282 BELL SYSTEM TECHNICAL JOURNAL 



the existence, and no one wishes to supplant them with quanta. Rip- 

 ples on the surface of a pond do furnish a precious example of wave- 

 motion, and I presume that the notion of an undulatory theory was 

 suggested originally by these; but it is precisely because they are vis- 

 ible that they fail to pose some of the questions which in dealing with 

 light and matter are the most perplexing. Watching the leaves and the 

 straws which float upon the surface of the water, one sees that they do 

 not advance with the ripples; they are heaved up and down as the 

 crests and the troughs of the wavelets pass them by. It is evident 

 that the waves are not to be identified with the water; rather they are 

 a form, a profile, a molding of the surface, which moves rapidly along 

 while the substance of the liquid oscillates only a little. Now in this 

 instance of the ripples on the pond, it is the relatively-immobile water 

 which seems substantial and real, while that which is propagated as 

 a wave appears to be merely a shape or a configuration, nothing more 

 than a geometrical abstraction. It would seem strange and whimsical 

 to assert that the liquid is a mere abstraction, but the waves are real. 

 Yet we have to embrace this apparent absurdity in dealing with waves 

 of light. 



The example of sound-waves shows forth the paradox quite clearly. 

 One can feel a tuning-fork; when it begins to act as a source of sound, 

 one can see that it is quivering, and with a stroboscope one can even 

 follow the actual course of its motion ; it is even possible to see conden- 

 sations and rarefactions travelling through the air, and there are 

 numberless indirect ways of showing that sounding bodies and sound- 

 transmitting media are matter in vibration. To the eye and to the 

 hand, the body which vibrates is material and substantial, but not so its 

 "vibration" — this word is only a way of saying that the shape, or the 

 position, or the density of the body is undergoing a continuous and 

 cyclic change. 



It happens, however, that we also possess a sense for which the 

 vibration is real but the vibrating substance is not. The ear takes 

 no cognizance of the steel of which the tuning-fork is made, nor of the 

 air which carries the undulations; but the ear perceives a tone. One 

 must fully realize that the sense of hearing does not disclose that 

 sound is vibratory. The ear does not report a sensation which goes 

 through a cyclic variation two hundred and fifty-six times (or whatever 

 the frequency of the fork may be) in every second. If it did, it would 

 be perceiving the vibrating medium, not the vibration. The ear 

 reports a sensation which is uniform, unvarying, constant; in fact, it 

 translates a steady vibration into a constant sensation. This we have 

 learned with case, because of the collaboration of the other senses 



