76 



NATURE 



[January 19, 1922 



tically eliminated by making the observations on a 

 bright, clear day at a high-level station, and the self- 

 illumination of the sky under the same conditions is 

 very small in respect of wave-lengths near the extreme 

 red end of the spectrum. The residual effect of self- 

 illumination in these circumstances may be computed 

 with sufficient accuracy by the method used by L, V. 

 King (Phil. Trans. Roy. Soc., A, vol. 212, 1913), 

 the uncertainties due to the neglect of the curvature 

 of the earth and other simplifying assumptions in the 

 calculation being then of little importance. 



In order to obtain material for testing these ideas 

 I made observations on the forenoon of December 4 

 last from the summit of Mount Dodabetta, in the 

 Nilgiris (8750 ft. above sea-level), the sky at the time 

 appearing beautifully clear, free from cirrus clouds, 

 and almost completely black when seen through a 

 deep red filter. The weaker component of polarisation 

 was found to have 13 per cent, of the intensity of the 

 stronger component. Diffuse illumination of the sky 

 is capable of explaining only a part of this, a weaker 

 component of about 8 per cent, intensity lieing indi- 

 cated by the calculations. The residual 5 per cent, 

 must therefore be ascribed to molecular anisotropy, 

 and this is in agreement with the laboratory deter- 

 minations of Rayleigh. 



Observations on the molecular scattering of light 

 in liquids made by the writer also show an imperfect 

 polarisation attributable to anisotropy. Experiments 

 in the same direction on the atomic scattering of light 

 in crystals are being made, and an attempt is also In 

 progress to discover the existence of an effect Indicated 

 by Sir J. J. Thomson's theory (Phil. Mag., October, 

 1920), namely, the dependence of the results on the 

 frequency of the scattered radiation. 



C. V. Raman. 



210 Bowbazaar Street, Calcutta, December 19. 



The Resonance Theory of Hearing. 



May I reply to Dr. Perrett's letter (Nature, Decem- 

 ber 29 last), in which he makes the objection to the 

 resonance hypothesis that it does not explain how we 

 perceive when there are two tones of the same pitch 

 sounding simultaneously? 



It seems to me that Dr. Perrett has made two 

 slight errors : — 



(i) There must be, he writes, one result, unique and 

 without alternative, when the tracing of the combined 

 wave-form of any two notes of the same frequency Is 

 submitted to Fourier analysis. 



But surely this cannot be true; for example, if in 

 one case the two tones are 256 vibrations per sec. 

 from an oboe and a flute simultaneously sounded, the 

 relative amplitudes of the overtones found bv Fourier 

 analysis would be quite different from those found for 

 the same tone sounded simultaneously on a violin 

 and a cornet. Not only would the amplitudes of the 

 overtones differ in the two cases relatively to the 

 fundamentals, but they would differ also relatively to 

 one another. 



(2) Dr. Perrett proceeds: "If .he ear acts as a 

 kind of practical Fourier's theorem, it can perceive 

 only one fundamental tone. But we Invariably 

 judge of the pitch of a note by its fundamental 

 tone. If, then, we hear at the same time two 

 notes of pitch n, the ear must be able to perceive 

 also at the same time two fundamental tones of fre- 

 quency n— -that Is to say, it must be able to perform 

 an analysis which Is not In accordance with Fourier's 

 theorem." 



Surely Dr. Perrett has omitted in the above reason- 

 ing to take into account the existence of beats, 

 overtones, and phases. If these did not exist, and if 

 NO. 2725, VOL. 109] 



the ear could still tell whether one or more than one 

 instrument were contributing to a tone, then the reson- 

 ance theory would have met with a serious difficulty. 

 But overtones do exist, and they are known to differ 

 for different instruments, also for one instrumeat 

 in different circumstances, e.g. the human voice 

 when sounding various vow-els. The resonance theory, 

 in that it explains the perception of overtones, even 

 when their intensity compared with the fundamental 

 is small, also explains how we can tell whether two 

 different Instruments are contributing to a tone or 

 one only. But there are other clues ; for besides that 

 given by overtones, whiqh In accordance with the 

 resonance hypothesis the ear might make use of, viz. 

 (a) if there were beats, due to the two instruments not 

 being exactly In tune, the observer might infer that 

 two were sounding, and not one ; (b) if the sound- 

 waves from one instrument reached the observer's 

 right ear S. little earlier (or later) than they reached 

 his left, whereas those from the other instrument 

 had different time relationships, he might Infer that 

 there were two sources of sound, from the observation 

 that the two sources did not occupy the same position 

 relative to his own plane of symmetry ; and (c) if 

 the sounds from the two instruments did not begin 

 and end together the observer might get information 

 from this also. All these possible methods of observa- 

 tion are compatible with the resonance theory, and 

 therefore it is quite unnecessary to assume that the 

 ear must be able to perform an analysis which is not 

 in accordance with Fourier's theorem. It seems to 

 me, therefore, that Dr. Perrett's objection must fail 

 on all the above grounds. 



May I take this opportunity of describing a fresh 

 piece of evidence in favour of the resonance theory? 

 Helmholtz showed, from physical considerations, that 

 the coefficient of " sharpness of tuning " should be 

 Inversely proportional to the "persistence" coefficient 

 In the case of resonators responding to tones of 

 different pitch. This relationship does not postulate 

 any special form of resonator, but appears to be a 

 general rule equally as applicable to an electrical 

 oscillating circuit as to a stretched string. If, then, 

 it could be shown that the ear obeys this rule, it would 

 be presumably very strong evidence indeed for the 

 existence of resonators in the cochlea. The following 

 table, calculated from observations by Mayer (pub- 

 lished in Am-er. Journ. Sci., January, 1894), shows 

 that the necessary evidence exists : — 

 A B C 



No. of vibrations BxC 



Per cent, differ- performed durine Tuning 



ence of tone a subliminal silent factor 



required to stop interval muliiplied by 



Mean tone in disonance (persistence persistence 



vibs. per sec. (tunine factor) factor) fscfor. 



128 1270 178 22-6 



256 1000 206 20-6 



320 945 2-19 20-8 



384 907 2- 18 19-8 



512 8-45 2-37 200 



640 815 254 207 



760 782 2-68 2I-0 



1024 7-22 ' 301 217 



Since multiplying tuning factor bv persistence factor 

 gives values nearly constant for different resonators (the 

 average error is less than 3 per cent.), as shown in the 

 last column in the above table, the tuning coefficient 

 must be very nearly inversely proportional to the per- 

 sistence coefficient. That is, the ear behaves quantita- 

 tively as it ought to do if it contained resonators. 



I find a correction Is necessarv In mv letter to 

 Nature of January 5. "Tide production " on line 20 

 should read "tide prediction." H. Hartridge. 



King's College, Cambridge. 



