34* MOLECULAR FKEE PATHS 425 



introduce X, the edge of the elementary cube containing one mole- 

 cule as given by the relation 



m 3 = i, 



we obtain 



X 3 - frrs 8 



V27TS 2 



Advantageous use of this improved formula has been made in 

 the investigation of the actual volume occupied by molecules 



( H7). 



G. Jage^has extended these considerations also to the 

 theory of viscosity. 



35*. Influence of Cohesion on the Free Path 



W. Sutherland 2 has obtained a second correction of the for- 

 mula which gives the molecular free path by calculating in what 

 ratio the probability of collision between two particles is increased 

 by their mutual attraction. We now proceed to give his calcula- 

 tion in order to put on a better footing what has been said 

 in 71 and 85 respecting this action of the forces of cohesion. 



Since we need not calculate the absolute motion of both 

 particles, but only their relative motion with respect to each other, 

 we may take one to be fixed, while we ascribe to the other a 

 velocity which is equal to the relative velocity with which they 

 move relatively to each other. The path of the moving particle 

 which is attracted by the fixed one lies in a plane which contains 

 also the position of the fixed particle, and we may therefore denote 

 the position of the moving particle at time t with respect to the 

 fixed particle at the origin by the coordinates p and r in that plane. 

 The attraction, which depends on the radius p only and is inde- 

 pendent of the angle T, being denoted by F(p), the motion is given 

 by the differential equations 



p _ p; 2 = _ F( P ) 



of which the second on integration leads to 



P 2 r = h. 



This constant h represents twice the area of the surface described 

 1 Wien. Sitzungsanz. 1899, p. 89. 2 Phil. Mag. 1893 [5] xxxvi. p. 507. 



