Viscous Traction of Lead and Tin Alloys. 193 



to be proportional approximately to the force of traction per 

 sq. cm. of cross-section, i. e. 



i-*5 CD 



F being the shearing force in dynes ; 



A being the area of cross-section in sq. cms. ; 



v being the velocity in cm.-secs. of any point distant 



x cms. from the point of support ; and 



X being the constant for the particular material, 

 this constant being termed by Trouton the coefficient of 

 viscous traction. 



Trouton and Rankine (Phil. Mag. 1904, viii. p. 538), in the 

 case of a lead wire stretched beyond its elastic limit (and for 

 this material the elastic limit is practically obtained with so 

 small a load as 10 grams, though not by the weight of the 

 wire itself), pointed out that : 



(1) The viscous flow has a larger initial rate than that 

 which obtains in the subsequent steady period. 



(2) The tractive force is hence not strictly proportional to 

 the rate of flow, so that 



T - T ^£> ( 2 ) 



a correction T being made for the initial effect. A close 

 connexion exists between the ordinary coefficient of viscosity 

 as usually determined and this new coefficient of viscous 

 traction, viz. 



This equation (Trouton, Proc. Roy. Soc. A. lxxvii. p. 438), 

 obtained, analytically, from the flow of a viscous cylinder of 

 incompressible material, was confirmed by direct comparison 

 of results from tractive experiments, sagging of a beam and 

 Poiseuille's capillary tube method. 

 Thus from a mixture of pitch and tar, 



X. r). X/V 



i 4-3 xlO 7 l-4xl0 7 3*07 



ii 3-3 xlO 7 1*0 XlO 7 3-30 



iii 12-9 xlO 7 4-2 xlO 7 3*07 



v In the present communication, this valuable method for 

 determining viscosity coefficients of solid bodies at the 

 ordinary temperatures has been applied to lead, tin, and 

 alloys of these metals. 



- The following conclusions, which have been deduced in a 

 Phil. Mag. S. 6. Vol. 17. No. 97. Jan. 1909. O 



