252 
PROFESSOR CLERK MAXWELL OX STRESSES IX RARIFIED 
The incident molecules are those which, close to the surface, have their normal com¬ 
ponent of velocity negative. We shall distinguish these molecules by the suffix ( 1 ). 
For these, and these only, is negative. 
The rebounding molecules are those which have £ positive. We shall distinguish 
them by the suffix Q. Those which are evaporated will be further distinguished by 
an accent. 
Symbols without any mark refer to the whole gas, incident, reflected, and evaporated, 
close to the surface. 
The quantity of gas which is incident on unit of surface in unit of time, is —p^ v 
Of this quantity the fraction 1 —f is reflected, so that the sign of £ is reversed, and 
the fraction f is evaporated, the mean value of £ in evaporated gas being where the 
accent distinguishes symbols belonging to unpolarized gas at rest relative to the sur¬ 
face, and having the temperature, O ', of the solid. 
Equating the quantity of gas which is incident on the absorbing part of the surface 
to that which is evaporated from it, we have 
fpi£i+fp-2&=° .(60) 
Equating the whole quantity of gas which leaves the surface to the reflected and 
evaporated portions 
/>a&=(/—!) PiZi+fPidi .( 61 ) 
If we next consider the momentum of the molecules in the direction of y, that of 
the incident molecules is p^iy v A fraction (1 —f) of this is reflected and becomes 
0-- i -f)pi£i*h, and a fraction f of it is absorbed and then evaporated, the mean value 
of y being now— v, namely, the velocity of the surface relatively to the gas in contact 
with it. 
The momentum of the evaporated portion in the direction of y is therefore —fp.'^v, 
and this, together with the reflected portion, makes up the whole momentum which is 
leaving the surface, or 
(/— 1) pAvv—fp-ztz' 0 .(62) 
Eliminating fp. 2 between equations (61) and (62) 
( 1_ DpiZiVi+Pi&z+'V [(!“ ■f)pi^i+P-Al= 0 • • • • (63) 
The values of functions of £ y and £ for the incident molecules are to be found by 
multiplying the expression in equation (22) by the given function, and integrating 
with respect to £ between the limits — co and 0, and with respect to y and £ between 
the limits ffi 00 • 
The values of the same functions for the molecules which are leaving the surface are 
to be found by integrating with respect to £” from 0 to oo. 
We must remember, however, that since there is an essential discontinuity in the 
