THE ANALYTIC PROPERTIES OF THE EAR. 1171 



not more in amplitude than '0004 mm. at the ear, or 01 of the wave 

 length of green light, and the energy of such a vibration on the drum- 

 head is not more than ^\^ billionth kilo., or T V of that produced upon 

 the same surface of the retina by a single candle at the same distance. 



Lord Kayleigh has investigated the question by two methods. 1 By the 

 first, he estimated that the amplitude of the movement of the aerial par- 

 ticles, with a sound just audible, " was less than the ten-millionth of a centi- 

 metre," and that under favourable conditions "an amplitude of 10~ 8 cm. 

 would still have been audible." 2 By the second method, he not only 

 determined the amplitude, but he estimated the energy emitted when the 

 sound was just becoming inaudible, at 42 '1 ergs per second. Further, in 

 considering the amplitude or condensation in the progressive aerial 

 waves, at a distance of 27*4 metres from the fork, in the second experi- 

 ment, he states that s, the maximum condensation^ 6 '0 x 10~ 9 , a. result 

 showing " that the ear is able to recognise the addition and subtraction 

 of densities far less than those to be found in our highest vacua." 

 Lastly, Lord Eayleigh contrasts the energy-emission of a source of light 

 with that of the fork in the second experiment, and arrives at a con- 

 clusion similar to that of Tbpler and Boltzmann, namely,;" that the 

 streams of energy required to influence the eye and ear are of the same 

 order of magnitude." 



The analytic properties of the ear. When we listen to musical 

 sounds, even the untrained ear perceives that they may differ much in 

 character although they may be of the same pitch. Thus the note c as 

 produced on a violin, a harp, a tuning-fork, a clarionet, an oboe, or by 

 the human voice, gives rise to a peculiar sensation, characteristic of the 

 instrument. No doubt this may be partly due to certain noises often 

 produced by the particular instrument ; but these noises quickly fade 

 away and disappear as we move away from the source of sound, while 

 the character of the sound still remains. It is well known that physi- 

 cally the waves of such sounds are not simple pendular vibrations, but 

 are more or less complex vibrations, produced by certain tones of shorter 

 wave-length being combined with the first or fundamental wave. When 

 we listen to certain sounds having a character or quality, even the 

 inexperienced ear can detect the fact that the sensation is not that 

 of listening to one sound but to a mixture of sounds, higher in pitch 

 than the tone that seems to give pitch to the sound. For example, if 

 we bow ut 2 somewhat roughly, we hear, in addition to the tone of the 

 fork, certain high ringing tones which rapidly die away. These tones are 

 peculiar, and do not belong to the harmonic scale of the fork. The forks 

 examined by Helmholtz showed a frequency of the first partial from 

 5*8 to 6 '6 times that of the proper tone. 4 When we listen to the syren, 

 we are also often conscious of tones much higher in pitch than those 

 accounted for by the stop we happen to be using and the speed of the 

 syren disc. If we sound strongly a reed having a frequency of 64 vibs. 

 per second, as in Appunn's apparatus, and place a large zinc cone over 

 the reed, we hear a vast number of tones, all of a pitch above 64 vibs. 

 per second, and if we sing a note or series of notes while the reed is 

 sounding, we have the curious sensation of always being in harmony with 



1 Proc. Roy. Soc. London, 1877, vol. xxvi. p. 248 ; London, Edinburgh, and Dublin 

 Phil. Mag., London, 1894, vol. xxxviii. p. 366. 



2 Rayleigh, op. cit., vol. ii. p. 435. 



3 Ibid.; footnote, p. 438. 4 Ibid., vol. i. p. 59. 



