114 Dr. Y\. D. Kleeman on the Kinetic 



towards the plane ABC, and the substance 4 towards the 

 plane DEF. Consider a molecule 3 moving in the direction 

 from E to B at right angles to DEF. Let l z denote the 

 distance it traverses till its further direction of motion is 

 equally probable in all directions. It is then in the same 

 state as one of the surrounding molecules. Let N 3 denote 

 the concentration of the molecules 3 at the beginning of the 

 path l 2 , and N 3 — N 3 ' that at its end. We have then 



/ N s -(N,-N,0 \ W ___ dNs 

 \ h / k "" da 9 



where ^- 3 is the concentration-o-radient. Let us suppose, 

 dx e L l 



as before, that the motion of the molecules is parallel to 

 three straight lines at right angles to one another, one of 

 which is at right angles to the plane DEF. Suppose n z 

 molecules 3 cross (in the direction from E to B) per cm. 2 a 

 plane situated parallel to DEF and passing through the 

 point where the path / 3 begins. The gain of molecules 3 in 



the plane at the end of the path h is then n* v^-or -jr- 3 -—r**. 

 1 JN 3 JN 3 dx 



The loss of molecules 4 in the same plane is -^ . — =— 4 , where 



1 JN 4 dx ' 



the symbols have corresponding meanings, x being measured 

 in the opposite direction in this case. Therefore, on the 

 whole, there is a gain of 



&■ 



\N 3 dx N 4 ' dx J 



molecules, v/hich may be written (M 3 — M 4 ), in the plane. 

 But the space occupied by these molecules is not zero. A 

 portion of the mixture must therefore be transported bodily 

 in the opposite direction to make room for these molecules. 

 Let r 3 and r 4 denote respectively the volumes of occupation 

 of the molecules 3 and 4 in the mixture, L e., the decrease 

 respectively of the volume of the mixture w r hen a molecule 

 3 or 4 is removed. It follows that v s and v 4 are connected 

 by the equation N 3 v 3 + N 4 v 4 = 1. Let x denote the number of 

 molecules in the portion of the mixture displaced to make 



* Thus the plane receives n molecules 3 per sec. from the other plane 

 and loses itself n(— ^— — - J molecules, since n may be taken proportional 

 to N 3 for small variations of N 3 , and the gain is therefore n ^~- 



