THE DECREMENT OF THE ARC OF VIBRATION OF A MICA PLATE. 
441 
This law is in accordance with Maxwell’s law, but does not by itself alone prove 
Maxwell’s law. It leaves the functional relation between the coefficient of viscosity 
and the density for any one gas arbitrary, and deduces from thence the relation for all 
other gases, this relation introducing merely one unknown constant for each. What 
the law gives may be put in a clear form by a geometrical illustration. I assume 
Boyle’s law, so that for any one gas the ratios of the densities in different cases or 
the ratios of the pressures may be used indifferently. 
Let, then, the relation between the viscosity and density be represented graphically 
by taking abscissae to represent densities and ordinates to represent coefficients of 
viscosity. Then the law found above may be enunciated by saying that the curves 
for all gases are geometrically similar, the origin being the centre of similitude. 
Maxwell’s law would give a particular case of such similar curves, namely, a 
system of straight lines parallel to the axis of abscissae. 
The deviation from uniformity of the logarithmic decrements for any one of these gases 
at these comparatively speaking high pressures is not therefore in any way inconsistent 
with Maxwell’s law, but is fully accounted for by the very natural supposition that 
the rarefaction is not yet sufficient to render the molar inertia of the gas insensible as 
regards its influence on the gas’s own motion, a supposition which can be shown to 
be true when we employ the approximately known absolute value of the coefficient 
of viscosity. The same consideration shows, moreover, that we have only to carry 
the exhaustion further in order to render the effect of that inertia insensible, and 
accordingly, if Maxwell’s law be true, to make the logarithmic decrement sensibly 
independent of the pressure. 
That such is actually the case is shown by Mr. Crookes’s tables or the diagram A, 
in which they are graphically represented. We observe a manifest tendency for the 
logarithmic decrement to become constant till the law is interrupted by the breaking 
down of viscosity attending extreme exhaustions, or by certain deviations which in 
some cases (as in those of oxygen and. kerosoline vapour) show themselves a little 
earlier : these deviations will be referred to further on; for the present I merely avoid 
exhaustions high enough to introduce them. This approximate constancy of logarithmic 
decrement is observed in hydrogen from the first, which is accounted for by the high 
index of friction of that gas as compared with the others at equal pressure. 
This evident constancy or tendency towards constancy in the viscosity as the rare¬ 
faction goes on supplies the missing link, and establishes Maxwell’s law on the basis 
of Mr. Crookes’s experiments even taken by themselves. It is not, of course, directly 
'proved for the higher pressures in the gases other than hydrogen; its extension to such 
pressures is a matter of inference, derived from observing, first, that it is found to be 
true within such limits of density that the condition of ideal simplicity supposed at 
the commencement of this note is presumably sensibly attained; and, secondly, that 
above those limits, though we are unable from mathematical difficulties to examine 
its truth directly, yet we are able to deduce from theory one inference on the 
