ARISING FROM INEQUALITIES OF TEMPERATURE. 707 



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& 



Of this quantity the fraction I-/ is reflected, so that the sign of f is 

 reversed, and the fraction / is evaporated, the mean value of in evaporated 

 gas being g, where the accent distinguishes symbols belonging to unpolarized 

 gas at rest relative to the surface, and having the temperature, 6', 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 



/Pi+//H&' = ................................. (60). 



Equating the whole quantity of gas which leaves the surface to the reflected 

 and evaporated portions 



If we next consider the momentum of the molecules in the direction of 

 y, that of the incident molecules is p^^. A fraction (I/) of this is reflected 

 and becomes (1 f) p^^, and a fraction f of it is absorbed and then evaporated, 

 the mean value of 77 being now v, namely, the velocity of the surface rela- 

 tively to the gas in contact with it. 



The momentum of the evaporated portion in the direction of y is there- 

 fore t-fpf&v, and this, together with the reflected portion, makes up the whole 

 momentum which is leaving the surface, or 



p^ = (f-l) Pl ^r ll -fp.;^v ........................ (62). 



Eliminating fp^ 3 ' between equations (61) and (62) 



(l-f)pr) 1 + p.r).> + v[_(l-f)p + p~} = ............... (63). 



The values of functions of 77 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 77 and between the limits + co . 



The values of the same functions for the molecules which are leaving the 

 surface are to be found by integrating with respect to from to oo . 



We must remember, however, that since there is an essential discontinuity 

 in the conditions of the gas at the surface, the expression in equation (22) is 



892 



