N. D. C. Hodges—Mean Free Path of a Molecule. 223 
how much denser the lower layers, from which molecules im- 
pinging on p come, are than those above, from which particles 
come to p. If dp is the obstruction met by a molecule in pass- 
cos 
met in the direction at an angle g with the vertical. The 
1 1 ; . 
=" ps dp gives the obstruction met by the mole- 
po 
ing vertically upward through a single layer, fe will be that 
integral 
ss cos 
cule from one end to the other of its path. This integral 
must be constant, for the length of path is independent of the 
direction, As the differential of the obstruction is the same as 
the differential of the densit ’ | . 
met 
COS Pel, ~~ COS @ 
when p, is the density at the point p and p,, that at the other end 
f se SO a 
of the be As cos 7 the numerator p,—p, must be 
beth to cos g. The pressure on p is proportional to this 
lifference, and the resultant component in the upward direc- 
tion to cos? ¢, 
When the surface is spherical (fig. 2), each element of the path 
offers an obstruction expressed by for the parts be- 
p 
cos (p — $4) 
low p, and by eet) for those above p, ais the angle 
between the radius of curvature at the point p and that to the 
2. 
g 
other end of the path. —ta is the mean value of the angle 
between the direction of the path and the normals to the surfa- 
ces of equal density for the parts below p, and g+4a the corre- 
Sponding angle for those above p. 
en ee This shows that. 
cos(p—fa)_———cos(p+4a)’ 
Whereas the difference in density above and below was the 
Same for a plane surface, in the case of curved surfaces the 
Pressure from below is greater, and that upward less. Or the 
ioe from below is greater, and that from above greater. 
his must cause a greater density at p. 
Integrating, 
