1 1 76 THE EAR. 



diminution of pressure, or between a push and a pull ; or, in other words, 

 it is affected by phase. 1 The fact, however, that it is affected by phase, 

 does not greatly interfere with the analytic power already discussed, 

 because when one listens to such an imperfect harmony with appropriate 

 resonators, one can still resolve the harmony into its constituents. 



S. P. Thompson 2 has discussed experimentally certain points regarding phase. 

 By leading the sound of a tuning-fork through a tube to each ear separately, 

 so that the phases could not mix in the air, and in such a way that the sound 

 waves struck each tympanic membrane in exactly opposite phase simultaneously, 

 the sound seemed to be localised at the middle of the back of the head. If, 

 on the other hand, the sound-waves struck each tympanic membrane in the 

 same phase simultaneously, the sound appeared to be localised in the ears. 



Again, if the sounds of two tuning-forks, which, when sounded together, 

 gave beats, were led to the two ears separately, in such a way that they could 

 not mix in the air, beats of great intensity were still perceived and appeared 

 to be localised in the middle of the back of the head. In this experiment the 

 peculiar fact was noticed, that the silences were not true ones, but rather that 

 the sound appeared to be going on all the time. Interference must therefore 

 have occurred within the ear, or in the nerve-paths, and thus it is obvious 

 that the ears can appreciate difference of phase. 



During recent years some experimenters 3 have attributed these "subjective 

 beats " to interference occurring, not in the ear itself or nerve-paths, but in 

 the bones of the head. If the latter view is correct, then the experiments 

 described above cannot be considered as proving that the ear or ears are able 

 to appreciate difference of phase. 



The question of the influence of phase has also been investigated by 

 Konig, 4 by means of an instrument termed a wave-syren, an invention of his 

 own; and there can be no doubt that his observations are not only of great interest, 

 but that they present the greatest difficulties in the way of the theory of Helm- 

 holtz. He first drew to scale the curves obtained by compounding partials up to 

 the tenth member of the series ; and he modified the curves so that they were 

 compounded first with zero difference of phase, then with all the upper 

 members moved one quarter, then with a difference of half a wave, and lastly 

 with a difference of three-quarters. The sounds of all these curves, according 

 to Helmholtz, should be exactly alike, although they differed in form and 

 position. These curves were cut out on the circumference of metallic 

 cylindrical hoops, which were then mounted on an axis and rotated rapidly. 

 Against these toothed edges (or edges showing sinusoidal curves) air was 

 blown under pressure through narrow slits, as the curves passed in front of 

 the slits; and thus sounds varying in phase from a quarter to three-fourths of the 

 wave-length were obtained. It was found that they varied in quality ; with 

 a phase of a J, the sound was loud of a peculiar shrill quality ; those of J differ- 

 ence were gentle and soft ; while the curves of and \ had a quality inter- 

 mediate in character. These were no doubt minor differences, and, according 

 to Lord Kayleigh, " the results are in harmony with the view that would 

 ascribe the departure from Ohm's law involved in any recognition of phase 

 relations to secondary causes." 6 It is clear, however, that the influence of 

 phase is not so absolutely negative as Helmholtz supposed. 



The phonograph, better than any other instrument, illustrates many of 

 these phenomena. The marks on the wave-cylinder correspond to the pitch, 



1 Kelvin, op. tit.; see also, at the end of the paper, curves showing the variations of 

 pressure with imperfect harmonies. 



2 London, Edinburgh, and Dublin Phil. Mag., London, 1877, vol. iv. p. 274 ; 1878, 

 vol. vi. p. 383 ; 1881, vol. xii. p. 351. 



3 K. L. Schafer, Arch. f. d. ges. Physiol., Bonn, 1895, Bd. Ixi. S. 544. 



4 Konig, " Quelques experiences d'acoustique," Paris, 1882, p. 236. 

 6 Rayleigh, op. cit., vol. ii. p. 469. 



