MATTER, A MODE OF MOTION 367 



threshold value which depends on the frequencies, the impedance involved, 

 and the constant of non-linearity. The transformed energy divides itself 

 between the generated modes in the ratio of their frequencies. In a non- 

 dissipative system, the frequencies of possible combinations of sustained 

 oscillations are determined by the energy of the system. Here also they are 

 connected by the quantu n formula. 



The particle wave pattern discussed above would approximate very 

 closely to such a non-dissipative non-linear system. We should therefore 

 expect its frequency to be related to its energy through the constants of the 

 ether. In the more complex wave patterns associated with more than one 

 particle, it is unlikely that the pattern representing, say, an electron could 

 maintain its identity as part of some arbitrarily chosen pattern, the magni- 

 tudes of which are not commensurable with its own. This suggests that the 

 stable states of the complex pattern would be confined to a sequence of 

 discreet patterns which are related to one another through some property of 

 the electron. These possible non-dissipative combinations of energy and fre- 

 quency would represent the stable quantum states of the atom. The radia- 

 tion process would then be similar to that referred to above in which energy 

 from a source of higher frequency distributes itself between two lower fre- 

 quencies in the ratio of the frequencies. The energy in the pattern of an 

 excited atom would serve as the source. One of the two lower frequencies 

 would be that of a pattern corresponding to a lower energy state to which 

 the transition occurs. The other would be that of the radiating wave which 

 carries off the energy lost in the transition. 



A Suggested New Particle 



We saw above that the observed variation of the energy of a particle 

 with its velocity calls for a mechanism in which the energy varies directly 

 as the frequency. The fact that a system, in which the stiffness varies with 

 the displacement, is characterized by this relation suggests that the energy 

 of a particle pattern depends mainly on variations in the stiffness of the 

 ether. However, the non-linearities of the ether equations cannot all be 

 interpretated as variable stiffnesses. The non-linearity which appears in (1) 

 when the displacements are iinite is equivalent to a variable inertia. It is 

 in order, therefore, to inquire into the properties of a pattern in which the 

 energy is determined by this kind of non-linearity. The variable inductance 

 of an iron-core coil constitutes such a variable inertia. Theoretical and ex- 

 perimental studies of circuits involving these coils have shown that they 

 behave very much as do systems having variable stiffness, with one im- 

 portant exception. The energy distributes itself in the inverse ratio of the 

 frequencies. 



If, then, we assume that the energy of a moving pattern is determined by 



