DRIFTING LIGHT- WA VES. 83 



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 traveller by one 

 should hear his own engine's bell, the bell of the approach- 

 ing engine, and the bell of the same engine receding, 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 recognized 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 quite 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 experiment 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 during which the rate of recession 

 gradually increases from nothing up to the actual rate of the 

 engines' velocities added together.* The change of tone 

 may be thus illustrated : 



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. When a bell is sounded on the 



* 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, towards or from an engine on the other, is never quite 

 equal to the engines' velocities added together ; but the difference 

 amounts practically to nothing, except when the engines are near each 

 other. 



