822 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
Dec 
that is 
and this is result VIII. 
c 
In order to compare different gases we have, when -is sufficiently large, 
D= 
V' 
IT 
.<•» 
Therefore 
Doc 
Vm' 
This gives the relative values of s for different gases; as, for instance, air and hydrogen. 
Graham found that the times of transpiration of these gases through a capillary tube 
are in the ratio 2’04. The ratio of the square roots of the molecular weights is 3 - 8. 
Hence at equal pressures and equal temperatures the mean range for hydrogen is to 
the mean range for air as 3'8 is to 2'04. 
It appears, however, at once from the equation that these ratios are not constant 
c , c 
unless-is very large. As - diminishes, the term involving \ 2 becomes important, and 
it is to this term we must look for the explanation of the result IX.—the marked 
non-correspondence of the curves for hydrogen and air. If V depends on the nature 
of the gas then this difference in shape is accounted for, which confirms the conclusion 
of Art. 98 that when the tube is large compared with 5 the effect of the impacts at the 
surface will probably depend on the nature of the gas. 
Q 
107. Result X. refers to the thermal differences of pressure when - is small. 
1 d/T 
In this case D=0, while —, and M are constant. 
t dx 
Equation (99) becomes 
1 dp> ! m' 1 dr m! 1 d^/r 
p dx ~ m t dm m \/r dx 
( 111 ) 
The exact relation between m and m would appear, as explained in Art. 101, to 
depend on the shape of the section of the tube, and to be somewhere between 1 and 
2 
1 -)—, its respective values for a fiat and round tube. This view, however, is based on 
77" 
the assumption that the molecules are uniformly distributed as regards direction, 
whereas it appears probable, from reasoning similar to that of Art. 98, that the mole¬ 
cules tend to assume a direction normal to the surface, and in this case for a tube of 
771 * 
curvilinear section the value of — would be reduced. 
m 
