734 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
The Laws established by the experiments. 
9. Law I.—When gas exists at equal pressures on either side of a porous plate across 
which the temperature varies, the gas will transpire through the plate from the colder 
to the hotter side, with velocities depending on the absolute temperature and chemical 
nature of the gas, the relation between the density of the gas and the fineness of the 
pores, the thinness of the plug, and the difference of temperature on the two sides of 
the plate. 
Law II.—In order to prevent transpiration through the plate, the pressure on the 
hotter side must be greater than the pressure on the colder side. This difference of 
pressure will depend on the chemical nature of the gas, the mean pressure of the gas, 
the absolute temperature, the relation between the size of the pores and the density 
of the gas, and the difference of temperature on the two sides of the plate, but not on 
the thickness of the plate. 
Law III.—For the same plate and the same difference of temperature when the gas 
is sufficiently dense, the difference of pressure is approximately proportional to the 
inverse density, but as rarefaction proceeds this law gradually changes, the increase in 
the difference of pressure becomes less and less until that difference reaches a maximum 
and begins to diminish, then on further rarefaction this diminution increases until the 
difference of pressure becomes approximately proportional to the density of the gas. 
Law IY.—After the rarefaction has reached that point at which the difference in 
pressure is nearly proportional to the density, then the difference in pressure will bear 
to the greatest pressure the ratio which the difference in the square roots of the 
absolute temperature bears to the square root of the greatest absolute temperature, or 
if A and B indicate the two sides of the plate, 
I'a ~ 1'b _ a/ t a V t b ) 
La \A a 
where p and r represent respectively the pressure and the absolute temperature in 
the gas. 
Respecting the results depending on the relation between the density of the gas and the 
fineness of the pores. 
Law V.—Both in the case of thermal transpiration and of transpiration under 
pressure, similar results will respectively be obtained when the density of the gas 
bears a fixed relation to the diameters of the apertures in the plates. 
Respecting the rate of transpiration arising from a difference of pressure on the 
tivo sides of the plate. 
Law VI.—When gas exists at different pressures on the two sides of a plate, and the 
difference of pressure bears a fixed ratio to the pressure on either side; then for a 
certain plate and a certain gas the time of transpiration of equal volumes will, when 
