20 On certain Vibrations of Solids. 



flatter, and the nodes slightly shift. This appears in fig. 13 ; 

 the numbers inside the figures give the superficial contents of 

 the segments under the assumption that the nodes are straight. 

 The corresponding lengths of the consonant monochord are : — 

 forC',Z = 628; forCV = 624; andforC'V = 609. The nodal 

 lines may be as much as 1 millim. curved away from the 

 chord. As such curvature does not appear to be a direct 

 consequence of the slackness of the clamping, but rather of 

 the inequality of clamping almost necessarily accompanying 

 such slackness, I have not further examined it. In all pre- 

 vious experiments the clamping was so hard that no further 

 clamping affected the nodal positions. 



§ 10. The numerical relationship of node in the cases of 

 torsional vibrations which I have examined are as follows: — 

 Calling A, the length of monochord in unison with A, etc., 

 then it was found that when there was simple torsional vibra- 

 tion as in fig. 3, 



A, = 116 ... width of A = 9-4 



„ B =22-0 

 . . „ C=32-0 



width of B 



B,< 



= 277 



<V 



= 395 



B, 



A," 



= 2-388 





= 1-462 



width of A 



width of G 

 width of B 



= 2-340 

 = 1-454 



Or the pitch of the note varies inversely with the width of 

 the lath. 



It was further found that when B had one natural node 

 besides the axial one (b), fig. 4, the unisonal monochord wire 

 was 94 millims. When B had two natural nodes besides the 

 axial one (d), fig. 6, the wire was 57 millims. long. And, 

 finally, the condition of C in (/), fig. 4, required 132 millims., 

 while that of C in (k), fig. 6, required 79 millims. Accord- 

 ingly 



length for (b) _ pitch for {d) _ -, .^k 

 length for (d) pitch for (b) 

 length for (/) __ pitch for (k) _.,*„ 

 length for (k) pitch for (/) 

 Which ratios are approximately equal. 



