190 Transactions of the American Institute. 



notice how the broken curve indicates that it travels faster in hydro- 

 gen than in the air ; also observe the faint reflection which has taken 

 place at the surface of the hydrogen. Hence, it is plain that Toepler's 

 observations are in perfect harmony with the ideas long ago developed 

 by the theory of wave-motion. 



Let us pass on to another point. "Waves of water, as you well 

 know, differ much in length, the great ocean waves stretching them- 

 selves out a hundred feet and more, while the tiny wavelets in quiet 

 water often measure less than an inch. So it is with sound ; the 

 deepest tones of the organ, which are almost felt rather than heard, 

 are produced by waves thirty-two feet long, while the shrill sounds 

 emitted by a child's whistle are due to waves only an inch or two in 

 length. The pitch of note depends on the length of the wave ; low 

 notes are given by long waves, high notes by those which are short. 

 I have here a couple of flute organ-pipes, which are so contrived as to 

 furnish aerial waves of about twice their own length. This two-feet 

 pipe is now sending through the house waves that are about four feet 

 long ; and, when we compare them with the waves furnished by the 

 shorter pipe, we notice that the latter note is just an octave higher 

 than the first. The long and short waves travel, however, with the 

 same velocity ; and, when I sound the two pipes together, both notes 

 reach your ears at the same instant, and this would happen if you 

 were a hundred times more distant from me. But, in order to do 

 this, the short wave must take twice as many steps as its longer com- 

 panion ; it must, in the same period of time, execute twice as many 

 vibrations J hence, finally, when long waves strike on the drum of 

 the ear, they cause it to vibrate slowly, while shorter waves compel it 

 to vibrate more rapidly. 



This leads us to the remarkable conclusion, that if, by any means, 

 we cause the drum of the ear to bend inward and outward, or to 

 vibrate slowly, we shall perceive a low note, while, if the process be 

 carried on rapidly, the sensation will be that of one which is high. 

 I have here a brass wheel, originally contrived by the celebrated 

 Savart, with its rim cut into teeth, and can cause them to strike, one 

 after the other, on this visiting card ; when this is done slowly, the 

 separate taps are distinctly audible over the whole house, but, as I 

 quicken the rate, the taps follow so swiftly that the ear fails to recog- 

 nize them individually, and we have in their place a musical note, 

 not quite pure, which, as you notice, rises and falls as I change the 

 rate of the wheel's rotation. If this, alteration in rate is effected 

 rapidly, the sounds may be made, as you hear, to resemble human 



