820 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
And since r and M are the same for both plates 
fim _ pm 
Ps Ps 
Hence in this case, according to the general equation (106), the common difference 
in the ordinates of corresponding points is the logarithm of the ratios of correspond¬ 
ing densities, while the difference in the abscissae is the logarithm of the ratio of the 
coarseness of the plates which is the reciprocal of the ratios of the mean ranges. If, 
therefore, as has just been assumed, the densities are proportional to the mean ranges, 
the common difference of the ordinates should be the same as that of the abscissae, and 
the same for these curves as for those of transpiration under pressure. 
Thus we have excellent opportunities of verifying the conclusion that s varies 
inversely as p, and the indication as to the manner in which c enters into the relation 
between clp and dr. 
This verification is complete, for although there is a slight discrepancy between the 
common difference for the ordinates and that for the abscissae, this, as has been 
explained in Art. 30, was in adl probability owing to certain discrepancies in the 
difference of temperature maintained on the two sides of the plates (see Appendix, 
note 4). And even if unexplained these discrepancies are small enough to be neglected. 
The actual differences are as follows :•— 
Plates. 
Meerschaum No. 3, and Stucco No. 1 
2 
?? >5 ^ 
Thus the dependence of transpiration on the ratio - first revealed by the theory as 
expressed in equation (101) has been completely verified by the experiments of trans¬ 
piration under pressure, and on thermal transpiration. And it must be noticed that 
while the verification has been obtained both for hydrogen and air, the experiments on 
either gas suffice for complete verification. And thus the exact agreement of the 
common differences both of ordinates and abscissae for the two gases (although the 
absolute ordinates differ widely, and the shapes of the curves differ considerably) not 
only affords a double verification, but precludes the possibility of accidental coincidence. 
It is further to be noticed, both with respect to the foregoing comparison of the 
theoretical with the experimental results, and also with respect of such further com¬ 
parisons as will be made, that the reasoning admits of being reversed; and instead of 
deducing the experimental results from the equation, it might have been shown that a 
similar equation is the necessary outcome of the experimental results. Indeed, this 
has been already done, and it is only out of regard to the length of tins paper that I 
refrain from including the inverse reasoning. 
106. The experimental results II. and III. follow at once from the fact that the 
Thermal Transpiration. Transpiration. 
Absciss®. Ordinates. Absciss®. 
•698 775 
745 -890 -819 
