PROPERTIES OF MATTER IN THE GASEOUS STATE. 
819 
moreover, that the difference between the abscissse of corresponding points for the 
different plates is the logarithm of the ratio of the coarseness of the plates whatever 
may be the nature of the gas. 
In the experiments we have an exactly similar agreement between the curves 
expressing the log. (densities) and the log. (times). 
Hence the only point of difference between the results deduced from the equation 
and those derived from the experiments is, that the one depends on * and the other 
upon p —the temperature being constant. Whereas it appears not only as in Art. 93, 
but in whichever way we examine s, that however s may vary with the molecular 
mass and with the temperature, it must be inversely proportional to the density. 
Therefore the fitting of the logarithmic curves is a direct inference from the form of 
the general equation (101). 
We also see that the common difference in the abscissae of the curves deduced from 
the equation is the logarithm of the ratio of the diameters of the interstices; and 
hence we infer that the difference in the abscissae of the experimental curves for 
meerschaum and stucco gives the ratio of the mean diameters of the interstices in 
these plates. (See Appendix, note 4.) 
The common difference in the ordinates is, according to the equation, the logarithm 
of the ratio — ; and although V m and V * are unknown, the experiments verify the 
(' m V s 
theory in as much as they show that the common difference is independent of the 
nature of the gas—the same difference being obtained with hydrogen as with air— 
and depends entirely on the plates. 
The fitting of the curves which express the logarithms of the thermal differences of 
pressure follows in a precisely similar manner from equation (101). 
1 dr 
In these experiments f2 = 0 and - — and M were constant, so that equation (101) 
becomes 
And putting 
*= ¥„(-)- Y 
\s/p dx \.sj t ax 
i d P 
y —log’ A 
J 6 dx 
X=lo2' 
o 
(106) 
we have as in the previous case, supposing the coefficient in F 1 and Fn to be the same 
for stucco as for meerschaum (see Appendix, note 4), where - = 
s* S»i 
i i 
X s —X m -\-iOg — 
s ‘ f 
2/,=y„+log^ J 
I J 3 J 
(107) 
