142 HEAT. 



But & 



p 2 P 



therefore the balance is attained when 



The pressures are then as the square roots of the temperatures on the 

 gas scale. 



The phenomena of thermal transpiration have been investigated by 

 Osborne Reynolds (Phil. Trans., part ii. 1879). He maintained the gas 

 at constant temperatures of 100 0. and 8 C. respectively, in chambers on 

 the two sides of a plate of biscuit, meerschaum, or stucco, and determined 

 the difference of pressure in the steady state. He found that at low 

 pressures the formula is nearly verified. As the pressure on both sides 

 increases, however, the difference of pressure is nearly inversely propor- 

 tional to the mean pressure. In his paper he gives a full investigation 

 of the theory, which agrees with his observations. 



The Mean Free Path. The very great velocity of the molecules 

 as calculated on p. 136 might lead us to expect that gaseous diffusion 

 would be extremely rapid, so that if, for instance, a gas-tap were turned 

 on in a room the coal-gas, with a molecular speed comparable with half 

 a mile a second, would almost instantly spread all over the room. But 

 this does not agree with observation. If the air in the room is free 

 from draughts it may be quite a considerable time before the coal-gas 

 is in sufficient quantity to be perceived, even a few feet from the tap. 

 The diffusion is hindered by the collisions of the molecules with each 

 other. If we could follow a given molecule we should see it continually 

 colliding with, or being interfered with by its neighbours, pursuing a 

 given direction only for a very short distance and a very small time, 

 then colliding with another molecule and changing its direction of motion 

 for another short distance, then colliding again, and so on. The mean 

 distance travelled between successive collisions is termed the mean free 

 path. We shall denote this by M.F.P. The number of collisions per 

 second made by a molecule is termed the Collision Frequency. Evi- 

 dently the collision frequency x the M.F.P. is equal to the mean velocity. 



We shall see later that we may estimate the M.F.P. in air at atmos- 

 pheric pressure as of the order of a hundred-thousandth of a centimetre, 

 and the collision frequency as more than a thousand million. During a 

 second, then, a molecule changes its direction of motion thousands of 

 millions of times, moving now forward, now backward, now up, now 

 down, now to this side, now to that. The different displacements will 

 to a very large extent neutralise each other, so that at the end of a 

 second a molecule will generally only be a very short distance from the 

 point it occupied at the beginning of the second. 



Molecular Dimensions. Molecular Sphere of Action. We 



cannot at present form a working hypothesis, useful for the kinetic 

 theory, of the structure of the molecule, or of the field of force around it. 

 We cannot, therefore, say how the molecules act upon each other when 

 they approach and are in collision- We must be content to take what 



