DRIFTING LIGHT-WAVES. 



317 



rest. If, on the contrary, the cork-thrower saun- 

 ters up-stream, the corks will be somewhat far- 

 ther apart than if he had remained at rest. And, 

 supposing the observer to know beforehand that 

 the corks would be thrown in at the rate of ten 

 a minute, he would know, if they passed him at 

 a greater rate than ten a minute (or, in other 

 words, at a less distance from each other than 

 the stream traversed in the tenth of a minute), 

 that the cork-thrower was traveling down-stream 

 or approaching him ; whereas if fewer than ten 

 a minute passed him, he would know that the 

 cork-thrower was traveling away from him, or 

 up-stream. But also, if the cork-thrower were 

 at rest, and the observer moved up-stream — 

 that is, toward him — the corks would pass him 

 at a greater rate than ten a minute ; whereas if 

 the observer were traveling down-stream, or from 

 the thrower, they would pass him at a slower 

 rate. If both were moving, it is easily seen that 

 if their movement brought them nearer together, 

 the number of corks passing the observer per 

 minute would be increased ; whereas if their 

 movements set them farther apart, the number 

 passing him per minute would be diminished. 



These illustrations, derived from the motions 

 of water, suffice in reality for our purpose. The 

 waves which are emitted by luminous bodies in 

 space travel onward like the water-waves or the 

 corks of the preceding illustrations. If the body 

 which emits them is rapidly approaching us the 

 waves are set closer together or narrowed, where- 

 as if the body is receding they are thrown far- 

 ther apart or broadened. And, if we can in any 

 way recognize such narrowing or broadening of 

 the light-waves, we know just as certainly that 

 the source of light is approaching us or receding 

 from us as the case may be, as our observer in 

 the second illustration would know from the dis- 

 tance between the corks whether his friend the 

 cork-thrower was drawing nearer to him or trav- 

 eling away from him. 



But it may be convenient to give another 

 illustration, drawn from waves which, like those 

 of light, are not themselves discernible by our 

 senses — I refer to those aerial waves of com- 

 pression and rarefaction which produce what we 

 call sound. These waves are not only in this 

 respect better suited than water-waves to illus- 

 trate our subject, but also because they travel in 

 all directions through aerial space, not merely 

 along a surface. The waves which produce a 

 certain note, that is, which excite in our minds, 

 through the auditory nerve, the impression cor- 

 responding to a certain tone, have a definite 



length. So long as the observer, and a source ■ 

 of sound vibrating in one particular period, re- 

 main both in the same place, the note is un- 

 changed in tone, though it may grow louder or 

 fainter according as the vibrations increase or 

 diminish in amplitude. But if the source of sound 

 is approaching the hearer, the waves are thrown 

 closer together and the sound is rendered more 

 acute (the longer waves giving the deeper sound) ; 

 and, on the other hand, if the source of sound is 

 receding from the hearer, the waves are thrown 

 farther apart, and the sound is rendered graver. 

 The rationale of these changes is precisely the 

 same as that of the changes described in the 

 preceding illustrations. It might, perhaps, ap- 

 pear that in so saying we were dismissing the il- 

 lustration from sound, at least as an independent 

 one, because we are explaining the illustration by 

 preceding illustrations. But in reality, while 

 there is absolutely nothing new to be said re- 

 specting the increase and diminution of distances 

 (as between the waves and corks of the preced- 

 ing illustration), the illustration from sound has 

 the immense advantage of admitting readily of 

 experimental tests. It is necessary only that the 

 rate of approach or recession should bear an ap- 

 preciable proportion to the rate at which sound 

 travels. For waves are shortened or lengthened 

 by approach or recession by an amount which 

 bears to the entire length of the wave the same 

 proportion which the rate of approach or reces- 

 sion bears to the rate of the wave's advance. 

 Now, it is not very difficult to obtain rates of ap- 

 proach or recession fairly comparable with the 

 velocity of sound — about 364 yards per second. 

 An express-train at full speed travels, let us say, 

 about 1,800 yards per minute, or 30 yards per 

 second. Such a velocity would suffice to reduce 

 all the sound-waves proceeding from a bell or 

 whistle upon the engine by about one-twelfth 

 part for an observer at rest on a station-platform 

 approached by the engine. On the contrary, af- 

 ter the engine had passed him, the sound-waves 

 proceeding from the same bell or whistle would 

 be lengthened by one-twelfth. The difference be- 

 tween the two tones would be almost exactly 

 three semitones. If the hearer, instead of being 

 on a platform, were in a train carried past the 

 other at the same rate, the difference between the 

 tone of the bell in approaching and its tone in 

 receding would be about three tones. It would 

 not be at all difficult so to arrange matters that, 

 while two bells were sounding the same note — 

 mi, let us say — one bell on one engine, the other 

 on the other, a traveler by one should hear his 



