56 On the Connexion between Viscosity and Density in Fluids. 



ing to 25°-l runs below both that corresponding to 32 0- 6 and 

 those corresponding to 15° and 20°. From this follows that 

 carbonic acid of such density, heated from 15° upward, must 

 show a minimum of viscosity between 20° and 32°"6. 



Poisson* has given a theory of liquid-friction which starts 

 from the representation that, with respect to a system of 

 simultaneous impacts, a liquid behaves, at the first moment 

 after the expiration of them, like an isotropic solid body. 

 Hence we can speak of the constants of instantaneous elas- 

 ticity of a liquid. For the coefficient of friction in Poisson's 

 theory we get the expression 



where K is the coefficient of instantaneous rigidity t» and T a 

 quantity of time which Maxwell has named the modulus of the 

 relaxation-period. For an ideal gas, Maxwell finds j K==p, 

 and hence T, at constant temperature, proportional to the mean 

 length of path. 



In a first approximation let us assume that T still has this 

 property when the volume of the molecules and the attraction 

 between them is taken into account ; then we get for fi a 

 theoretical expression in which K alone remains unknown — 

 namely 



K vA b.s\ 



where for the temperature to which //, refers, fi and .% denote 

 the values of jjl and s for the pressure P of one atmosphere. 

 A is the normal density of carbonic acid, and b van der Waal's 

 constant, namely four times the molecular volume, the volume 

 of the substance at 0° and the pressure of one atmosphere 

 being taken as the unit of volume. The equation holds so 

 long as $<2b — that is, for carbonic acid, approximately as 

 long as s < 0*4. 



According to this equation, the occupation of space by the 

 molecules produces a diminution of friction with increasing 

 density, and consequently the opposite deviation from Max- 

 well's law to that produced by the attraction between the 

 molecules. From the same equation, according to our expe- 

 riments, for carbonic acid of density 0*38 at 32°*6, K comes 

 to 7*2 kilograms upon the square millimetre — that is, about 

 3§r0 °f i ts amount for glass, and somewhat more than for 

 tallow§. 



Journal de VEcole Poll/technique , 1831, t. xiii. p. 139. 

 t In Kirchhoff's notation ( Vbrktungen, p. 400). 

 % Phil. Mag. [4] xxxv. p. 211 (1868). 

 § Pogg. Atut'cxxxxi. p. 295 (1869)/ 



