Theory of Mr. B. Hamilton's String-Organ. 103 



observed successions of overtones may not be devoid of interest. 

 There are four notes of the arrangement which I shall call I., 

 and three notes of II. The pitch in semitones is appended for 

 comparison. In both cases the point of attachment was nearly, 

 though not exactly, in the middle of the string. 



No. of 

 segments. 



I. 



Note 

 observed. 

 A 



Pitch of overtone, 

 in semitones. 



3 



b, 



14 



5 



°L 



aj) 



23 



7 



1 



d 2 -e.p 



II. 

 G 



29-5 



3 



b 



16 



5 



aft 



25 



Comparing these numbers with the overtones indicated in 

 column 3 of the calculated Table, it will be seen that they follow, 

 as far as they go, the general course indicated by theory in the 

 hypothetical case assumed ; and it may be inferred that this 

 case furnishes a rough representation of the circumstances of the 

 two experiments examined. 



The above results are the only experimental ones which I 

 know of. 



The calculation of the length of the middle segment in the 

 hypothetical case follows easily from the numbers in column 1 

 of the calculated Table. The fundamental, of course, has for 

 its segment the whole string. In the other cases, expressing 



/ in terms of-, which is the length of each segment except the 



middle one, we get the middle segment at once, since we know 

 the actual number of segments. (It is hardly necessary to remark 

 that the numbers of segments in the successive overtones are 

 the odd integers, by the symmetry.) 



2-882 



X 



Number 



of 

 segments. 



3 



Ratio of middle seg- 

 ment to any other 

 segment. 



-882 



4-714 



2 



X 



5 .... 



-714 



6-590 



'2 

 X 



7 



........ '590 



8-50 



'2 



X 



9 



-50 





'2 "•• 







