PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
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Large densities. 
43. As the density of the gas increases, the times of transpiration diminish, at first 
slowly, and then more rapidly. According to Law VII., ultimately the time of trans¬ 
piration becomes inversely proportional to the density : this rate was not reached in 
the present experiments, the nearest approach being with air through stucco. The 
shape of the curves, however, shows that the limit has not been reached. 
In order, however, to show that the rate of variation of the times of transpiration of 
equal volumes reaches but does not pass beyond the rate of variation of the inverse 
density, we have Graham’s experiments on capillary tubes, this being the exact law 
which was found to hold with all the gases and all the tubes. These tubes may be 
considered as corresponding with an extremely coarse plate. 
Graham’s results reconciled. 
44. It is thus seen how the apparently different laws obtained by Graham for 
capillary tubes and plates of different coarseness, which led him to suppose that the 
passage of the gas through the finer plates more nearly resembled effusion than 
transpiration, are all reconciled and brought under one general law, involving, besides 
the nature of the gas, nothing but the ratio which the density of the gas bears to the 
fineness of the plate. 
The verification of Law L. 
45. The deduction of the comparative rates of thermal transpiration which would 
have ensued had the tap D in the thermo-diffusiometer have been open, is now only 
a matter of calculation. We have only to calculate by Law VI. the comparative rates 
of transpiration that would have resulted from the thermal differences of pressure. 
Hence it will be seen that Law I. follows from Laws II. and VI., Art. 9, and as these 
have both been verified, Law I. has also been verified. 
Section IV. —Experiments with very Small Vanes. 
First experiments. 
46. Before commencing the experiments on thermal transpiration described in 
Section II., I made an attempt to ascertain how far were borne out the theoretical 
conclusions that the necessity for extremely small pressures in the radiometer was 
owing to the comparatively large size of the vanes, and that with smaller vanes similar 
results would be obtained at proportionally higher pressures. 
The pressures at which the impulsive force in the radiometer first becomes sensible 
is so extremely small that this pressure may be increased several hundred fold without 
becoming what may be called sensible—measureable by a mercurial gauge. So that 
