GASES ARISING FROM INEQUALITIES OP TEMPERATURE. 
235 
known convection currents are set up. These also interfere with the simplicity of the 
problem and introduce very complicated effects. All that we know is that the rarer 
the gas and the smaller the vessel the less is the effect of the convection currents, so 
that in Mr. Crookes’ experiments they play a very small part. 
We now proceed to the calculations :— 
(1.) Encounter between tivo Molecules. 
The motion of the two molecules after an encounter depends on their motion before 
the encounter, and is capable of being determined by purely dynamical methods. If 
the encounter of the molecules does not cause rotation or vibration in the individual 
molecules, then the kinetic energy of the centres of mass of the two molecules must 
be the same after the encounter as it was before. 
This will be true on the average, even if the molecules are complex systems capable 
of rotation and internal vibration, provided the temperature is constant. If, however, 
the temperature is rising, the internal energy of the molecules is, on the whole, 
increasing, and therefore the energy of translation of their centres of mass must be, 
on an average, diminishing at every encounter. The reverse will be the case if the 
temperature is falling. 
But however important this consideration may be in the theory of specific heat and 
that of the conduction of heat, it has only a secondary bearing on the question of the 
stresses in the medium; and as it would introduce great complexity and much guess¬ 
work into our calculations, I shall suppose that the gas here considered is one the 
molecules of which do not take up any sensible amount of energy in the form of 
internal motion. Kundt and Warburg * have shown that this is the case with 
mercury gas. 
Let the masses of the molecules be M, and M 3 , and their velocity-components 
£\, and 77.,, £ 3 respectively. Let V be the velocity of relative to M 3 . 
Before the encounter let a straight line be drawn through Mj parallel to V, and let 
a perpendicular b be drawn from M 3 to this line. The magnitude and direction of 
b and V will be constant as long as the motion is undisturbed. 
During the encounter the two molecules act on each other. If the force acts in the 
line joining their centres of mass, the product bV will remain constant, and if the 
force is a function of the distance, Y and therefore b will be of the same magnitude 
after the encounter as before it, but their directions will be turned in the plane of 
Y and b through an angle 20, this angle being a function of b and Y, which vanishes 
for values of b greater than the limit of molecular action. Let the plane through V 
and b make an angle <f> with the plane through V parallel to x, then all values of <f> 
are equally probable. 
If £1 be the value of after the encounter, 
* Pogg. Ann., clvii., 1876, p. 353. 
2 H 2 
