1895.] 



on the Physical Work of von Helmholtz. 



493 



given by the siren was nearly the same as before, and in the other 

 case when it was about a tone higher. 



The results are summed up in the table. 



Summation Tones. 



I venture to think that these experiments prove the accuracy of 

 von Helmholtz. They show that the siren, at all events, does produce 

 objective tones, the frequencies of which coincide with those of the 

 first difference and summation tones, and that this statement is valid 

 as regards the difference tone, whether it is or is not coincident with 

 Konig's beat tone. 



I have now in one single case tried to convey to you some idea of 

 the complexity of the problems with which von Helmholtz dealt. 

 He was the first man who detected a relation between the surging 

 mass of partials and combination tones and our sensations of concord 

 and discord. The main facts of his theory are, I believe, generally 

 accepted. On some points modern opinion has tended to stray from 

 his views ; one of these we have studied afresh this evening. 



It was the fact that I had to deliver this discourse which led me 

 to investigate the question anew, and therefore I felt bound to tell 

 you the results we have at present attained. Had it not been for 

 this, I should not have published them as yet. We have several 

 improvements of the apparatus in view. We do not pretend to have 

 covered the field. I do not, therefore, wish to generalise. My object 

 has been to refute hasty generalisations. I am content if I have 

 convinced you, as I have convinced myself, that Helmholtz was 

 correct in stating that the siren produces objective tones whose 

 frequencies are equal to the sum and difference of their primaries, 

 and that the methods we have employed have brought to light no 

 facts opposed to his view that these notes cannot be explained as 

 secondary effects of partials, but as phenomena of the first order — in 

 other words, as real combination tones. 



But brief space now remains to discuss the vast remainder of his 

 work, and as I have already published an appreciation of that,* I must 

 content myself with trying to give you, in a few sentences, some idea 

 of the range of his intellect. 



His investigations on optics were not less important than those 



Fortnightly Eevicw,' November 1894, 



