Dr Searle, A bifilar method of measuring the rigidity of wires 61 



A bifilar method of measuring the rigidity of wires. By G. F. C. 

 Searle, Sc.D., F.R.S., University Lecturer in Experimental 

 Physics. 



[Read 3 May 1920.] 



§ 1 . Introduction. In this method the couple due to the torsion 

 of two similar wires is balanced against the couple due to the load 

 carried by the wires and arising from bifilar action. 



The method is hardly suitable for accurate measurements of 

 rigidity, but, as an exercise in the use of a bifilar suspension, it has 

 proved useful at the Cavendish Laboratory. 



§ 2. Bifilar cowple. We first consider two light flexible strings. 

 Let the strings AB, CD, each I cm. in length, hang from two fixed 

 points A, C, which are at a distance 2a^ cm. apart in a horizontal 

 plane. The lower ends B, D of the strings are attached to a rigid 

 body of mass M grm., the points B, D being 2^2 cm. apart. The 

 centre of gravity of the body is symmetrical with regard to B and 

 D and thus the tensions of the strings are equal. The line BD will 

 then be horizontal. If, now, a couple, whose axis is vertical, is 

 applied to the body, the body will be in equilibrium when the 

 couple due to the obliquity of the strings balances the applied 

 couple*. 



In Fig. 1, A', B', C, D' are the projections of A, B, C, D on 

 a horizontal plane. In our symmetrical case, A'C, B'D' bisect each 

 other in 0. When the body has turned through 

 6 radians from the zero position, in which the 

 strings are in the vertical plane through A'C, qt 

 then B'D' will make an angle 6 with A'C nT 

 Let ON be the perpendicular from on A'B'. 

 Let the tension in each string be T dynes. 



If the vertical distance of BD below AC 

 is h cm., the vertical component of the tension is Th/l, and the 

 horizontal component is T .A'B' jl. Since the weight of the body 

 equals the sum of the vertical components, 



Mg = 2Thll. 



The horizontal component of the tension at B acts along a line 

 whose projection is A'B', and hence its moment about the vertical 



* For the general theory of the bifilar suspension, see Maxwell, El. and Mag.^ 

 Vol. n, § 459; A. Gray, Absolute Measurements in El. and Mag., Vol. i, p. 242;. 

 Kohlrausch, Physical Measurements (1894), p. 226. 



