138 Mr. J. C. Maxwell an the Dynamical Theory of Gases. 



I shall then apply these calculations to the determination of 

 the statical cases of the final distribution of two gases under 

 the action of gravity, the equilibrium of temperature between 

 two gases, and the distribution of temperature in a vertical 

 column. These results are independent of the law of force be- 

 tween 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 13 M 2 , and let their 

 velocities resolved in three directions at right angles to each 

 other be (j v r} v £ and £ 2 , rj 2 , £ 2 . The components of the velo- 

 city of the centre of gravity of the two molecules will be 



£M 1 + g 2 M 2 vJ^±vM_ 2 fcM. + g.M, 



M x + M 2 ' M, + M 2 ' M A + M 2 ' 



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 asym- 



77" 



ptotes inclined at an angle - — 6 to the line of apses. The 



asymptotes of the orbit of M t will be at a distance b 1 from the 

 centre of gravity, and those of M 2 at a distance b 2 , where 



MA = MA. 



i"i 



The distance between two parallel asymptotes, one in each 

 orbit, will be 



b = b x + b % . 



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 M 2 to M 2 , and draw from M 2 a perpen- 

 dicular to this line, the length of this perpendicular will be b, 

 and the plane including b and the direction of relative motion 

 will be the plane of the orbits about the centre of gravity. 



