of Consonances of the Form h : 1. 429 



The beats in question were only heard in the first two cases. 

 The third set was 



c' :g" 



c f : d" 



The beats in question were only heard in the first case. 



33. In the few experiments hitherto made with notes of 

 higher pitch, the beats of mistuned consonances of the form 

 h : 1 were not heard when the beats of the harmonics were 

 eliminated, unless the power of the notes was very greatly in- 

 creased. In this region, however, Konig's own observations 

 are very full and complete. 



34. We notice at once the decrease in the range within which 

 the phenomena are heard as we rise in the scale. This is at 

 once accounted for on the hypothesis of transformation, by the 

 consideration that the displacements to which the higher notes 

 give rise are much smaller than those of the lower notes. If 

 we knew the law of the decrease, we might obtain a relation 

 between the coefficients of the different terms in the expres- 

 sion for the character of the transforming mechanism. Konig 

 has attempted to formulate a law of decrease; and I have done 

 so on a previous occasion ; but this part of the subject is as 

 yet too hypothetical to admit of satisfactory treatment. 



Objective and Subjective Phenomena. 

 Resonators, 



35. On beginning work I endeavoured, in the first instance, 

 to ascertain what evidence resonators are capabable of fur- 

 nishing as to the nature of binary combinations. There are a 

 few points connected with their use which require attention. 



36. I have always found difficulty in getting results of a 

 definite character with resonators, whether applied directly to 

 one ear in the manner described by Helmholtz, or connected 

 with one ear by means of a flexible tube, as practised by others. 

 There are three difficulties which occur : (1) pressing the tube 

 or orifice into the ear is apt to close the inner passage of that 

 organ; (2) if the tube or orifice is applied lightly, it does not 

 completely occupy the passage, and external sound comes past 

 it into the ear; and (3) it is impossible so to stop the unused 

 ear as to prevent the external impressions from arriving there 

 and causing confusion. 



37. The method I ultimately adopted was as follows: — A 

 copper tube of \ inch diameter was bent into a semicircle, the 

 diameter of which was nearly 8 inches. At the middle of the 

 tube, and at right angles to its plane, another copper tube was 



Phil Mag. S. 5. Vol. 11. No. 70. June 1881. 21 



