EVAPORATION AND CONDENSATION 311 



In order to be able to estimate the magnitude of the effects produced 

 by this difference in the origin of the attractive and repulsive forces, let us 

 consider the case of the following model : 



B 



O 

 -® — &- 



Fig. I. 



O 



In Fig. I, let ^ be an atom of mass wu which is attracted by a group of 

 atoms B, each of mass lUo. Consider that all the atoms are elastic spheres 

 initially at rest. Let O be the common center of gravity of all the atoms. 

 Then the atoms will all move toward 0. If we consider the one dimensional 

 problem only, then we may assume that A will collide with one of the 

 atoms B (say C) at the point 0, and those two atoms will continue to 

 move along the line AO. Let n be the number of atoms in the group 7), 

 excluding C, the one which collides with A. If Vi and V2 are the velocities 

 (all measured from left to right) of A and C respectively just before their 

 collision, and F/ and F2' are the velocities just after their collision, then 

 we have by the principles of the conservation of energy and momentum : 



WiFi2 + W2F22 = Wi(Fi')- + m^OWy-, (14) 



miVi + mo{i + n)V2 = o, (15) 



vnVi + moVo = miVi' + WoTV- (16) 



Let the ratio of the velocity of A before and after the collision be /5, thus 



fl.lL (.7) 



and let 



W2 

 If we substitute these in equations (14), (15) and (i6j and solve for /5, 



_ yn ± {y + n -\- i) (^^^^-^ 



. ^ ~ "(w+ i")(7+ I)'' 



For the case in hand it can be readily seen that we should take the 

 negative sign. Equation (19) thus becomes: 



' + Avrn) 



^=- — r+y—- (-°) 



