448 Dr. C. V. Burton on some 



subjective depression of pitch accompanying increase of 

 loudness without change of frequency, the fork will appear to 

 be lower in pitch when close to the ear and higher when 

 further away, the effect becoming less marked as the vibration 

 gradually dies down. This is what observation shows to be 

 actually the case, and it is evidently nothing of the nature of a 

 Doppler effect with which we are here concerned. In the 

 first place, the motion of the fork from one position to the 

 other may be made quite slow; and in the second place, the 

 difference of pitch is observed, not between the fork approach- 

 ing and the fork receding, but between the nearer and further 

 positions of the fork. 



3. In some of these observations a fork giving the note c' 

 (256 complete vibrations per second) has been used, the effect 

 with forks of higher pitch being less marked. When the 

 vibration was made as strong as possible by means of bowing, 

 the lowering of pitch was found to amount to a full semitone 

 (15:16). Mr. Womack, Prof. Ramsay, and Dr. G. F. 

 McCleary, vdio repeated the experiment, all agreed pretty 

 nearly with my estimate : in each case the greatest apparent 

 flattening observed was as much as a semitone. 



With a large fork giving c (one octave lower) the effect was 

 more striking. In this case the fork with its resonance-box was 

 too unwieldy to be moved bodily to and fro, so it was allowed 

 to stand on a table while the observer's head was lowered so as 

 to bring one ear opposite to the opening of the resonance-box 

 at a distance of a few inches. Thus the fork was heard with 

 great intensity, while on raising the head through half a metre 

 or so the loudness was greatly diminished. Here the lowering 

 of pitch due to the greatest intensity of vibration which I 

 could excite in the fork amounted usually to a minor third 

 (5 : 6) or even more. Thus, repeating the experiment on 

 different days, I have estimated the interval sometimes as 

 rather more and sometimes as rather less than a minor third. 

 Mr. Womack heard something between a minor and a major 

 third ; Professor Ramsay a full tone ; Dr. McCleary more 

 than a minor third. 



4. Before saying more concerning the observations, it will 

 be convenient to mention a physiological theory by which I 

 have attempted to account for the observed effects. Helm- 

 holtz's discussion of the vibration of the basilar membrane in 

 the cochlea is applicable only to infinitesimal amplitudes, in- 

 asmuch as all his equations of motion are linear, and though 

 the introduction of terms of higher order would have made 

 the investigation very lengthy and an exact solution im- 

 possible, it is not difficult to see on general grounds what 



