[ 342 ] 



XXXIY. On the Laws of Viscosity. By Ladtslas Natanson, 

 Professor of Natural Philosophy at the University of 

 Cracow*. 



THE fundamental conception on which the present 

 investigation is based is dne to Poisson f. Consider a 

 fluid, originally in equilibrium, which is subjected to a 

 deformation. According to Poisson, the fluid, in order to 

 adapt itself to the deformation impressed upon it and arrive, 

 even approximately, at a new state of equilibrium, requires a 

 certain time which, for different substances, is of very different 

 duration. The period of transition is characterized by 

 inequalities of pressure which, called into play by the 

 deformation, tend to disappear of their own accord, but a 

 complete disappearance of which does not take place until the 

 new state of equilibrium has become fully established. Thus 

 Poisson succeeded in bringing into prominence an intricate 

 phenomenon, termed relaxation, which is only one example 

 of that fundamental property possessed by matter but not by 

 the luminiferous aether, of the "constraint" of perturbations 

 produced in its interior J. 



The reality of the phenomenon of relaxation has, after 

 Poisson, been admitted by Sir Gr. Gr. Stokes §, as well as by 

 Olerk-Maxwell, who, in his memoir || on the kinetic theory of 

 gases, has made a detailed study of it. Maxwell, however, in 

 the course of some general considerations which serve as an 

 introduction to the memoir to which we have just alluded, 

 has shown how the conception of Poisson may be reduced 

 to its essential features. In our studies on this subject, we 

 have tried to develop this method of Maxwell's, which is 

 purely descriptive and independent of any hypothesis. On 

 account of this method, Poisson's ideas regarding the nature 

 of the fluid state appear to us to be destined to play an 

 important part in the dynamics of viscous bodies. It will be 

 seen, in fact, from what follows that they lead to a generalized 



* Translated from the Bulletin de VAcademie des Sciences de Crctcovie, 

 February 1901. Communicated by the Author. 



t Memoire sur les Equations Generales de l'Equilibre et du Mouvement 

 des Corps solides elastiques et des Fluides, In a l'Academie des Sciences 

 le 12 Octobre, 1829. Journal de VEcole Poly technique, xx. Cahier, 

 tome xiii., Fevrier 1831. 



% Bulletin international de V Academie des Sciences de Cracovie, A.nnee 

 1893, p. 348 ; Annee 1894, p. 295 ; Annee 1896, p. 117 : Annee 1897, 

 p. 155. 



§ Transactions of the Cambridge Philosophical Society, vol. viii. 

 p. 287 (1845) ; ' Mathematical aud Physical Papers/ vol. i. p. 75 (1880)." 



|| Philosophical Transactions, vol. clvii. p. 49 (1867). Scientific Papers,' 

 vol. ii. p. 26 (1890). 



