84 PLEASANT WA YS IN SCIENCE. 



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. 



However, the apparent variation of sound produced by 

 rapid approach or recession has been tested by exact experi- 

 ments. On a railway uniting Utrecht and Maarsen "were 

 placed," the late Professor Nichol wrote, " at intervals of 

 something upwards of a thousand yards, three groups of 

 musicians, who remained motionless during the requisite 

 period. Another musician on the railway sounded at inter- 

 vals one uniform note; and its effects on the ears of the 

 stationary musicians have been fully published. From these, 

 certainly from the recorded changes between grave and the 

 more acute, and vice versd confirming, even numerically, 

 what the relative velocities might have enabled one to pre- 

 dict, 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 indi- 

 vidual 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 altered 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 him- 

 self, 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 questioned, and after careful examination of 

 the arguments urged against it by one or two mathematicians, 



