MATTER, A MODE OF MOTION 361 



relative to the ether. When account is taken of the non-Hnearity of the 

 ether the result to be expected should differ from that just found for the 

 linear case only by the small difference between the linear and non-linear 

 patterns, which may easily be too small to measure. Thus the principal 

 obstacle to the older ether theory is removed. 



While the special theorj^ of relativity is usually written in the form 

 which corresponds to a being unity in (8), it has long been recognized that 

 there is no theoretical basis for this particular value. The ether patterns 

 are consistent with the more general formulation. In order to pin down 

 the value of a for the ether patterns we resort to another experiment. 

 Ives and Stillweir found that a molecule which emits radiation of fre- 

 quency CO when at rest emits a frequency - when in motion. This moving 

 frequency is taken relative to axes moving with the molecule, and so is to 

 be compared with the frequency of oscillation- co in (8). This indicates that 



in order to represent a component of the pattern which results when the 

 fixed pattern is set in motion, we are to put a equal to unity. 



Another observed relation is that the energy of a moving particle is /3 

 times that of the same particle at rest. This information should be useful 

 in checking any theory of the mechanism by which the non-lmearity of the 

 medium determines the energy of the pattern. All we shall do here is to point 

 out one relation, the significance of which from the standpoint of mecha- 

 nism will be discussed below. In (7), where the frequency is expressed rela- 

 tive to the same axes as the energy of the moving pattern, if we put a 

 equal to unity, the frequency also varies as /3. Hence if the pattern conforms 

 to experiment with respect to its energy, the energy must be proportional 

 to the frequency. 



Obviously, if we define the mass of the particle-pattern as its energy over 

 C-, the particle will conform to relativistic mechanics. The mass of a particle 

 as so defined, while dimensionally the same as that of the ether, is in other 

 respects quite different. Since it is derived from the energy associated with a 

 disturbance of the ether, it would be zero in the undisturbed ether, while 

 the ether mass would be finite. The momentum of a particle would be deter- 

 mined by the flow of energy associated wuth it. Also within a particle, if the 

 mode of oscillation were such that the wave propagated continuously around 

 the axis in one direction, the resulting rotation of the energy would be 

 interpreted as an angular momentum or spin. This concept of spin was 

 suggested by Japolsky^ in connection with cylindrical waves in a linear 

 medium. There is, therefore, no a priori reason to expect that the motion 



6 H. E. Ives and C. R. Stillwell, Jour. Opt. Soc. Am., 28, 215, 1938 and 31, 369, 1941. 



■ N. S. Japolsky, Phil Ma^. 20, 417, 1935. 



