1884.] struck at one-eighth of its Length. 367 



his pianofortes. Kiitzing says that when he was an assistant he had 

 to " equalise " instruments where the striking place was between -^ 

 and y the vibrating length, and it is the latter place which Helraholtz 

 has adopted for his table of experiments (ibid., p. 135), in which the 

 Oth harmonic is made very weak, and the 7th disappears altogether. 



Now the table I have given shows that though the striking place 

 was adjusted with great accuracy to ^ the vibrating length, not only 

 the 7th and 9th harmonics, but also the 8th and even the 16th, were 

 brought out distinctly. The 7th was particularly strong and clear, 

 and the 9th was very good indeed. The 8th harmonic was not so 

 strong, but it was perfectly clear, and it was got out at three of its 

 nodes. Of course, it has 7 nodes, but of the 4 where it was not 

 brought out, 2 were nodes of the 4th harmonic, and 1 a node of the 

 2nd harmonic, and the 8th was, of course, absorbed in these, while 

 the remaining node was the striking place itself. Perhaps the reason 

 why the 8th harmonic did not disappear was that the striking surface 

 of the hammer was not a perfectly hard edge, but a yielding surface, so 

 that the blow spread on both sides of the intentional striking place, 

 and thus excited the string at very slight distances from the node 

 itself. But whatever may have been the cause the result was quite 

 distinct, and recognised clearly by Dr. Huggins and Mr. Ellis, as well 

 as myself and Mr. Hartan. So that there is no doubt whatever that 

 striking with a pianoforte hammer at a node does not obliterate the 

 corresponding harmonic. 



For the 16th harmonic there are 15 nodes, 1 at the striking place, 



1 between the striking place and the wrestplank-bridge, neither of 

 which could be tried, 3 which were also nodes of the 8th harmonic, 



2 of the 4th, and 1 of the 2nd. The remaining 7 belong to the 16th 

 harmonic alone, and of these it was thought sufficient to try two, 



.which produced the sound quite clearly. The neighbouring 15th and 

 17th harmonics also came out well. These are an additional proof 

 that a pianoforte hammer striking at a node does not destroy the 

 harmonic due to that node. Subsequently I had an opportunity of 

 trying the middle c' string of one of Steinway's grand pianofortes. 

 This string was 28'75 inches long, and was struck at 3'2 inches from 

 the wrestplank-bridge, that is, at of its length. I got out the 6th, 

 7th, 8th, and 9th harmonics just as in Broadwood's piano, the 6th 

 and 7th both beautifully strong ; the 8th and 9th weaker, but clear 

 and unmistakable a further confirmation of the fact that the piano- 

 forte hammer does not obliterate the harmonic at whose node it 

 strikes. 



