THE DECREMENT OF THE ARC OF VIBRATION OF A MICA PLATE. 
445 
would tend to become parallel to the axis of p, and the curvature where the curve 
cuts the axis of l would vary from one gas to another directly as the square of the 
density at a standard pressure and inversely as the coefficient of viscosity. For the 
gases examined the curvatures near the axis of l would therefore vary 
for Air O N and CO CO, H 
as 14 , 42 3 -p 1 - 000, 16 3 ^- 1*117, 14 3 -f0'970, 22 3 -f0'823, C-pOOOO, 
or as 1-000, 1*102, 0-971, 2'828, 0 010. 
It will be seen in Mr. Crookes’s diagram A, that if we imagine the curves continued 
upwards on their old lines, cutting off the changes which take place at very high 
exhaustions, the tangent tends to become vertical, and, moreover, the rate at which 
the direction of the tangent changes as we go down agrees well, as far as the eye can 
judge, with the above figures. We may notice in particular the extreme flatness of 
the hydrogen curve. 
As we proceed upwards to the higher exhaustions, the first thing that strikes us 
(first in order of occurrence, very far from first in order of magnitude) is the curious 
increase which is observed in the logarithmic decrement in the case of oxygen and of 
kerosoline vapour. Small as this is, Mr. Crookes considers it real. It puzzled me at 
first, since it occurs while the pressure is still comparatively high, such as 15 millims. 
or 20 millims., so that the mean free path must still be extremely small, and might, one 
would naturally suppose, be treated as infinitely small considering the dimensions of 
the apparatus. It occurred to me afterwards that it is probably referable to the 
thinness of the vibrating body. As the lamina moves there must in the immediate 
neighbourhood of the edge be a thin stratum or cushion of gas in which there is a 
very intense shearing motion. The intensity of the shearing makes up in good 
measure for the narrowness of the cushion, and renders the effect of the cushion a 
not insignificant fraction of the whole. The narrowness of the stratum may well be 
such as to forbid us to treat the mean free path as infinitesimal long before we are 
prohibited from so regarding it in comparison with the dimensions of the vessel, or 
the lateral dimensions of the lamina. That among- the four unmixed gases examined 
oxygen should be the one to show this effect, seems to be connected with the fact that 
at comparatively low exhaustions (such as 0"76 millim.) it shows repulsion effects much 
the most strongly; and both phenomena seem to indicate that for oxygen the length 
of path (I do not say free path) is comparatively large, “ path ” here meaning the 
space throughout which a molecule preserves approximately its original direction of 
motion. 
When we come to those high exhaustions at which the decrement of arc gives way, 
the law of proportional logarithmic decrements at corresponding (and those pro¬ 
portional) pressures, which we hitherto found to be so accurately obeyed, breaks down 
altogether. A single example will suffice to show this. Take hydrogen at 330 M, 
3 m 2 
