THE COCHLEA. 1169 



distinguishable. When a tone of lower pitch than 30 is sounded, the 

 ear instinctively picks up the octave, probably because the octave is 

 faintly produced by the instrument. 1 From these tones of low pitch, as 

 we listen to sounds rising in pitch to the upper limits, there is no break 

 in our sensations, but a gradual passage through tones of ever-increasing 

 pitch. This experience is similar to that of running the eye along a 

 pure spectrum. When we get above 4000 vibs. per second, there is 

 again much difficulty in detecting musical intervals, but we observe the 

 gradual rise of pitch, till we reach, with cylindrical steel bars, tones 

 corresponding to 20,000 to 30,000 vibs. per second. Sensitive flames 

 give out even higher perceptible tones. 2 



In these experiments, the sounds are heard in succession, but an 

 interesting question arises as to the smallest difference in pitch that can 

 be appreciated by the ear when beats are produced by two tones sound- 

 ing at the same moment. 



Beats.— If we simultaneously sound two forks that are in unison, say 

 two forks ut iy the waves coincide and one sound is heard. Let us then 

 place on one of the forks, near the end of one of its prongs, a brass 

 clip (see above), and sound the fork by bowing. It will be found 

 to be considerably flattened as regards pitch. If we then sound the 

 two forks simultaneously, a rapid, rattling, beating sound is heard, 

 peculiar in its character, unlike a tone, but conveying no idea of two 

 sounds. Let us then slip the clip farther down the prong. On again 

 sounding the two forks, a slow soft throb is heard, and the number of 

 throbs can be readily counted. If we know the pitch of the higher 

 note, the pitch of the lower is at once determined by subtracting the 

 number of beats per second from the number representing the pitch of 

 the higher note. Thus, if one fork makes 100 vibs. while the other 

 makes 101 vibs., then 100 waves from one source are superposed on 101 

 equal waves from another source. When the two waves are in the same 

 phase, one wave increases the amplitude of the other. But after 50 waves 

 from the first fork have passed, 50| waves will have passed from the 

 second fork. The two waves will then be in opposite phases ; that is to 

 say, the onward movement of the particles of the first wave will be 

 neutralised by the backward movement of those of the second wave, and 

 the particles will be at rest. This rest may last through several waves, 

 and then the waves again change gradually, until they again coincide 

 after 100 waves have passed from the first fork. The same phenomenon 

 will occur with every 100 waves. There will thus be a waxing and 

 waning of the auditory sensation. 3 The number of beats per second is 

 equal to the difference of the frequency of the tones. As an interval 

 depends on the ratio of frequencies, it is evident that the number of 

 beats given by two tones nearly in unison will be doubled if the two 

 tones are sounded an octave higher. It is thus possible, by means of 

 beats, to ascertain the sensitiveness of the ear, even to fractions of a 

 vibration per second, and it appears that in no part of the scale can 2 

 vib. per second be distinguished with certainty. The sensitiveness varies 

 with pitch. Thus, at 120 vibs. per second, 04 vib. per second ; at 500, 

 about 0*3 vib. per second ; and at 1000, - 5 vib. per sec. can be distin- 



1 Preyer, "Physiol. Abhandl.," Jena. 1876; van Schalk, quoted by Rayleigli (op. cit.), 

 fixes the lower limit at 26 vibs., Arch, nierl. d. sc. exactes, tome xxix. p. 87. 



2 Rayleigh, op. cit., vol. ii. p. 433. 



,f Airy, op. cit., p. 215 ; Rayleigh, op. cit., vol. i. p. 22. 



VOL. II. — 74 



