Mechanical "Resonance " under Double Forcing. 455 



photographs again show the random phases of the resonators 

 responding to the two different periods of forcing in use. 

 The cases of a hump at one side and the cubic are again 

 illustrated. The increased sharpness of resonance suggested 

 pushing the periods of the two drivers nearer to equality with 

 the view of noting how closely two maxima of resonance 

 could occur, and yet be detected without coalescence of 

 behaviour on the part of the responders. This detection 

 of separate maxima in spite of some spreading of the re- 

 sonance is somewhat analogous to the case of resolution of 

 points by lenses and lines by prisms in spite of diffraction. 



The idea of such resolution was accordingly followed 

 up in the experiments whose results are given in Plate VI. 

 tigs. 13-18, consisting of four time exposures and two flash 

 photographs. Of these four time exposures, the driving pen- 

 dulums had the greatest difference of lengths for fig. 16, they 

 are closer for fig. 13, closer still for fig. 17, and are in exact 

 agreement of lengths and periods in fig. 18. Indeed the result 

 shown in fio-. 1# is indistinguishable in character from that 

 of tig. 19 (also on Plate VI.), in which only a single driver 

 was employed. The two flash photographs, figs. 14 & 15, 

 are for the same drivers as used in the time exposure fig. 13, 

 and show the change of phase introduced by the slightly 

 different periods of forcing. 



In Plate VI. figs. 19-24 are given the results obtained by 

 using a single driver whose length was very slightly changed 

 from each figure to the next. Thus the discrimination of 

 frequency of a driving vibrator which can be effected by a set 

 of graduated responding vibrators is seen to be carried to a 

 fineness much closer than that of the difference of frequencies of 

 the successive responders themselves. For in passing through 

 this series of six figures (19--24) we do not cover the interval 

 between the frequency of one vibrator and its neighbour. 



Conclusion. — Some find difficulties in accepting a resonance 

 theory of audition on the ground that there may not be in 

 the internal ear sufficient responding vibrators provided with 

 separate nerves to give one nerve for each perceptible pitch 

 throughout the range of hearing. To such the above simple 

 experiments with pendulums may afford some help by 

 analogy. These experiments, at any rate, show that the 

 resonance theory of audition, whether it stands or falls, does 

 not fall on this account. 



It is hoped to deal more particularly with this and other 

 points as to the resonance theory of hearing in another paper 

 for which the experiments are already completed, and to 

 which this paper forms a natural introduction. 

 Nottingham, 

 February 14th, 1919. 



