in the Use of Bifilar Suspensions. 435 



but that of minimum elastic after-effect, and preliminary 

 observations of the deflexion showed that there was a gradual 

 increase of the reading, reaching a limiting value according 

 to the expression 



y = A + Be- ct , ...... (1) 



where y represents the distance from an arbitrary origin at 

 the time t after producing a given deflexion, and A, B, and 

 C are constants. This means that there is a slow decrease 

 in the controlling couple, and as the measurement of this 

 couple depends on the observations of the period of small 

 oscillations of the suspended system, it is necessary to obtain 

 the instantaneous value for a deflexion reading taken at a 

 given time after its production. A formula has been obtained 

 which enables the deflexion observation for a Weber electro- 

 dynamometer to be obtained to within one part in 40,000. 



Theoretical Considerations. 



In order to calculate the magnitude of the creep at a given 

 time after producing a deflexion, it is necessary that the 

 w r ires should be in a known elastic state, and also that it 

 should be possible to prepare the experiment and take 

 readings at both extremities any number of times, at the 

 same time maintaining the bifilars in known condition. It 

 will be seen that for most purposes it is sufficient to obtain 

 a solution of the following problem : — 



" Given a system supported by a suitable bifilar sus- 



" pension (adjusted for use according to Gray*), upon 



" which a constant external couple can be applied in 



" either direction, it is required to find the equation 



'* representing the creep after the deflexion has been 



" reversed every T minutes for a comparatively long 



" period, and to express this with reference to the instan- 



" taneous position of the first deflexion." 



Certain assumptions can be made, which are suggested by 



the form of equation (1), and also by the known fact that 



the behaviour of elastic after-effects is analogous to that of 



electric absorption in condensers. 



Assume for the first deflexion that the rate of creep is 

 proportional to the distance from an asymptotic value, and 

 that subsequently the creep is complicated by the after- 

 effects of deflexions made first in one direction and then in 

 the other. If the wires have been at rest for a long time 



* Gray's ' Absolute Measurements in Electricity and Magnetism,' 

 vol. i. p. LM2. 



