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XIY. The Beats of Mistimed Consonances. 

 To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



I HA YE just seen Prof. Silvanus Thompson's Note in your 

 January Xumber. I have no books with me ; but I think 

 I can close the controversy, as far as I am concerned, without 

 them. 



As to the word " subjective," I am quite content to have 

 Prof. Helmholtz and his translator (Mr. Ellis) as authorities 

 for my use of it; and I fear I shall require some further autho- 

 rity before 1 shall feel called upon to give up a use now 

 well established, sanctioned by custom and by the highest 

 authorities. 



As to the law that the beats of mistuned consonances of the 

 form h : 1 consist of variations of the lower note, (the law is 

 not true for imperfect consonances in general,) no doubt I 

 expressed myself hastily, and, as was evident, without refer- 

 ring to Kcenig's papers. 



Notwithstanding this, I cannot admit that the citations 

 made by Prof. Silvanus Thompson contain any demonstration 

 of the law in question, though undoubtedly the last quotation 

 contains a suggestion of the law. I must point out that the 

 sentence translated by Prof. Silvanus Thompson is not quite 

 correctly given; the preceding qualifying clause showing that 

 it is only an assumption, not a definite conclusion. Further, 

 there is no such experimental establishment of the law as to 

 amount to a demonstration. 



I have in fact recently learned, through a private source, 

 that Kcenig had, some time ago, convinced himself of this 

 result. But the experiments which were shown to my infor- 

 mant all bore the character of beats still associated with varia- 

 tions of the upper note ; and my informant, a most competent 

 person, was wholly unable to verify the conclusion. This 

 agrees entirely with my own observations made with similar 

 means. I therefore consider that the quotations from Koenig 

 made by Prof. Thompson contain nothing but assumption or 

 inference on this point; and, indeed, they do not purport to be 

 more. 



I consider that, in my experiments, the disturbing effects of 

 the harmonics are entirely separated out, so that direct de- 

 monstration of the law in question is obtained. 

 Yours truly, 



E.'H. M. Bosaxquet. 



