102 



Mr Bryan, On the beats in the 



[Nov. 24, 



glass all the time, beats will again be heard, showing that the 

 nodal meridians do not rotate with the same angular velocity as the 

 glass and observer. If the glass be attached to a revolving turn- 

 table it is easy to count the number of beats during a certain 

 number of revolutions of the table, and it will thus be found that 

 the gravest tone gives about 2'4 beats per revolution. As this 

 type of vibration has 4 nodes we should hear 4 beats per revolution 

 if these nodes were to rotate with the glass, we conclude therefore 

 that the nodal angular velocity is in this case about f of that of 

 the body. 



It may not, perhaps, be out of place to explain from first prin- 

 ciples why the nodal meridians revolve less rapidly than the body. 

 Take the case of a ring or cylinder revolving in the direction 

 indicated by the arrows in figure 1, and consider the mode of 

 vibration with four nodes, B, B, F, H. Suppose also that at the 

 instant considered the ring is changing from the elliptic to the 

 circular form indicated in the figure. 



Owing to the rotatory motion, the points A, E where the ring 

 is initially most bent will be carried forward and parts initially 

 less bent will be brought to A and E. Similar remarks apply to 

 the points G, G, where the ring is initially least bent. Hence the 

 points of maximum and minimum curvature, and therefore, also, 

 the nodes must be carried round in the same direction as the ring, 

 and cannot remain fixed in space. 



Fig. 1. 



Fig. 2. 



To show that the nodes do not rotate as if fixed in the ring, let 

 the small arrows in Fig. 1 represent the directions of relative 

 motion of the particles exclusive of the components due to rotation. 

 At A, E, the particles are moving towards the centre 0. This will 

 of course increase their actual angular velocity and will give them 

 a relative angular acceleration in the direction of rotation, as 



