PROPERTIES OE MATTER IJS T THE GASEOUS STATE. 
753 
Logarithmic homologues of the curves in figs. 4 and 5. 
2S. It appeared, however, that as a method of obtaining the corresponding pressures 
the comparison of the ratios was not entirely satisfactory, for it involved the assump¬ 
tion that the ratio of corresponding differences of pressure should be exactly the same 
as the ratio of corresponding mean pressures ; whereas this would only be the case if 
the differences of temperature were exactly the same for both plates. It seemed 
desirable therefore to find a means of comparing the curves for the two plates on the 
assumption that the corresponding abscissae might bear one ratio and the corresponding 
ordinates another, or if 1 and 2 are corresponding points, x i — ax l while y^—by x . 
A graphic method of doing this simply and perfectly was found by comparing not 
the curves themselves, but what may be called their logarithmic homologues. 
Instead of plotting, as in figs. 3 and 4, the mean pressures and differences of pressure 
as the abscissae and ordinates of the points on the curve, the logarithms of these 
quantities are plotted. Thus, x. 2 = logaq, y\— log y x , where x x y x may be taken to be 
a point on any one of the curves already plotted, and x\y\ the corresponding point 
on the logarithmic homologue. It is thus seen that if for two curves (1) and (2), 
x. 2 =ax 1 and y 2 =by x , then x' 2 =x\-\- log a and y' 2 =y' x -\- log h; or the logarithmic 
homologues will all be similar curves but differently placed with regard to the axes, 
such that the one curve may be brought into coincidence with the other by a shift of 
which the coordinates are log a log b. 
Eig. G. 
Log. Pressure. 
Fig. 6 shows the logarithmic homologues of the curves for stucco No. 1 and meer¬ 
schaum No. 3 both for hydrogen and air. By tracing the log curves for stucco No. 1, 
together with the axes, on a piece of tracing paper, and then moving the tracing (so 
that the axes remain parallel to their original direction) until the traced curves fit on 
to the curves for meerschaum No. 3, it is found that the fit is perfect, a portion of 
the traced curve e f (stucco) coinciding with a portion of a b, while at the same time 
5 d 2 
