the Beats in the Vibrations of a Revolving Bell. 371 



Mr. G. H. Bryan has given the mathematical theory of the 

 rotation of the nodal meridians in a revolving cylinder or beli. 

 According to his analysis, the number of beats per revolution 

 due to this rotation of the nodal meridians is independent of 

 the velocity of revolution, and is given in the case of two- 

 dimensional oscillations by 2s(s 2 — l)/(s 2 -\-l), 2s being the 

 number of nodal meridians, and in the general case by 

 2s(s 2 + \— l)/(s 2 + X s +l), \ s being a quantity which can 

 never be negative. 



Mr. Bryan's own experiments with two different champagne- 

 glasses gave " about 2"6 and 2'2 beats per revolution respec- 

 tively for the gravest tone," of which " the latter is too small 

 to be compatible with " the theory, and it was at his suggestion 

 that we have undertaken some experiments at the Clarendon 

 Laboratory in order to test the same. The results already 

 obtained appear of sufficient interest to warrant this pre- 

 liminary note on the subject, pending a fuller investigation 

 with more accurate apparatus. 



The glass to be experimented upon was rigidly attached to 

 the disk of a whirling- table carrying a graduated scale : and 

 an index, which could be held in a fixed position in space, was 

 carried round with the disk when released by the observer. 

 The glass was caused to vibrate by means of a bow : when the 

 note obtained was free from beats and of the required pitch 

 the disk was rotated. In order to prevent complicating the 

 experiment by the acceleration of the disk several beats were 

 first observed, and when the intervals at which they occurred 

 appeared to be uniform the index was released on hearing a 

 beat, and after the observation of a certain number the disk 

 was stopped. The whole number of turns were counted, and 

 the position of the index when the disk was stopped gave the 

 fraction of a turn. 



In order to concentrate the sound and to prevent any 

 motion of the ear during the observations, the beats were 

 observed through a tube fixed with one extremity close to the 

 revolving glass. A difficulty arose in obtaining glasses which 

 gave a pure tone, and it was found that, even after careful 

 selection of the glass, accuracy was only to be arrived at when 

 the vibrations were excited with great care by means of a 

 violin-bow. The glasses selected were bell-shaped. 



The following were the results obtained, and it will be 

 observed that in each case the mean is slightly above the 

 value calculated from the two-dimensional theory. 



202 



