66 Dr Searle, A bifilar 7nethod of measuring the rigidity of wires 



The first 8 are the preliminary readings, and only the last 17 are 

 used. 



If cf) goes through a complete cycle, and 6 is plotted against (j), 

 a narrow hysteresis loop will be obtained. When readings are taken 

 as above, there will be two values of 6 for each value of </> except 

 (j) = — 7T. With careful work, the two values of d for <f) = tt will be 

 exactly or very nearly identical; for the wires used in § 7, I have 

 seldom found a difference between these two values as great as 

 one minute. As a rough method of eliminating the effects of 

 hysteresis, the mean of the two values of 6 for each value of (f> is 

 taken as the value of 9 for that value of cf) . 



The effect of bends in the wires near their upper ends. A, C 

 (Fig. 2), will be the same as if these points described small horizontal 

 circles about the centres Aq, Cq, as in Fig. 5. Let </> be measured 



Fig. 5. 



from CqAqX, and let AAqX = (p + a, CCqX = cf) + y, while 

 AqA = r, CqC = s, AqCq = 2ai. Then, if e is the small angle between 

 AC and AqCq, 



r sin ((/) + a) — s sin (^ + y) 

 2ai + r cos (^ + a) — s cos {<p + y)' 



When r and s are small compared with 2ai, tane may be replaced 

 by 6 and the variable terms in the denominator may be neglected. 

 Then, putting 



[r sin a — s sin 7)/2ai = P, {r cos a — s cos y)l'2ax = Q, 



we have 



6 = P cos(/> + ^ sin ^. (8) 



Here P and Q are the values of e when cf) = and ^ = Jtt. 



If the line BD makes an angle 9 with AqCq when the heads 

 read </>, the angle between BD and ^C is ^ — 6. The wires will not 

 be quite free from torsion when the heads read zero; let rj be the 

 mean twist of the wires when </> = 0. We must thus write sin {9 — e) 

 for sin 9 and cf) +rj — 9 for ^ — ^ in the equilibrium equation (5), 

 which thus becomes 



sm{9-€) = C{cf)+r)-9). (9) 



To evade difficulties, 9 is kept small. Then, since e is also small, 

 we may replace the sine by the angle in (9), and thus obtain 



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