TRANSACTIONS OF SECTION B. 987 
film. This amount of work is far more than can be admitted, and the conclusion 
is inevitable that a water film falls off greatly in its contractile force before it is 
reduced to a thickness of || (14, millimetre. Such a falling off in the contractile 
force would indicate that there are not several molecules in this thickness of 
water, 
4, Argument from the Kinetic Theory of Gases.—Supposing the molecules of a 
gas to be hard elastic globes all of one size, influencing one another by actual 
contact only, each molecule will move along in a zigzag path consisting of rectilinear 
portions, with abrupt changes of direction. Clausius has shown the average length 
of a free path of a particle, from collision to collision, to bear to the diameter of 
each globe, the ratio of the whole space in which the globes move to 6,/2 times 
the sum of the volumes of the globes. Or if \ be the average length of free path, 
o = diameter of a globe, v = volume of the globes in 1 c.c. of gas, then ¢ =6,/2 v X.° 
Since it is inadmissible to suppose that, in the liquefaction of any of the ordinary 
gases, they could be made 40,000 times denser than at ordinary temperature 
and pressure, without reducing the whole volume to less than that of the sum of 
the globes, the free path must not be more than 5,000 times the diameter of the 
gaseous molecule. The average length free path of each molecule from collision to 
collision in the case of oxygen, nitrogen, or air, has been shown to be _1_ of a 
100,000 
centimetre. The diameter of the gaseous molecule, therefore, cannot be less than 
amma centimetre, ze, 2x10-° or 4 M (millionth of a millimetre), Nor 
can the number of molecules in a c.c. of gas be greater than 6x 1074. Since the 
densities of known liquids and solids are from 500 to 16,000 times that of air, at 
ordinary pressure and temperature, the number of molecules in a c.c. may be from 
5x 10* to 10°, Assuming a cubic arrangement of molecules, the distance from 
centre to nearest centre in solids and liquids may be estimated at from aaa 
to ayo Millimetres. 
These four lines of argument show that in liquids and transparent solids the 
mean distance between the centres of contiguous molecules is something between 
jth and ;4.th of a millionth of a millimetre. 
Quite recently Professor F. Exner has shown that v in the formula ¢ =6./2 vA, 
mentioned above, may be calculated in another way. Starting from Faraday’s 
assumption that a dielectric consists of particles of conducting substance dis- 
tributed throughout its mass and separated from each other by absolutely non- 
conducting (void) spaces, and supposing » =the sum of the conducting particles in 
lec. of dielectric, Clausius has shown, supposing the particles to be spheres, the 
following simple relation to hold between v and the specific inductive capacity of 
K-1 
the dielectric viz., aoe Further, according to Maxwell’s theory, K=n’, 
+2 
where n=the refractive index of the substance. Hence in the case of gases the 
K-11 n?-1 
formula v = —,—., may be applied. The values obtained by this method 
K+Z n?+2 
for the diameter of a. molecule are smaller than those obtained by the other 
methods, but of the same order of magnitude. 
The author goes on to give a brief account of the experiments on soap films, 
conducted by himself conjointly with Professor Riicker (‘ Nature, vol. xxxii., p. 210), 
the results of which, even when the highly complex character of the liquid em- 
ployed is considered, are not out of accord with the estimate of Sir W. Thomson 
as to the size of molecules, although the upper limit given in 1873 by the latter 
(viz., 3 M), is probably tvo high. 
6. An approvimate determination of the Absolute Amounts of the Weights 
of the Chemical dtoms.’ By G. Jonnstone Sroney, D.Sc., F.R.S. 
Several inquiries (see Professor Loschmidt, ‘Zur Grosse der Luftmolecule,’ 
Academy of Vienna, Oct. 1865; G. Johnstone Stoney on ‘ The Internal Motions of 
Gases, Phil. Mag. August, 1868; and Sir William Thomson on ‘The Size of 
