168 BELL SYSTEM TECHNICAL JOURNAL 



the wavefronts is not to be identified with the measured speed of light. 

 It does seem absurd to set up a corpuscle-theory, and then say that the 

 speed of the corpuscles is not necessarily the same as that of light. 

 Yet it may turn out in the end that a theory of either kind is strength- 

 ened, and made more competent to account for a variety of facts, by 

 abandoning that easy and natural identification. I will try to prove 

 by actual examples that it does so turn out. Meanwhile I summarize 

 this section in a sentence: 



If we wish to interpret light, or electricity, or matter, by both a corpuscle- 

 theory and a ivave-theory, the momentum of the corpuscles must be supposed 

 to vary inversely as the speed of the ivaves. 



I have omitted the special reference to refraction, for any more 

 general theory must include that particular case, or fall down com- 

 pletely; I have added allusions to electricity and matter, for the test 

 of any alteration of the two classical assumptions will depend chiefly 

 on whether it helps in understanding the wavelike properties of these 

 two, and not of light alone. 



We now carry the wave-theory a great step beyond the primitive 

 form in which Huyghens left it, by introducing the ideas oi frequency 

 and wave-length. 



Wave-length of Waves and Momentum of Corpuscles 



Instead of the single "wavefront" of Fig. 1, suppose a train of sine- 

 waves of frequency v, period T{— 1/f), wave-length X and wave 

 number /x(= 1/X) travelling through air along the course LMN. For 

 definiteness, think of sound-waves. The condensation ^ of the air 

 conforms to the equation: 



p = Po sin 2ir {vt — p.s -{- a), (8) 



wherein 5 stands for distance measured from some arbitrary plane 

 perpendicular to LM, and a for some constant. I write the equation 

 down because one like it (or more than one) occurs in every wave- 

 theory. In that of light there are six such equations, with components 

 of electric and magnetic field strength replacing p; but it will be 

 sufificient to think of one. In the wave-theory of matter there is one, 

 with a quantity of very abstract meaning replacing p. 



Now when the wave train passes through into the water, its fre- 

 quency remains the same. With sound-waves, or any mechanical 

 vibrations of matter, this is obvious; two pieces of matter in con- 

 tinuous contact must vibrate in unison, or not at all. We generalize 

 this statement to cover light-waves, and waves of other varieties later 



^ The excess of the density over the normal vahie, dulded by the normal value. 



