82 DISPLACEMENT INTERFEROMETRY APPLIED TO 



counterpoise, io 6 dynes) acts on the length of 17.5 cm. of wire. Hence, if 

 T is the twist per linear centimeter, n the rigidity of the steel wire of radius 

 r = 0.02 5 cm., and dd/dt the angular yield per second, 



2 PL n-c 



71 ~Trr*de/dt~ dd/dt 



This equation (as I showed elsewhere *) is found by an integration of the vis- 

 cosity equation, from the axis to the circumference of the wire. But dd/dt 

 = A(dN /di) cos i/b in the above notation for the interferometer, so that 



zPLb i 



7i ~irr 4 cosi A(dN/dt) 



A(dN jdi) being the micrometer displacement per second, given in the curves, 

 figure 103. If r 4 =io~ 7 X3.9, 



2Xio g XiiXio i =TrL u v 2 -53 



3:MX3-gXio~ 7 Xo.7i 



If equation (3) were true, ^(dN/dt)=/3(Ay) i /A, where /3 must be reduced 

 to seconds. 



Taking &(dN/dt) from the graphs, figure 103, in case of series (drawn 

 hard) and 2 (tempered) at successive times t, the following data hold per 

 second respectively 



t 5 io 20 50 100 min. 



A(dN/dt')Xio i = 6.7 6.0 4.7 4.0 3.0 2.0 1.2 i.o 0.8 0.8 



7jXio~ 20 = o.38 0.42 0.54 0.63 0.84 1.26 2.1 2.5 3.2 3.2 



Thus the absolute viscosity for the given twist and diameter in these cases 

 increases in 100 minutes from about 4Xio 19 to 3Xio 20 and thereafter 

 is nearly constant. The single rate of twist is about (M) (50 717.5) = 1.4 per 

 linear centimeter; but in alternating the twist the effect of this is doubled. 

 It is clear the 77 must depend on the rate of twist in relation to the thickness 

 of wire, inasmuch as the outer fibers probably yield most. This is among the 

 reasons for the inadequacy of equation (2). If this is used in the form (3), 

 the mean viscosity between 3 and i7 m comes out 7j = 5Xio 19 and between 

 io m and 30 8Xio 18 for the drawn wire. 



71. Twist in one direction only. The actual torsi onal weighing by passing 

 the counterpoise from pan to pan is in itself a delicate operation when inter- 

 ference fringes are used. Moreover, the variation of viscosity is particularly 

 large at the beginning. If the weight remains on one side, the viscous de- 

 formation not only grows indefinitely smaller and subject to simpler equa- 

 tional conditions, but the apparatus itself may be made less cumbersome 

 and steadier. Thus in figures 104, 105, if w is the wire stretched between 

 torsion-heads (the wire running normal to the balance-beam) and mm' are the 

 auxiliary minors of the interferometer rigidly attached to the beam, the latter 



"Phil. Mag., XXIX, p. 337-55, 1890; Clark Univ. Lectures in Physics, 1909, p. 149. 



