178 PHENOMENA DEPENDENT ON MOLECULAR PATHS 75 



free path ; for a velocity is not, like a path, measured only 

 by a length, but for its complete specification it requires a 

 time unit also to be laid down. It is therefore well not to 

 express the numerical values of the friction in the way usual 

 for values of pressure, but, after deduction of the formula, 

 which on replacement of Nm by the density p we bring 

 into the form 



y = ipGL, 



to refer them to the units of density, length, and time. We 

 thereby obtain also this advantage, that the numerical values 

 become independent of the value of gravity, which alters 

 with the latitude of the place of observation. I shall there- 

 fore give the numerical values of the viscosity which follow 

 in such units that they contain the density of water, the 

 centimetre or square centimetre, and the second as funda- 

 mental units. 



76. Theoretical Laws of Gaseous Friction 



The final formula of the kinetic theory of viscosity, 

 which was found by Maxwell, 1 leads to a very surprising 

 result if we introduce into it the value of the free path. 



Since we have worked out the above considerations as if 

 all the molecules possessed equal speeds and attained equal 

 free paths a mode of calculation which is sufficient only for 

 an approximation we must use the Clausius expression 

 for the free path, and not that of Maxwell. Referring to 

 the Mathematical Appendix ( 46*-48*) for the stricter 

 calculation of viscosity, we put here 



L = fX 3 / 2 



with Clausius, and find for the viscosity-coefficient the 



value 



97 = 



In this formula N is the number of molecules per unit 

 volume, and X 3 the volume occupied by a single molecule ; 

 consequently JVX 3 = 1, as we have already ( 63) several 



1 Phil. Mag. 1860 [4] xix. p. 31 ; Scientific Papers, 1890, i. p. 390. 



