the Laws of Viscosity. 347 



final pressure p is a function of the final density p and the 

 temperature 6; (2) the density and the temperature of a given 

 portion of the fluid do not vary as a result of the phenomenon 

 of relaxation pure and simple. We have, then. 



/ a\ dp — d Q ~&P i dp "dp {Q \ 



Neglecting variations of temperature, we get 



t=-»"|> ^ 



which may be written 



4— *■> < u > 



if we put 



*=o| ( 12 > 



Now equation (12) is in agreement with the definition, 

 given above in §§ 2 and 3, of the constant k characteristic of 

 the medium; but it involves a complementary hypothesis, viz.: 

 the deformation which persists (if, in general, it does persist) 

 when the final state is reached is incapable of giving rise to 

 fresh inequalities of pressure. This deformation is defined 

 by the following values of the variables : 



€ = ^ = ^=:iA; « = 0; /9 = 0; 7 =0. . . (13) 



The equation (11) found above is included in the general 

 case of equation (4) given previously and is identical with 

 it if the equality h = k be admitted ; it appears probable that 

 this equality holds for all fluids in nature, either as an absolute 

 law or as a close approximation. 



§ 6. From what has been said it follows that the equation 



f = "*» CD 



may be regarded as an expression of the hypothesis regarding 

 the existence, for fluids in equilibrium, of a characteristic 

 equation, since this hypothesis consists in supposing that for 

 the final state of a fluid there exists an equation of the form 



P=1>(.P,0) (2) 



In generalizing equation (1) it is therefore possible to 

 enlarge the commonly accepted idea of the characteristic 



