﻿Barus and Strouhal — Viscosity of Steel. 449 



Elimination of Errors. — 1. The steel wires to be used in 

 these experiments are all about O'l 001 in thickness. Hence to 

 determine the condition of equilibrium or motion in the tor- 

 sional apparatus described, it is necessary to consider the respec- 

 tive moments of the bifllar couple (M b ), of the torsional couple 

 (Mt) and of the flexural couple (M f ), by which the movable 

 end is actuated. 



The moment of the bifilar couple has the well-known form* 



H' 

 M b — ijr mg sin cp . . . (1) 



where I and V are respectively the distance apart of the upper 

 ends and the lower ends of the bifilar wires, L the vertical dis- 

 tance and <p the horizontal angle between the lines I and l ; , mg 

 the weight of the whole suspended adjustment. To mg should 

 be added one-half the weight of the wires. 



The moment of the torsion couple is M T =r<p, where r is the 

 sum of the torsional coefficients of the wires. This applies 

 because the sum of the stored torsional moments, for <p=0, 

 is <p+{ — </>)=0. We may give the equation M T an experi- 

 mentally convenient form by substituting for r the approxi- 

 mate value* derived in elastics. We obtain 



,^ 27T Ep* . . 



where p is the radius of the steel wires used, E the C. G. S. 

 valuef of the modulus of elasticity of steel. 



The moment of the flexural couple is more involved. If p 

 be the distance apart of vertical planes passing through the 

 bifilar wires, if f be the horizontal component of the flexural 

 force, then the flexural couple is M f —fp. We have however 

 by geometry, p= {IV sin <p)/s, where s is the sum of the horizon- 

 tal projections of the wires. We have moreover given us in 

 elastics 



E-*f ^ l 



2 

 and therefore the couple in question becomes 



„_ 37T ll'p* ^ . , . 



Mf== T -j7 E * m * • * ' (8) 



The equations 1, 2 and 3 enable us to choose the dimensions 

 of the wire and of the apparatus as well as to select conditions 



* C. F. Maxwell, ii, p. 108, 1881; Kohlrausch Leitfaden, p. 167, 1884. 

 f Poisson's coefficient is in the following estimate taken at £. 

 % If E' be the current technical modulus referred to the kilogram and square 

 millimeter, E—E'g x 10 5 . 



