364 Mr. A. J. Hipkins. The. Harmonics of a String [Nov. 20. 



and unmusical, but immediately afterwards the harmonic corre- 

 sponding to the node touched, sang out, always clearly enough to be 

 unmistakably recognised, and sometimes, especially where the node 

 corresponded to several harmonics, with a long clear ring, that was 

 made brighter and longer by removing the stopper from the string, 

 which then vibrated in the small loops conditioned by the node 

 touched. 



The following are the first 20 harmonics of this C determined 

 theoretically. Against each is placed its number of vibrations, and 

 the name of the nearest note on the equally tempered scale, which 

 was that of the piano used, with the theoretical number of hundredths 

 of an equal semitone which had to be added to, or subtracted from, 

 the pianoforte note, in order to give the true pitch of the harmonic. 

 This list enabled the note heard to be immediately identified, by 

 touching the corresponding notes on the pianoforte. Finally in the 

 last column is given the number of inches from the belly-bridge at 

 which one or more of the nodes of the harmonic would lie theo- 

 retically, for all the harmonics actually observed and brought out on 

 the 29th July, 1884, in the presence of Dr. William Huggins, F.R.S., 

 who verified the position of the node by a scale after the harmonic 

 had been produced, and Mr. Alexander J. Ellis, F.B.S., who recorded 

 the results. The examination of the numerous other positions of the 

 nodes of these and other harmonics was omitted for brevity, as those 

 possessing most interest had been already produced, but those 

 obtained on other occasions are inserted in a parenthesis. Except in 

 a few instances considered below*, the practi<>.al place of the node did 

 not differ from the theoretical by more than '02 or '03 inch, within 

 which limits it was difficult to be sure of the measurement. 



In calculating out the positions of all the nodes it was found that 

 some lay very close together. Thus a node of the 17th harmonic lay 

 at 5'29 inches from the bridge, between one of the Oth harmonic at 

 5 inches, and another of the 8th at 5'62, so that these nodes were 

 only '3 inch apart. All these harmonics were brought out separately, 

 but great care was necessary to hit the precise spot. On the other 

 hand the node of the 2nd harmonic at 22'5 inches lay between one of 

 the 19th at 21'32 inches, or 1'2 inches nearer the bridge, and another 

 also of the 19th at 23'68, or 1'2 farther from the bridge. Hence there 

 was a space of 2'36 inches with only one harmonic node within it. 

 Probably in consequence of this the 2nd harmonic could be brought 

 out by touching the string at a considerable distance on either side 

 of the theoretical place, because apparently the string had no other 

 shape which it could assume. It was determined that the limits 

 within which the 2nd harmonic could be brought out were from 22'1 

 to 22'95 inches from the bridge, allowing "85 inch play, but at 22'05 

 and 23'0 inches from the bridge the harmonic would not speak. 



