280 Mr. R. H. M. Bosanquet on the History of the 



of overtones under similar circumstances, and showed that 

 they do exist. Helmholtz (Tonemp. 4th ed. pp. 263, 264) 

 comes to the same conclusion ; also Preyer (Akustische 

 Untersachungen). And it was only by the application of the 

 new methods recently placed at my disposal that I was able 

 to recognize the insufficiency of this explanation, and to place 

 the matter on the footing developed in my recent paper. 



It only remains to notice Konig's paper in Wiedemann's 

 Annalen, 1880, p. 857; and I cannot refrain from expressing 

 my admiration for the clearness and thoroughness with which 

 every point is examined experimentally. I cannot pretend 

 to explain all the phenomena recorded ; but I will endeavour 

 to make clear the general point of view from which I regard 

 them. 



The proposition Konig sets himself to maintain is — that a 

 (pure) tone can excite also all the tones of its harmonic series. 

 This proposition was maintained by Wheatstone ; and there is 

 a not inconsiderable number of well-informed persons who are 

 disposed to admit it. Its complete discussion is a matter of 

 very great importance. As a matter of mathematics it is quite 

 inadmissible, unless we admit either the impurity of the " tone " 

 employed or the existence of transformation. 



It is generally understood and admitted that a very small 

 excitation, operating on a vibrating body of the same period, 

 is capable of exciting large vibrations in the vibrating body. 

 Suppose, for instance, that in Konig's pendulum with the 

 spring arrangement at the top (p. 867), the pendulum and 

 weighted spring were arranged to swing in exactly equal 

 periods ; then, how large would the movements of the pendu- 

 lum have to be to set the spring in vibration with large ampli- 

 tudes? There can be no doubt that an extremely minute 

 movement of the pendulum, so small as to be scarcely percep- 

 tible, would be sufficient for the purpose. 



Now, suppose the pendulum arranged as Konig had it, so 

 that the pendulum swung as a fundamental, and the spring in 

 the period of a harmonic. Then, if the movement of the pen- 

 dulum contained ever so little of the harmonic in question, the 

 spring would certainly be set in vibration with large ampli- 

 tudes, just as in the former case; only that, the minute amount 

 of the higher harmonic motion of the pendulum being masked 

 by the fundamental motion, it would appear as if the funda- 

 mental itself was exciting the spring in the period of the har- 

 monic. We have then only to inquire, Is it possible that the 

 fundamental vibration of the pendulum can have been accom- 

 panied by a small amount of harmonic ? And we answer, it is 



