Dr Searle, A bifilar method of measuring the rigidity of wires 65 



and the rigidity of the metal n dyne cm.~^. Since the wires are 

 nearly vertical, the couple, due to torsion, exerted by the fair upon 

 the bar is Trnr^ {(f) — 6) /I*, to a close approximation. 



The small couple due to the bending of the wires assists the 

 bifilar couple; Kohlrauschf takes account of this small couple by 

 writing in place of (1), 



G = ^^^^}^.Mg, (3) 



where V = I - r^ {iTrEjMgY, (4) 



and E is Young's modulus. 



Equating the torsional to the (corrected) bifilar couple, we have 



^md=C{4>-d), (5) 



^^^^^ ^ = ]^r ^^) 



Then n = ^^r.MC. (7) 



§ 5. Experimental details. The distances AC = 2^1, BD = 'la^ 

 are measured. The diameters of the wires are taken at a number of 

 points and the mean radius is found. 



The total mass, M grm., of the system carried by the wires is 

 found. The masses of the screws are found before they are soldered 

 to the wires. 



The torsion heads are first set to zero, and the scales on which 

 the pointers K, L are read are adjusted to be perpendicular to KL. 

 If a goniometer is used, it is set so that its arm is in the central 

 position when the goniometer wire coincides with its own image. 



To eliminate errors due to slight bends in the wires, the readings 

 must be taken over the range — tt to tt for ^ ; the theory assumes 

 absence of hysteresis. But in experimental work in elasticity 

 we must realise that hysteresis effects are unavoidable, when the 

 strains are more than infinitesimal. To ensure that the effects of 

 hysteresis shall be orderly and not irregular, the torsion heads are 

 taken through a complete cycle from tt to — tt and back to it. To 

 make the two readings for <^ = tt agree as closely as possible, a 

 preliminary half cycle from — tt to tt is done. To make the conditions 

 uniform throughout the cycle and a half, the readings for the pre- 

 liminary settings are taken and recorded ; this will secure approxi- 

 mately constant time intervals between successive readings. Thus 

 the heads are set in succession at the following multiples of 7r/4 : 

 -4,-3,-2,-1, 0, 1, 2, 3, 

 4, 3, 2, 1, 0, - 1, - 2, - 3, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4. 



* G. F. C. Searle, Experimental Elasticity, § 39. 

 •f- Kohlrausch, W jet?. ^rt,«., xvu, p. 737, 1882. 



VOL. XX. PART I. 5 



