 rigid body. We have found that when in motion this envelope behaves as 

 does the rigid body, and the time relations conform to those of a moving 

 clock. These latter may also be interpreted as a multiplying factor which 

 has the form of a plane wave of the DeEroglic type. In wave mechanics,, 

 this is treated as a wave of a single frequency and of a variable phase veloc- 

 ity greater than that of light. In the ether theory this wave is interpreted 



