366 Mr. A. J. Ilij.kins. Tlie Harmonics of a String [Nov. 20, 



clearly the high harmonics even to the 19th came out. Also it was 

 noticeable that the harmonic could be brought out by touching at any 

 owe of its nodes, even at those very far distant from the striking- 

 point, showing how accurately a comparatively stout string of great 

 tension could resolve itself into minute sub- vibrations. Thus the 19th 

 harmonic was quite distinctly brought out, so as to be easily com- 

 pared with e""[>, by touching the string at its second node from the 

 bridge, leaving 40'26 inches of string to be agitated by the blow. 



The object of the experiment was to determine, if possible, the 

 effect of the striking place on the harmonics quenched. Heimholtz 

 ("Tonempfindungen," fourth edition, p. 133) says that the striking 

 place is from ^- to the length, between which, of course, lies , and 

 observes (ibid.) that " an essential advantage of this striking place 

 appears to be that the seventh and ninth partial tones disappear, or, 

 at least, become very weak." I do not know of any pianos with the 

 striking place at | the length. Harpsichords and spinets, which were 

 set in vibration by quill or leather plectra, had no fixed point for 

 plucking the strings. It was generally from | to T ^ of the vibrating 

 length. Although it had been observed by Hnyghens and the Ant- 

 werp harpsichord maker, Jan Couchet, that altering the plucking 

 place altered the quality of tone, giving rise to the ' lute stop " of 

 the eighteenth century, no attempt was nrade to fix a uniform plucking 

 place. On the latest improved spinet, a Hitchcock, of the early part 

 of the eighteenth century, in my possession, the striking distances 

 for the C's vary from to $- And on the latest improved harpsichord, 

 a Kirkman, of 1773, also in my possession, the striking distances of 

 the C's vary from ^ to T ^, and the lute stop from to ^ of the 

 string. The bass or longest strings giving, of course, the shortest 

 striking measures, and the same was true of the early pianofortes, 

 as those of Stein, Mozart's favourite pianoforte maker. The great 

 length of the bass strings as carried out on the single belly-bridge, 

 copied from the harpsichord, made it impossible to equalise the striking 

 place for that part of the scale. It was John Broadwood, in 1788, 

 who first endeavoured to equalise tlie scale in tension and striking 

 place. Assisted by Signor Cavallo and the then Dr. Gray of the 

 British Museum, he produced the divided belly-bridge which enabled 

 him to reduce the length f the bass strings, and hence gained a 

 uniform striking place. He adopted ~ the vibrating length, allowing 

 much latitude in the treble, C. Kiitziug (" Das Wissenschaftliche 

 der Fortepiano-Baukunst," Bern, Chnr, und Leipzig, 1844, pp. 41-2) 

 says the maximum should be ^, and the minimum i the length, but 

 that the latter requires a softer hammer to bring out a pleasant tone, 

 and that ^ is much better. The present head of the house of Broad- 

 wood (Mr. Henry Fowler Broadwood) has arrived at the same con- 

 clusions, and adopted ^ the vibrating length as the striking place for 



