224 N. D.C. Hodges—Mean Free Path of a Molecule. 
The tendency for a particle to move from the liquid into the 
surrounding atmosphere is due to the difference in density of 
its liquid and of its vapor. For small changes in the density, 
the change in this tendency may be assumed as proportional 
to the change of density. It must be found what diag in 
density takes place at p. As the change in density is due to an 
increase of pressure on p, this increase must be equal in all 
directions. So it is only necessary to consider one direction. 
Take the direction tangent to the curved surface at p. The in- 
crease in pressure is, therefore, proportional to the difference in 
density of the layer through f and that through A, or to the 
length fh. It is evident that aa 
of curvature, and L the length of the mean free path. 
he change of tension ae 
the tension of the vapor at plane surface” 7 
Sir William Thomson has shown that the change in tension 
at a curved surface is equal to the pressure of a column of the 
bs a of the height to which the liquid would rise in a capillary 
tube of a diameter of twice the radius of curvature of the sur- 
when r is the radius 
Hence we have 
ace. 
In a tube of diameter 1-294™ water rises to a height of 
23°379™™. The data for the calculation are: 
Weight of a liter of water vapor (at 100° C.) °80357 grams 
as “4 mere 1EDi9 7 
Tension of water vapor at 20° C, 18°495™™ 
The height of a column of mercury equivalent to the column 
of water vapor of height 23°379™ is 
"80357 100 18°495 23°379 
Mt CMD” C1 
The first factor is the fraction of a liter of mercury which 
a liter of water equals. The second reduces the height of this 
The third gives the result at 20° C., supposing 
the vapors to follow Boyle’s law. The fourth is the fraction of 
a liter there was to be considered. 
The expression for the mean free path in these surface vapors 
is then 
4L= °647 
80357 5), 18495 1  23°879 ,, _ g4r, 
13,579’ ° 760 7 18°495 100 
This gives L = -0000024™". 
If the law according to which the density of the vapors vary 
with the depths was known, the free path of a molecule in 4 
gas at the ordinary pressure could be found. 3 
Physical Laboratory, Harvard College, Cambridge, U. S. A., January 27, 1880. 
