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PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
Comparison of the logarithmic homologues. 
31. In Plates 48 and 49 the curves for meerschaum are drawn in the same position 
with reference to the axis, 0 M, 0 N. But while in Plate 48 the curves for stucco 
No. 1 and No. 2 are shown in the position as plotted from the columns of logarithms 
in the Tables VI., VII., XII. and XIII., in Plate 49, these curves have all been shifted 
until they coincide with the curves for meerschaum No. 3, in each case the two 
curves for air and hydrogen being shifted together. The axes are also shown as shifted 
with each pair of curves. The fitting of these curves is very remarkable ; nor is it 
only the curves, for the points indicating the results are shown, and these all fall in so 
truly that it was hardly necessary to draw a line until the points of low pressure are 
reached. There is a slight deviation of that part of the curve for hydrogen, stucco 
No. 1, which represents the pressures below 1 inch; but this has been already ex¬ 
plained as being due to the infusion of air through the india-rubber. In order to fully 
appreciate the force of this agreement, it must be borne in mind that it is not merelv 
the portions of the curves that overlap that agree in direction, but the distance 
between the curves for hydrogen and air which have been shifted in pairs. 
Nothing could prove more forcibly than this, that the different results obtained with 
different plates are quite independent of the nature of the gas so long as the densities 
are in the ratio of the fineness of the plates. 
So far, therefore, as thermal transpiration is concerned, we have an absolute proof of 
Law V., Art. 9. 
The relative coarseness of the 'plates. 
The shifts in Plate 49 to bring the curves into coincidence being the logarithms of 
the corresponding pressures, it follows from Law V. that these shifts are the logarithms 
of the relative coarseness of the plates. Hence for the mean (after some law) 
diameters of the apertures we have : 
Plate. Coarseness. 
Meerschaum No. 3.1 
Stucco No. 1.5 
Stucco No. 2.5'6 
Further comparison of the results with the laws of Art. 9. 
32. So far as the manner of variation of the differences of pressures with the density 
of the gas, this is completely shown by the shapes of the curves in figs. 3, 4, and 5, 
and is strictly according to Laws II. and III. 
The agreement of the log. curves has been shown to confirm Law V. It only remains, 
therefore, to notice the laws of variation at the greatest and smallest pressures, to see 
how far these conform to the limits given in Laws III and IV. 
