4 Lord Rayleigh on Bells. 



of the observer as well as upon the vigour of the vibrations 

 themselves. Indeed, by suitably choosing the place of 

 observation it would be theoretically possible to obtain beats 

 with perfect silences, wherever (in relation to the nodal sys- 

 tems) the blow may be delivered. 



There will now be no difficulty in understanding the proce- 

 dure adopted in order to fix the number of cycles corresponding 

 to a given tone. If, in consequence of a near approach to 

 symmetry, beats are not audible, they are introduced by 

 suitably loading the vibrating body. By tapping cautiously 

 round a circle of latitude the places are then investigated 

 where the beats disappear. But here a decision must not 

 be made too hastily. The inaudibility of the beats may be 

 favoured by an unsuitable position of the ear, or of the mouth 

 of the resonator in connexion with the ear. By travelling 

 round, a situation is soon found where the observation can 

 be made with the best advantage. In the neighbourhood of 

 the place where the blow is being tried there is a loop of 

 the vibration which is most excited and a (coincident) node 

 of the vibration which is least excited. When the ear is 

 opposite to a node of the first vibration, and therefore to a loop 

 of the second, the original inequality is redressed, and dis- 

 tinct beats may be heard even although the deviation of the 

 blow from a nodal point may be very small. The accurate 

 determination in this way of two consecutive places where 

 no beats are generated is all that is absolutely necessary. 

 The ratio of the entire circumference of the circle of latitude 

 to the arc between the points represents 4n, that is four times 

 the number of cycles. Thus, if the arc between consecutive 

 points proved to be 45°, we should infer that we were dealing 

 with a vibration of two cycles — the one in which the defor- 

 mation is elliptical. As a greater security against error, it 

 is advisable in practice to determine a larger number of 

 points where no beats occur. Unless the deviation from 

 symmetry be considerable, these points should be uniformly 

 distributed along the circle of latitude*. 



In the above process for determining nodes we are sup- 

 posed to hear distinctly the tone corresponding to the vibra- 

 tion under investigation. For this purpose the beats are of 

 assistance in directing the attention ; but with the more 

 difficult subjects, such as church bells, it is advisable to have 

 recourse to resonators. A set of Helmholtz's pattern, manu- 

 factured by Koenig, are very convenient. The one next higher 



* The bells, or gongs, as they are sometimes called, of striking clocks 

 often give disagreeable beats. A remedy may be found in a suitable 

 rotation of the bell about its axis. 



