﻿932 Mr. J. H. T. Roberts on Transverse Vibrations of 



attachment o£ the string. The results obtained by different 

 observers were so widely different as to render the method 

 useless, in its simple form, for the determination of the 

 frequency of a fork. 



The theory of these experiments has been given by Lord 

 Rayleigh *, who discusses the modification to which the 

 adjustment of pitch must be subject in practice, in order 

 that the experiment may succeed. 



According to the usual theory, the maintenance will be 

 most vigorous when the period of the string, as calculated 

 from its length, tension, and linear density, is exactly twice 

 that of the fork, and this period is calculated for small 

 vibrations. This is not so, however, for, calling the length 

 obtained from the formula the theoretical length, the ampli- 

 tude of the string increases as the length is made greater 

 than the theoretical length, and the string is still able to 

 begin from infinitely small vibrations. Jf the string is 

 maintained with small amplitudes, its length is much less 

 than the theoretical length. The period of the string appears 

 to accommodate itself, not only by alteration of amplitude, 

 but also by alteration of plane ; it seems not improbable that 

 on account of gravity the period of vibration in a vertical 

 plane will be different from that in a horizontal plane : this 

 view is supported by the fact that frequently the string will 

 choose either of two planes at equal angles on opposite sides 

 of the vertical. It is difficult to study the problem with the 

 simple apparatus referred to above : in order to find out 

 whether the frequency of a fork could really be determined 

 from a knowledge of the period of a maintained string, and 

 to investigate this example of maintenance by a force of 

 double frequency, the following experiments were under- 

 taken. 



The apparatus consists of a massive fork about 36 cm. 

 long, supported vertically and placed so that the vibrations 

 take place in the direction of the length of the string ; the 

 fork is maintained electrically, the electromagnet being in- 

 serted between the prongs at their upper ends, and the 

 string is attached at a point 7 cm. from the shoulder of the 

 fork : in this way considerable driving force is obtained, 

 and the actual motion at the end of the string is extremely 

 small (0'22 mm.). The string consists of a plaited flax cord, 

 of mass *01347 grm. per cm., pulled by a weight suspended 

 over a pulley. In order to make the length of string definite, 

 two stops consisting of straight-edges with V-shaped notches 

 * Phil. Mag. 18S3; 'Sound/ vol. i. ch. 3. 



