﻿a String maintained by Forces of Double Frequency. 935 



Table II. 

 Conditions as in Table I. 



Frequency 



of 



Fork. 



Length (cm.) when 



plane becomes 



vertical. 



Calculated 

 length 

 (cm.). 



32-15 



189-4 



187-7 



39-34 



153-9 



153-3 



40-0 



151-0 



150-9 



42-85 



141-0 



140-8 



44-72 



136-3 



134-9 



49-18 



1221 



1227 



52-94 



1140 



1140 



It might be expected that the theoretical length would 

 occur with very small amplitudes ; at present this does not 

 appear to be the case, but it must be remembered that 

 although the amplitude of the fork at the point of attach- 

 ment of the string is so small (0*22 mm.) it may, neverthe- 

 less, be too great for the theoretical conditions to be realized. 

 It is not surprising that the maintenance at the theoretical 

 length is not the most vigorous, for the theory shows that a 

 large amplitude may be necessary for the requisite accom- 

 modation of pitch. It is remarkable that with the large 

 amplitudes of the string the reaction upon the fork should 

 be sufficient to damp down its vibrations so much, considering 

 the powerful electrical maintenance ; it is no doubt due to 

 an adjustment of phase difference. It is to be noticed that 

 the mode of action of the string is not precisely the same 

 when under free vibration and when under maintenance of 

 the kind considered ; for in the former case the condition of 

 the string is symmetrical about the mid-point, while in the 

 latter case every point of the string describes a curve convex 

 to the fork ; in the former case also the tension is greatest 

 at the furthest point of a swing, in the latter it is not. 

 In some cases the pulley was observed to be rotating 

 slowly. 



In order to find out whether a vibration were merely 

 maintained with an adjustment of amplitude for the requisite 

 accommodation of pitch, the string was supported in the 

 same manner as before, except that it was attached to a 

 support and detached from the fork ; the stroboscope disk 



