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PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
direction from C to H (suppose them on a truck). The inequality in the force 
would set them in motion in this direction, which motion would increase until the 
actual velocity of the shot from C equalled the actual velocity of the shot from H; 
then all inequalities in the reactions would cease, and there would be no reactions on 
the limiting batteries. 
In this case the limiting batteries are obviously analogous to the sides of a tube, 
and the interval between the planes H and C corresponds with a layer of gas at equal 
pressures, but across which the heat is being conducted by the greater velocity of the 
molecules which move from H to C ; and the conclusion is that such a layer of gas 
when maintained at rest exerts a tangential force on the sides of the tube tending to 
move the tube in the direction of the flow of heat, whereas if the gas were free to 
move it would flow towards the hottest end; and this is the phenomenon of thermal 
transpiration. 
59. The foregoing illustration, with the exception that the action is confined to a 
plane instead of being distributed through a space, is more than analogous : it is 
strictly parallel to the case of gas as long as the gas is so rare that the molecules 
proceed straight across the intervals between the plates or sides of a tube. When 
this is the case, therefore, the example of the batteries explains the phenomena of 
thermal transpiration as well as the phenomena of the radiometer. But when the gas 
is so dense that in crossing the interval between the surfaces the molecules undergo 
several encounters, the parallelism no longer holds. Even then, however, the analogy 
holds, for the gas at any point may be considered as consisting of two sets of 
molecules which are moving across a plane from opposite sides. And by examining 
the difference in the velocity of these two sets of molecules a general explanation of 
many of the phenomena may be obtained without recourse being had to a strict 
analytical investigation. The analogy has, however, been pursued far enough to serve 
the purpose of an introduction. 
Before proceeding to the mathematical investigation, which is novel and somewhat 
intricate, I have thought it advisable to further introduce it by a short description of 
the method used and the assumptions involved. 
Prefatory description of the mathematical method.. 
60. The characteristic as well as the novelty of this investigation consists in the 
method by which not only the mean of the motions of the molecules at the point under 
consideration is taken into account, but also the manner in which this mean motion 
may vary from point to point in any direction across the point under consideration. 
It appears that such a variation gives rise to certain stresses in the gas (tangential 
and normal), and it is of these stresses that the phenomena of transpiration and 
impulsion afford evidence. 
Instead of considering only the condition of the molecules comprised within an 
elementary unit of volume of the gas, what is chiefly considered in this investigation 
