210 Professor Silvanus P. Thompson [June 13, 



tones : tliese are vital to the theory of harmony. Equally vital is 

 it to know what the timbres of sounds are, and whether they can 

 be accurately or adequately represented by the sum of a set of pure 

 harmonics corresponding to the terms of a Fourier-series. 



And here let me take the opportunity of saying that the views 

 which 1 am about to propound, and which for to-night I must be con- 

 sidered to adoj)t, are those which have been jDut forth as the result 

 of a quarter of a century of patient work by Dr. Eudolph Koenig 

 of Paris. 



Dr. Koenig, whose recent visit to this country will be remembered 

 by some here present, is, as is well known, the constructor of the 

 finest and most accurate acoustical instruments in the world, and 

 is not only a constructor but an investigator of great distinction, and 

 author of numerous memoirs on acoustics which have from time to 

 time appeared in the Annalen of Poggendorff, and in those of Wiede- 

 mann, and elsewhere. The splendid apparatus around me belongs to 

 him, and forms but a very small part of the collection which adorns 

 his atelier on the Quai d'Anjou. He lives and works in seclusion, 

 surrounded by his instruments, even as our own Faraday lived and 

 worked amongst his electric and magnetic apparatus. His great 

 tonometer, now nearly completed, comprises a set of standard tuning 

 forks, adjusted each one by his own hands, ranging from 20 

 vibrations per second up to nearly 40,000, with perfect continuity, 

 many of the forks being furnished with sliding adjustments, so as to 

 give by actual marks upon them any desired number of vibrations 

 within their own limits. Besides this colossal masterpiece. Dr. 

 Koenig's collection includes several large wave-sirens, and innumer- 

 able pieces of apparatus in which his ingenious manometric flames are 

 adapted to acoustical investigation. There also stands his tonometric 

 clock ; a timepiece governed, not by a pendulum, but by a standard 

 tuning-fork, the rate of vibration of which it accurately records. 

 Lest I should forget it at a later stage, let me here return my most 

 cordial thanks to Dr. Koenig for the extreme kindness and courtesy 

 with which he has put at my disposal for this discourse all the 

 apparatus wherewith to illustrate the various points in his researches. 



In investigating beats and combinational tones Dr. Koenig deemed 

 it of the highest importance to work with instruments jiroducing the 

 purest tones ; not with harmonium reeds or with polyphonic sirens, 

 the tones of which are avowedly complex in timbre, but with massive 

 steel tuning-forks, the pendular movements of wliich are of the 

 simplest possible character. Massive tuning-forks properly excited 

 by bowing with a violoncello bow, or, in the case of those of high 

 pitch, by striking them with an ivory mallet, emit tones remarkably 

 free from all sounds of subdivision, and of so truly pendular a 

 character (unless over-excited) that none of the harmonics corre- 

 sponding to the members of a Fourier-scries can be detected. No 

 living soul has had a tithe of the experience of Dr. Koenig in the 

 handling of tuning-forks. Tens of thousands of them have passed 



