On certain Vibrations of Solids. 15 



of load caused to approach the centre or another side of the 

 ring. 



Accordingly, if the wire has attained its constant state, 

 variations of the loading within the limits of the experiments 

 exercise no sensible influence upon either its temporary or its 

 permanent torsion. 



[To be continued.] 



II. On certain Vibrations of Solids. 

 By Frederick Guthrie*. 



[Plates II. & III.] 

 § 1. npHE transverse vibrations of rods, prisms, or laths 

 J- have been examined by Euler, Poisson, Cauchy, 

 Seebeck, and Chladni. These calculators and experimenters 

 have considered the notes and nodes in such bars when both 

 ends are free. The following numerical experimental results 

 may be of use to those studying the vibration of such solids. 

 They to a considerable extent are in accord with the results 

 obtained by previous experimenters. 



I propose to consider here : — (I.) The actual position of the 

 transverse nodes in a lath rigidly clamped along one narrow 

 edge and vibrating in segments ; and (II.) the torsional and 

 torsio-transverse vibrations of a lath similarly clamped. 



I. The material used was hammered sheet-brass cut into 

 strips or laths, clamped firmly in a heavy horizontal vice. The 

 brass was 2*5 millims. thick. The free ends were always, unless 

 otherwise stated, 280 millims. long. Three such laths were 

 used, which were of various widths. The laths will in the 

 sequel be called A, B, and 0. 



A was 280 x 2*5 x 9*4 millims. 

 B „ 280 x 2-5 x 22-0 „ . 

 C „ 280x2-5x32-0 „ 



The total length of each lath was 305 millims. (say 1 foot). 

 That the effect of the tail of the lath behind the vice's jaws is 

 negligible will appear in § 4. The nodes were determined 

 in the usual way by fine dry sand, the lath being vibrated by 

 a bow. Let us call the line of the vice's jaws the artificial 

 node, and the other nodes the natural ones ; and let us call 

 the piece of lath from the free end to the first node the first 

 segment, and so on, the last segment being the piece bounded 

 at one end by the vice's jaws. We may represent in the cases 

 of segmental vibration the fixed point by a double transverse 



* Communicated by the Author. 



