May 20, 1922J 



NATURE 



649 



it is desired to represent the Russian " soft sign," the 



postrophe may be used. To take Dr. Brauner's 



xamples, the Permanent Committee for Geographical 



Names would write Chicherin, Jemchujni, Mendeleev, 



Kon', Tatyana, Pushkin, Dyadya, Mechnikov. 



Complete tables, not only of transcription from 

 Russian but of the English values of other European 

 and Near-Eastern alphabets, may be found in " Alpha- 

 bets of Foreign Countries transcribed into English 

 according to the R.G.S. II. System," recently pub- 

 lished by and now obtainable at the Royal Geo- 

 '-:raphical Society. 



Edward Gleichen, 

 Chairman, Permanent Committee 

 on Geographical Names. 

 Royal Geographical ^Society, Kensington Gore, 

 London, S.W.y, May 7. 



The Helmholtz Theory of Hearing. 



Dr. E. W. Scripture, in his letter on the above 

 subject in Nature of April 22, p. 518, has dealt with 

 the case in which the note is continuously changing, 

 and shows that when this is so every resonance organ 

 of the ear must act at every instant for every vibra- 

 tion of the voice. Now suppose a pure fundamental 

 note {i.e. one without harmonics) to be started and 

 continued. At the start it would, on the principle of 

 the apparatus designed by Dr. Hartridge, cause all 

 the resonance organs of the ear to act, and we should 

 hear a certain quantity of sound. Then gradually 

 all, except one, of the resonance organs would cease 

 to act, and we should hear only by means of the one 

 which was synchronous with the pure note, and if 

 this were so, presumably the quantity of sound would 

 then appear to us much less than at the start. Has 

 such an effect ever been recorded ? If not, there 

 would appear to be something wrong with the 

 hypothesis. A. S. E. Ackermann. 



1 7 Victoria Street, Westminster, 

 London, S.W.i, April 27. 



Prof. Scripture has advanced in his letter in 

 Nature of April 22, p. 518, an argument which, if it 

 were sound, would indeed necessitate the abandon- 

 ment of the resonance theory. He must, therefore, 

 excuse me if I point out what I consider to be the 

 weak links in his chain of reasoning. 



The first statement in his letter with which I find 

 myself at variance is that according to the resonance 

 theory only one resonator should respond to one tone. 

 This is not only in disagreement with what Helmholtz 

 wrote, but is also in disagreement with experiment. 

 The resonance model referred to by Prof. Scripture, 

 of which a photograph is reproduced in Fig. i, showed 

 that beside the intune resonator marked C being in 

 vibration, there is also obvious movement in the one 

 to the right-hand, side as well. If there had been 

 other pendulums of intermediate length mounted on 

 either side of " C," there is no doubt that a number 

 of these would also have been set into vibration, the 

 actual number varying with the degree of damping 

 applied to each. Helmholtz worked out the case of 

 the ear resonators by means of calculations which 

 appear to apply equally to all types of oscillating 

 systems. He estimated that for tones about the 

 middle of the musical scale, resonators having 

 natural periods different from the incoming vibration 

 by one semitone would be performing forced vibrations, 

 the amplitudes of which would be approximately one- 

 tenth that of the strictly intune resonator. 



Now I have already stated (Brit. Journ. Psych., 

 April 1922, p. 370) the reasoning on which is based 

 the estimate that some 600 resonators correspond to 

 each octave in the musical scale. One semitone on 



NO. 2742, VOL. 109] 



either side of the intune resonator would, therefore, 

 include about 100 resonators, and all these must be 

 vibrating with one - tenth the amplitude (or more) 

 of that of the intune one. 



We see then how completely this estimate is at 

 variance with Prof. Scripture's suggestion that 

 according to the resonance theory only one resonator 

 should be in vibration. 



The second statement with which I cannot agree 

 is that every vibration in a glide (since each vibration 

 is different from the one which preceded) or every 



spoken word (since the voice tone is continually 

 changing) must therefore set every resonator into 

 motion from the highest to the lowest, and I have 

 never observed any behaviour on the part of my 

 resonance model which would give any basis for such 

 a supposition. I have attempted to calculate what 

 would happen to a series of resonators which are set 

 into vibration, not by a fixed tone, but by a tone 

 changing in pitch. 1 find that, as in the case of a 

 fixed tone, a group of resonators is set swinging, but 

 that this group is larger than that set swinging by a 

 pure tone, and I infer that the centre of this group 

 moves up the scale with the same rate per second 

 as does the incoming sound, but with a small time lag. 

 For example, if the pitch of the tone is changing by 

 as much as one octave per second the group of 

 resonators appears to be only two or three times as 

 large as that set swinging by a pure tone. Presum- 

 ably then the tone will be quite recognisable, although 

 it will not have the purity that a fixed tone possesses. 

 This latter effect may possibly be correlated with the 

 unpleasant character of a rapidly changing tone, 

 e.g. the commencement of a steam syren blast. 

 Whereas there does not appear to be any evidence at 

 present by which the above estimate can be checked, 

 yet I think that it must be at variance with the 

 facts to state, as Professor Scripture has done, that 

 when the pitch of the incoming vibrations vary, all 

 resonators irrespective of length must be set equally 

 into vibration. 



I regret that it was my model which raised these 

 doubts in Prof. Scripture's mind concerning the 

 resonance theory. I should have made it quite 

 clear to him that there was roughly a semitone 

 difference of pitch between each pendulum and its 

 neighbour. The model was not designed to demon- 

 strate the better -known phenomena of resonance, 

 but to elucidate the effect of interrupting temporarily 

 a musical tone ; for this purpose a few rather widely 

 spaced pendulums sufficed. If the number of 

 pendulums in the model had approximated more 

 closely to the number apparently to be found in the 

 ear, then Prof. Scripture would, I feel sure, never 

 have criticised the resonance theory as he has done. 



H. Hartridge. 



King's College, Cambridge, April 26. 



