Vibrations of Solids. 19 



From these several examples of torsio-segmental vibration 

 we may gather that with a long narrow lath such as A (that 

 is, one being twenty- eight or thirty and more times as long as it 

 is broad), all the segments excepting the first are approximately 

 equal, and the length of the first is just half that of the others. 

 The segment is here supposed to be the length between the 

 ends of two neighbouring nodal lines measured from where 

 they cut the edge of the lath. The same result is obtained if 

 one measures between the points of intersection of the middle 

 line of the lath and the lines joining the extremities of oppo- 

 site nodal lines. With the lath B the same generalization is 

 distinctly traced, while with the broad lath C it is conside- 

 rably obscured. With a lath as wide as C, indeed, an alte- 

 ration in the position of the nodal lines may be brought about 

 by altering the pressure in the vice. This will be considered 

 in § 9, where the note is considered. 



§ 7. A few asymmetrical figures can be obtained as in 

 fig. 11 (a) and (b). The figure (b) is of course derivable from 

 C, fig. 6. The distribution (b) gives identically the same note 

 as (a), fig. 11. 



III. Notes. 



§ 8. The notes given in several cases were determined by 

 the monochord of No. 25 B. W. Gr. stretched by a weight of 

 21 lb. Calling I the length of the monochord in unison with 

 the lath, we find with the lath B in the case of two natural 

 nodes ^ = 337, with three natural nodes Z // = 200, and with 

 four natural nodes l" f = 119. Calling the segments s/, sj ', s/, 

 and s^, s 2 f/ , s 3 r/ , s/', and s/", s 2 m , s{" , si" , s 5 /f/ , respectively, 

 as in fig. 12, 



y= 0-517 and L- ±=0-595 



"\2 . / e W\2 



(y 2 = 0-523 and g£) =0-587 

 (^'J = 0-514 and (^J =0-601 



(« f// v 2 



0-608 



The number of vibrations, therefore, or pitch, varies in- 

 versely with the square of the length of the second segment — 

 that is, as though the second segment were free at one end. 



§ 9. If the biting of the vice is relaxed, the notes get 



C2 



