Viscosity of Solids and its Physical Verification. 191 



5. The following tables exhibit the new results for hard steel. 

 About 20 rods (diameter 2p= '081 centim.) were examined. 

 Table I., after enumerating the rod (" No.") and stating the 

 temperature at which it was annealed (" An.") from glass- 

 hardness, gives the amount of twist t (radians) temporarily 

 imparted per unit of length, and 2 (cf) + <f) f ) the mean amount 

 of viscous detorsion, in radians, per unit of length, observed 

 immediately after the end of the experiment. 2 (<£ + <£/) is 

 therefore the mean viscous effect of r stored in the system of 



2-7T 



two vertical wires. Hence t + 2 (<£ + (£/) =^-. Further- 

 more 0' is the temperature of the lower wire, 6 that of the 

 • it 



upper wire, and - — — (radians) is the amount of viscous 



angular detorsion, as observed at the index between the wires, 

 at the time specified, per unit of r. Regarding this differen- 

 tial quantity, which is the chief datum of these tables, it is 

 merely necessary to call to mind that 2</> is the amount of 

 viscous detorsion, in radians, per unit of length of the upper 

 wire, for the rate ot twist r ; and 2<j>' has the same significa- 

 tion relatively to the lower (normal) wire. The reference to 

 unit t is a convenience permissible when t, as in the present 

 work, has nearly the same value throughout *. 



The normal wire, No. 1, with which all the other steel 

 wires are compared, is annealed from hardness at 450°, and 

 has been twisted back and forth till viscosity is practically 

 unchanged by further twisting within the same limits. It is, 

 therefore, in a state of extreme viscosity, and, at the same 

 time, less liable to permanent set than a soft steel wire. Its 

 dimensions are Z' = 30 centim, p' = -0405 centim., so that 1 = 1'. 

 The wire of unknown viscosity is examined at 20° (nearly), 

 and immediately after at 100°. Two experiments are made 

 at each temperature with r alternately positive and negative. 

 When t and ((/> — </>') /r have like signs (the usual case), the 

 lower wire (No. 1) has the greater viscosity. In case of 

 = 100°, only a part of the upper wire, a = a— /3, could be 

 heated ; the remainder /3 being kept at the lower temperature 

 6'. Time is conveniently given in minutes. 



* In how far such reductions are generally permissible, cf. Weidmann, 

 Wied. Ann. xxix. pp. 220, 222, 1886. 



