248 Free Path Phenomena [CH. xn 



time the molecules have reached this second layer we must suppose that 

 their velocities are divided into two parts, namely, 



u u , v y w and M O , 0, 

 for the first, and 



u u , v, w and u , 0, 



for the second. The first part in each case will represent molecular-motion, 

 and the second part will represent mass-motion. Now in equation (32), we 

 saw that the total energy of the gas could be regarded as the sum of the 

 energies of the molecular and mass-motions. The sum of the energies of the 

 molecular-motions of the two molecules now under discussion is, however, 



| m [(u - w fl ) 2 + & + w 8 ] + \m [( - u - M ) 2 + v 2 + w], 



which can be written 



m (w 2 + ?; 2 + w 2 ) + mu 2 . 



The first term is equal to the energy of the molecular-motion of the two 

 molecules at the start ; the second term represents an increase which must 

 be regarded as gained at the expense of the mass-motion of the gas. Thus 

 the phenomenon of viscosity in gases consists essentially in the degradation of 

 the energy of mass-motion into energy of molecular-motion ; and is therefore 

 accompanied by a rise of temperature in the gas. 



The phenomena of viscosity in liquids and of friction in solids (as 

 explained in 3) can of course be accounted for in a similar way. 



Corrections when Molecules are assumed to be Elastic Spheres. 



303. For want of definite knowledge of the molecular structure we have 

 introduced two errors into our calculations. In the first place, we have 

 neglected the persistence of velocities after collision, and in the second place 

 we have ignored the difference between two different ways of estimating the 

 mean free path. If we assume the' molecules to be elastic spheres, it is 

 possible to calculate the amount of error introduced by both these simplifica- 

 tions. This we now proceed to do. Both of the necessary corrections are 

 small, so that we shall calculate them as independent corrections, and sum 

 the results. 



304. We can begin by an exact calculation of Xc, to replace the as- 

 sumption of equation (568). The required value of Xc is 



Xc 



= f *f(c)\ c cdc (574), 



J o 



where X c is the same as the X c of 282. Substituting the value given for X c 

 by equation (539), and putting 



