56 G. Jounsrone Srongy On Polarization Stress in Gases. 
results from plotting it down are such that (owing to the term containing ,) 
there is that separation between the origin of radii and the centre of figure which 
gives a sufficient value to the function #,, but that (the co-efficient of »’ containing 
only very small quantities) the solid is not elongated in the way which would allow 
the function &, to attain any considerable value. That the function h, is not wholly 
absent, 1s because of such causes as the slight distortion of figure before men- 
tioned, which give rise to very small* terms of the form /,, h,, &c. 
This almost total absence of the elongated form arises from Clausius’s fundamental 
hypothesis that the motions of the molecules emitted by a stratum may be 
represented by radii drawn to a sphere from an excentric point, whereas it appears 
from the discussion in the earlier part of the present memoir that the encounters 
that take place within each of the two streams into which the gas may be divided, 
give to the surface to which the radii are to be drawn an elongated form. This 
omission from Clausius’s hypothesis does not sensibly affect the spherical harmonics 
of the first order, and accordingly his hypothesis is adequate as regards the flow 
of heat, which depends exclusively on one of these ; but it renders the hypothesis 
an insufficient one as regards polarization stress, or any other phenomenon which 
depends on spherical harmonics of the second order. 
* That £, is very small, if we adopt Clausius’s hypothesis, may also be seen by comparing equation 
(18) with experiments on spheroidal drops. Observation shows that, at atmospheric temperatures and 
pressures, a spheroid of water some millimetres in diameter will be supported at a distance of about a 
fourth-metre (a metre divided by 10*) from the heater, when the difference of temperatures is about 10°C. 
In G CS (gramme, centimetre, second) systematic measures, the hyper-milligram, ([ of the gravitation 
of a milligram, g being gravity measured in metres per second per second) per square centimetre is the 
unit of stress. Hence the Crookes’s stress which supports this drop must amount to some hundreds. of 
these units. This is the amount indicated by experiment. 
Formula (18) assigns to it a very different value. Clausius estimates the flow of heat across air 
between a heater and cooler each a square metre in surface and a metre asunder, and kept at temperatures 
which differ by 1° C., as amounting per second to zoppoq0 Of the quantity of heat which will warm a 
kilogram of water 1°C. About ten times this, or zo$go9 Of this calory per second, would be the flow of 
heat between two square centimetres at a distance of a fourth-metre asunder and kept at temperatures 
that differ by 10°C. To turn this into kinetic measure we must multiply by 41600 x 1000000; so that 
G would amount to about 1144000 in G C'S kinetic measure (7.¢. in Hyper-fifth-grammetres per second), 
Again we may take as rough approximations— 
1 
Po 800 
oie =T 
fp? = 2'6 
P, = P, = 1000000 
Introducing these values into equation (18) we find approximately— 
«= 0-001 
of a hyper-milligram per square centimetre—an amount which, as it ought to be, is vastly smaller than 
that indicated by experiment, 
