THE DYNAMICAL THEORY OF GASES. 35 



equilibrium of temperature between two gases, and the distribution of tempe- 

 rature in a vertical column. These results are independent of the law of force 

 between the molecules. I shall also consider the dynamical cases of diffusion, 

 viscosity, and conduction of heat, which involve the law of force between the 

 molecules. 



On the Mutual Action of Two Molecules. 



Let the masses of these molecules be M lt M 3 , and let their velocities 

 resolved in three directions at right angles to each other be ,, TJ I} , and 

 17,, ,. The components of the velocity of the centre of gravity of the two 

 molecules will be 



The motion of the centre of gravity will not be altered by the mutual 

 action of the molecules, of whatever nature that action may be. We may 

 therefore take the centre of gravity as the origin of a system of coordinates 

 moving parallel to itself with uniform velocity, and consider the alteration of 

 the motion of each particle with reference to this point as origin. 



If we regard the molecules as simple centres of force, then each molecule 

 will describe a plane curve about this centre of gravity, and the two curves 

 will be similar to each other and symmetrical with respect to the line of apses. 

 If the molecules move with sufficient velocity to carry them out of the sphere 

 of their mutual action, their orbits will each have a pair of asymptotes inclined 



TT 



at an angle - 9 to the line of apses. The asymptotes of the orbit of M l 



I 



will be at a distance &, from the centre of gravity, and those of M t at a 

 distance 6 3 , where 



The distance between two parallel asymptotes, one in each orbit, will be 



If, while the two molecules are still beyond each other's action, we draw 

 a straight line through M 1 in the direction of the relative velocity of Jf, to 

 M t , and draw from M t a perpendicular to this line, the length of this perpen- 



52 



