56 
ME. CLEEK MAXWELL ON THE DYNAMICAL THEOEY OE GASES. 
rature between two gases, and the distribution of temperature 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„ M 2 , and let their velocities resolved in three 
directions at right angles to each other be and £ 2 , yj 2 , £ 2 . The components of 
the velocity of the centre of gravity of the two molecules will be 
£iMj + £ 2 M 2 ijjMj + rjgMg ^M 1 + ? 2 M 2 
M x + M 2 ’ M x + M 2 ’ Mj + 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 asymptotes inclined at an angle 6 to the line of apses. The 
asymptotes of the orbit of M, will be at a distance b 1 from the centre of gravity, and 
those of M 2 at a distance b 2 , where 
MA=M 2 5 2 . 
The distance between two parallel asymptotes, one in each orbit, will be 
b=b l -\-b 2 . 
If, while the two molecules are still beyond each other’s action, we draw a straight 
line through M, in the direction of the relative velocity of M x to M 2 , and draw from M 2 
a perpendicular 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. 
When, after their mutual action and deflection, the molecules have again reached a 
distance such that there is no sensible action between them, each will be moving with 
the same velocity relative to the centre of gravity that it had before the mutual action, 
but the direction of this relative velocity will be turned through an angle 2d in the plane 
of the orbit. 
The angle 6 is a function of the relative velocity of the molecules and of b, the form 
of the function depending on the nature of the action between the molecules. 
If we suppose the molecules to be bodies, or systems of bodies, capable of rotation, 
