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THE POPULAR SCIENCE MONTHLY.— SUPPLEMENT. 



own engine's bell, the bell of the approaching 

 engine, and the bell of the same engine reced- 

 ing, as the three notes, do, mi, sol, whose wave- 

 lengths are as the numbers 15, 12, and 10. We 

 have here differences very easily to be recog- 

 nized even by those who are not musicians. 

 Every one who travels much by train must have 

 noticed how the tone of a whistle changes as the 

 engine sounding it travels past. The change is 

 not cpiite sharp, but very rapid, because the other 

 engine does not approach with a certain velocity 

 up to a definite moment and then recede with the 

 same velocity. It could only do this by rushing 

 through the hearer, which would render the ex- 

 periment theoretically more exact but practically 

 unsatisfactory. As it rushes past, instead of 

 through him, there is a brief time during which 

 the rate of approach is rapidly being reduced to 

 nothing, followed by a similarly brief time dur- 

 ing which the rate of recession gradually in- 

 creases from nothing up to the actual rate of the 

 engines' velocities added together. The change 

 of tone may be thus illustrated : ' 



A B 



C D 



A B representing the sound of the approaching 

 whistle, B C representing the rapid degradation 

 of sound as the engine rushes close past the 

 hearer, and C D representing the sound of the 

 receding whistle. Where a bell is sounded on 

 the engine, as in America, the effect is better 

 recognized, as I had repeated occasion to notice 

 during my travels in that country. Probably this 

 is because the tone of a bell is in any case much 

 more clearly recognized than the tone of a rail- 

 way-whistle. The change of tone, as a clanging 

 bell is carried swiftly past (by the combined mo- 

 tions of both trains), is not at all of such a na- 

 ture as to require close attention for its detec- 

 tion. 



However, the apparent variation of sound 

 produced by rapid approach or recession has 

 been tested by exact experiments. On a railway 

 uniting Utrecht and Maarsen " were placed," the 

 late Prof. Nichol wrote, " at intervals of some- 

 thing upward of a thousand yards, three groups 

 of musicians, who remained motionless during 



1 Even this statement is not mathematically exact If 

 the rails are straight and parallel, the ratio of approach 

 and recession of an engine on one line toward or from an 

 engine on the other is never quite equal to the engines' 

 velocities added together ; hut the difference amounts 

 praeticallv to nothing, except when the engines are near 

 each other. 



the requisite period. Another musician on the 

 railway sounded at intervals one uniform note • 

 and its effect on the ears of the stationary musi- 

 cians have been fully published. From these 

 certainly — from the recorded changes between 

 grave and the more acute, and vice versa — con- 

 firming, even numerically, what the relative ve- 

 locities might have enabled one to predict, it 

 appears justifiable to conclude that the general 

 theory is correct ; and that the note of any sound 

 may be greatly modified, if not wholly changed, 

 by the velocity of the individual hearing it ; " or, 

 he should have added, by the velocity of the 

 source of sound : perhaps more correct than 

 either is the statement that the note may be al- 

 tered by the approach or recession of the source 

 of sound, whether that be caused by the motion 

 of the sounding body, or of the hearer himself, 

 or of both. 



It is difficult, indeed, to understand how doubt 

 can exist in the mind of any one competent to 

 form an opinion on the matter, though, as we 

 shall presently see, some students of science and 

 one or two mathematicians have raised doubts as 

 to the validity of the reasoning by which it is 

 shown that a change should occur. That the 

 reasoning is sound cannot, in reality, be ques- 

 tioned, and after careful examination of the argu- 

 ments urged against it by one or two mathema- 

 ticians, I can form no other opinion than that 

 these arguments amount really but to aD expres- 

 sion of inability to understand the matter. This 

 may seem astonishing, but is explained when we 

 remember that some mathematicians, by devoting 

 their attention too particularly to special depart- 

 ments, lose, to a surprising degree, the power of 

 dealing with subjects (even mathematical ones) 

 outside their department. Apart from the sound- 

 ness of the reasoning, the facts are unmistakably 

 in accordance with the conclusion to which the 

 reasoning points. Yet some few still entertain 

 doubts, a circumstance which may prove a source 

 of consolation to any who find themselves unable 

 to follow the reasoning on which the effect of 

 approach or recession on wave-lengths depends. 

 Let such remember, however, that experiment in 

 the case of the aerial waves producing sound 

 accords perfectly with theory, and that the waves 

 which produce light are perfectly analogous (so 

 far as this particular point is concerned) with the 

 waves producing sound. 



Ordinary white light, and many kinds of col- 

 ored light, may be compared with noise — that is, 

 with a multitude of intermixed sounds. But 

 light of one pure color may be compared to 



