492 Mr. R. H. M. Bosanquet on the Beats 



(y) The refraction-equivalents of organic compounds so 

 closely depending on the chemical constitution of those bodies 

 shows the very close relation which exists between the par- 

 ticles which transmit light and the elements of the body. 



(8) The study of optical rotation affords an insight into the 

 close relationship between matter and light. 



(e) The action of light in altering the electrical resistance 

 of bodies and also in producing sound shows that there is no 

 break in continuity between sound and light. 



LXY. On the Beats of Consonances of the Form h : 1. 

 By E. H. M. Bosanquet. 



[Concluded from p. 435.] 



Combination-Tones arising from Terms of Orders higher than 

 the first, in the Transforming-structure of the Ear. 



57. TTELMHOLTZ pointed out the way in which the 

 JlJl hypothesis of asymmetry in the transmitting 

 mechanism of the ear gives rise to the combination-tone of 

 the first order, which he called the difference-tone. This 

 asymmetry was represented in his investigation by a term 

 of the second order in the force called into play by a given 

 displacement. Helmholtz further indicated the tones to 

 which the existence of terms of the third order gives rise, 

 and pointed out that tones of the fourth order &c. would give 

 rise to other combination-tones not further specified. 



58. In specifying those combination-tones which arise from 

 the terms of the third order, Helmholtz pointed out that one 

 of them was a combination-tone of the second order " in the 

 sense indicated by Hallstrom." This is also the sense in 

 which the expression "combination-tone of the second order" 

 is used by Helmholtz himself in the text of his work ; and it 

 means apparently a combination-tone which arises from a 

 combination-tone or combination-tones of the first order when 

 combined with any other notes present, or with each other, 

 according to the law of combination-tones of the first order. 



59. It is clear, however, that the principal combination- 

 tones which arise from the terms of higher orders in the trans- 

 mitting mechanism of the ear, are derived directly from the 

 primary tones, and are not materially influenced by the second- 

 ary series of tones. This is obvious, on the one hand, since 

 all the resultant tones, according to the principles of their 

 origin, are of the nature of small quantities compared with the 

 primary tones, and, on the other hand, because the tones 

 derived from the terms of higher orders are in fact produced 



