Lord Rayleigh on Bells. 



13 



already alluded to, of the deformation by pure bending of 

 thin shells in the form of hyperboloids of revolution, and in 

 certain composite forms built up of cylinders and cones so as 

 to represent approximately the actual shape of bells. In the 

 case of the hyperboloid of one sheet (fig. 2) , completed by a 



Fig. 2. 



crown in the form of a circular disk through the centre, and 

 extending across the aperture, it appeared that there was no 

 nodal circle for n = 2. The investigation is appended to this 

 paper. 



The composite forms, figs. 4 and 5, represent the actual bell 

 (fig. 3*) as nearly as may be. At the top is a circular disk, 



Fig. 3. 



and to this is attached a cylindrical segment. The expanding 

 part of the bell is represented by one (fig. 4), or with better 

 approximation by two (fig. 5), segments of cones. The cal- 

 culations are too tedious to be reproduced here, but the results 

 are shown upon the figures. In both cases there is a circular 

 node N for n==2, not far removed from the rim, and in fig. 5 

 very nearly at the place which represents the sound-bow of an 

 actual bell. In the latter case there is a node W for n = o 

 near the middle of the intermediate conical segment, 



* Copied from Zamminer, Die \Musik und die musikalischen Instru- 

 mente. Giessen, 1855. 



