364 BELL SYSTEM TECHNICAL JOURNAL 



and its solution will not be attempted here. Some conclusions may, however, 

 be drawn. Since the amount of retiected energy generated by an element of 

 the medium depends on powers of the instantaneous disturbance higher 

 than the first, the superposition of a second pattern will alter the standing 

 wave pattern of the first, and vice versa. Also, as pointed out in the com- 

 panion paper, the propagation of both the main and reflected waves also 

 depends on higher powers of the instantaneous disturbance there. The result- 

 ing variations in the propagation will also affect the conditions for a stable 

 pattern. Neither pattern, then, can satisfy its stability conditions inde- 

 pendently of the other; but if the combined patterns are to be stable they 

 must together satisfy a new set of conditions common to both. How much 

 each is altered by such a union will depend on the degree of coupling be- 

 tween them, that is, on the amount of energy which must be regarded as 

 mutual to the two. 



The effect of this coupling will be very different, depending on whether 

 the frequencies of the two patterns are the same or different. When they 

 are different the non-linear terms give rise to frequencies related to the first 

 two by the quatum formula. The transfer of energy to these frequencies 

 may, under favorable conditions, set up a new mode of oscillation the sta- 

 bility conditions of w'hich are better satisfied than those of the original 

 frequencies. The new mode might be that of an e.xcited atom. Or the fre- 

 quency of one or both of the patterns may be changed to that corresponding 

 to the particle in motion with a particular velocity. In either of these proc- 

 esses some of the energy may be released as radiation at one of the dif- 

 ference frequencies. 



If, however, the frequencies of the two patterns are identical, no new 

 frequencies will result from their superposition. If the combined pattern is 

 to persist there must be a stable mode for the combination, the frequency 

 of which is identical with that of the separate patterns. This is hardly to be 

 expected. Also the oscillations of the second pattern, being of the same 

 frequency as those of the first, would have a much greater disturbing effect 

 on its conditions for stability. It would appear, then, that if it were possible 

 to bring two patterns of identical frequency into superposition, they would 

 mutually disintegrate. This does not mean that two particles of the same 

 type cannot exist in the same neighborhood. If they have different velocities, 

 for example, their frequencies will be different. The similarity of these 

 considerations to Pauli's exclusion principle is obvious. 



If the second pattern has much greater energy than the first, as it will if 

 it represents a much heavier particle, its stability conditions may be little 

 affected by the presence of the first. The behavior of the first, an electron, 

 may then be discussed on the assumption that it exists in a medium, the 

 properties of which vary with |)ositi()n in accortlancc willi the fixed j)attern 



