C. Barus — Viscosity of Solids. 185 



irig to (f^ be known, this equation is similar to the preceding. 

 In general and intermediate cases, correction members must be 

 investigated. 



If a series of detorsions <p be observed at 0°, and another 

 series, 0, at 6°; if (p=(p Q F{6) and <{>=n/£J? (Gauss' method of 

 angular measurement), then <p o (F 1 {0)-F(d))=(]S r -n)/ 7?Zln#, 

 where R is the distance between mirror and scale in cm and 

 where N and n are the scale parts (cm) corresponding to 0° 

 and 6°, respectively. Hence the distance of the individual 

 curves for 6' and 6° apart varies directly as <p This result, 

 though simple enough, has special bearing on the text below. 



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

 About twenty rods were examined. Table 1, after enumerat- 

 ing 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 

 %(<p+<p'\ the mean amount of viscous detorsion, in radians per 

 unit of length, observed immediately after the end of the 

 experiment. %((p-\-(p') is therefore the mean viscous effect 

 of r impressed on the system of two vertical wires. Hence 

 r-\-2(<p-}-(p / )=27r/ L. Furthermore, 6' is the temperature of 

 the lower wire, 6 that of the upper wire, and (<p—(p')lz (radi- 

 ans) is the amount of viscous detorsion, as observed at the 

 index between the wires, at the time specified, per unit of r. 

 Regarding this differential quantity, which is the chief datum 

 of the tables, it is merely necessary to call to mind that %<p is 

 the viscous detorsion, per unit of length of the upper wire, for 

 the rate of twist r ; and %<p' has the same signification relatively 

 to the lower (normal) wire. The reference to the unit of r is 

 a convenience permissible when r, as in the present work, has 

 nearly the same value throughout* 



The normal wire, No. 7, 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 

 l'=S0 cm , radius=/> = O0405 cm , so that l'=l. The wire of un- 

 known viscosity is examined at 20° (nearly), and immediately 

 after at 100°. Two experiments are made at each tempera- 

 ture with t alternately positive and negative. When r and 

 {(p-(p')lT have the sarrie signs (the usual case), the lower wire, 

 No. 1, is of greater viscosity. In case of 0=100°, only a 

 part of the upper wire, length a=a—/3, could be heated; the 

 remainder being kept at the lower temperature 0'. Time is 

 conveniently given in minutes, reckoned after twisting. 



* In how far such reductions are generally permissible, cf. Weidraann : Wied. 

 Ann., xix, p. 220, 222, 1886. 



