436 Mr. Norman Shaw on Increased Accuracy 



their condition is approximately normal, and we have a 

 definite static controlling couple. Suppose a deflexion is 

 now produced. The instantaneous steady deflexion, if it 

 could be read, would depend on the known static controlling- 

 couple of the bifilars, but immediately subsequent to the 

 deflexion the structure of the wire gradually changes under 

 the strain, the couple consequently decreases, and we get an 

 increase of the deflexion. We can therefore, according to 

 our initial assumption, express this creep in the form 



d £=W-y\ ...... (2) 



where y is the distance from the instantaneous deflexion at 

 any time t, D represents the distance of the asymptotic limit 

 from this origin, and k is the proportionality constant which 

 will depend on the torsional rigidity of the material, and 

 upon the dimensions of the system. D will depend on the 

 magnitude of the deflexion. Now suppose after the creep 

 has proceded a certain distance, that the deflexion is reversed 

 by the same force applied in the opposite direction. Assume 

 that the reversal may be made instantaneously. The rale in 

 this case will be increased, as not only do we have the 

 original movement, but there is also a recovery creep to be 

 added on. If the suspension had been allowed to come to 

 the undeflected position, the recovery would take place 

 according to the law representsd by 



. a=- fc ^ 



where z is the distance from the undeflected original position; 

 hence we may assume that the part of the creep due to the 

 recovery can be represented by 



$~* w 



Upon any reversal of the deflexion we shall always have a 

 rearrangement of the structure of the wire in the opposite 

 direction to what it was before. In the special case of this 

 problem, we may assume that the recovery part of the curve 

 will always be given by equation (I). If now we solve 

 equations (2) and (4), and equate x to the sum of the two 

 results for y, we obtain the equation for a curve which shows 

 the behaviour of any final creep, where x is the distance 

 from the initial instaneous deflexion, or from its equivalent 

 in the opposite direction. In order to do this we must know 



