182 BELL SYSTEM TECHNICAL JOURNAL 



of time, but retains the same value throughout except for the change 

 of direction; if we were to apply a Fourier analysis to this motion, we 

 should find not only the frequency ///2c?, l)ut all of its overtones. Let 

 us think however only of this fundamental frequency. Now it 

 is evident that there is nothing, in our ordinary conceptions of particles 

 rushing back and forth and rebounding from walls, to distinguish any 

 value of speed or frequency above any others. The phenomenon of 

 resonance sets certain wave-lengths apart from others, but there is 

 nothing to correspond to resonance in this latter case, and set certain 

 speeds apart from others. 



But instead of sound, think of some kind of radiation which we have 

 interpreting both as corpuscles and as waves — light, for example. 

 Light enclosed between parallel reflecting walls forms stationary 

 waves,''' provided that its wave-length is related to the distance d 

 between the walls by the equation (41), which I rewrite: 



X = Id/u, ;/ = 1, 2, 3 . . . (42) 



The parallel reflecting walls, or the limitation which they set upon the 

 space accessible to the light, thus single out certain characteristic 

 wave-lengths and distinguish them from all others. How interpret 

 this fact by corpuscle-theory? 



Well, we have been associating waves of wave-length X with cor- 

 puscles of momentum p = h/\; let us continue to do so. The reflecting 

 walls, then, single out certain characteristic values of momentum given 

 by this equation, derived straight from (42): 



p = nh/ld, (43) 



which I proceed to rewrite thus, 



2d-p = uh ;/ = 1, 2, 3 . . . (44) 



These values of momentum, I have said, are set apart from all the 

 rest. If waves and corpuscles are interchangeable as bases for a 

 theory of light, then the feature of wave-motion known for short as 

 "resonance" obliges us to make that supposition. But in what way, 

 and to what extent, are they set apart? According to modern quan- 

 tum-theory, they are actually the only possible values. A particle 

 describing a cyclic motion of this character, in which it moves a fixed 

 distance with a fixed momentum and then moves the same distance 

 backward with the same momentum reversed and so forth ad infinitum, 

 is constrained by something in the order of nature to have one or 



'^Interference f)atleriis are essentially of this type, thoiii'li iisiiali\- they are 

 formed between mirrors ol)liciiie to one another. 



