to obtain rates of approach 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 1800 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, after the engine had passed him, the sound-waves proceeding from the same bell or whistle would be lengthened by one-twelfth. The difference between 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 traveller by one should hear his own engine’s bell, the bell of the approaching 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.[12] The change of tone may be thus illustrated:— [Illustration] 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 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 railway whistle. The change of tone as a clanging bell is carried swiftly past (by the combined motions of both trains) is not at all of such a nature as to require close attention for its detection.