180 0. Bar us — Viscosity of Solids. 



stress in virtue of the occurrence of internal friction.* The 

 results to which Meyer's formula eventually leads are incom- 

 plete and were not fully verified by subsequent experiment. 

 The theory is therefore sharply antagonized by Boltzmann,f by 

 Streintz,J and by Kohlrausch. § In a later paper Meyer [ 

 partially assents to these adverse views, acknowledging that 

 the theory does not reproduce the phenomenon actually ob- 

 served. It also fails, as Kohlrausch (1. c.) pointed out, in pre- 

 dicting an insufficiently slow time of occurrence. After giving 

 reasons for dissenting from Boltzmann's and from Neesen's 

 hypotheses, Meyer proceeds to partially develop an older idea 

 of Weber's.^" This physicist referred viscosity in solids, to 

 partial molecular rotation, a view adopted by Kohlrausch,** by 

 whom it has been more clearly interpreted. The rotations 

 underlying Weber's phenomenon are considered identical with 

 the rotations of molecule postulated by Clausiusff in discussing 

 shear. Following Meyer and others, " elastische Nachwirkung " 

 is a possible occurrence in liquids. 



Boltzmann's^ theory, amplifying deductions of Lamy and of 

 Clebsch, is based on the assumption that the elastic forces are 

 dependent not only on the present but on the preceding de- 

 formations of the body. The effect of earlier states of stress 

 on the existing stress diminishes with the intervening time 

 but is independent of intervening states of stress. Different 

 viscous deformations are superposable. Boltzmann's theory, 

 therefore, presupposes the phenomenon§§ and brings the laws 

 of viscosity tersely into formulse. If co is an interval of time 

 reckoned back from t-co, when the strain d^ existed, then 

 Boltzmann's law may be clearly exhibited in its application to 

 the problem of vibration of a viscous solid. Given a wire of 

 the solid of length I and radius R. Let the upper end be 

 lixed, and the lower end be attached to a heavy bob, whose 

 moment of enertia for the given conditions is K. Then the 

 equation of motion is (slow oscillation presupposed) 



* Following the usage of the term by JSTavier, Cauchy, Poisson, St. Yenant, 

 Stokes, Stefan. Cf. Meyer, 1. c. 



f Boltzmann: Pogg. Ann, Erganzb. vii, p. 624, 1876. 



% Streintz: Pogg. Ann., civ. p. 588, 1875; ibid., cliii, p. 405, 1874. ■ 



§ Kohlrausch: Pogg. Ann., clx, p. 225, 1877. 



| Meyer: Wied. Ann, \\\ p. 249. 1878. 



If Weber: Pogg. Ann., xxxiv, p. 247, 1835; ibid., liv. p. 1, 1841. 



** Kohlrausch: Pogg. Ann., cxxviii, p. 413, 1866: cf. also ibid., cxix. p. 337, 

 1863. 



ff " Wenn ein solcher Korper fremden Kraften unterworfen wird, die von ver- 

 schiedenen Seiten ungleich unf ihn wirken, also z. B. nach einer Dimension ge- 

 dehntwird, wahrend er nach anderen Diraensionen frei bleibt oder gar zusammen- 

 gedriickt wird, dann die Molekule neben ihrer Verschiebung sich auch etwas 

 drehen konnen, iodem sie in Bezug auf ihre Kraftrichtung den ungleichen Spann- 

 ungen etwas folgen. ..." Pogg. Ann., Ixxvi, p. 66, 1849. 



±\ Boltzmann: Pogg. Ann., Erganzb., vii, p. 624, 1876. 



§| Kohlrausch : Pogg. Ann., clx, p. 227, 1877. 



