300 
NATURE 
[Aug. 14, 1873 
Calculating from the data of Table I., the viscosities | 
of the gases, and comparing them with those found by 
O. E. Meyer and by myself, and reducing all to centi- 
metre, gramme, second measure, and to 0° C._— i 
TABLE II, 
Coefficient of Viscosity 
Gas. | Loschmidt. O. E. Meyer. Maxwell. 
H o'000116 9'000134 "000097 
Oo 0000270 0'000306 
co 0000217 0°000266 
co, 0°000214 0'00023I O‘OOO161 
The numbers given by Meyer are greater than those 
derived from Loschmidt. Mine, on the other hand, are 
much smaller. I think, however, that of the three, Lo- 
schmidt’s are to be preferred as an estimate of the abso- 
lute value of the quantities, while those of Meyer, derived 
from Graham’s experiments, may possibly give the ratios 
of the viscosities of different gases more correctly. Lo- 
schmidt has also given the coefficients of interdiffusion of 
four other pairs of gases, but as each of these contains 
a gas not contained in any other pair, I have made no 
use of them, 
In the form of the theory as developed by Clausius, an 
important part is played by a quantity called the mean 
length of the uninterrupted path of a molecule, or, more 
concisely, the mean path, Its value, according to my 
calculations, is 
Sit: ys 
J2nsN Inv & 
Its value in tenth-metres (1 metre X 10~*°) is 
TABLE III. 
For Hydrogen. . 965 Tenth-metresato°C.and 760B 
For Oxygen . . 500 
For Carbonic Oxide 482 
For Carbonic Acid 430 
(The wave-length of the hydrogen ray 7 is 4,861 tenth- 
metres, or about ten times the mean path of a molecule 
of carbonic oxide.) 
We may now proceed for a few steps on more hazar- 
dous ground, and inquire into the actual size of the 
molecules. Prof. Loschmidt himself,in his paper “Zur 
Grésse der Luftmoleciile” (Acad, Vienna, Oct. 12, 1865), 
was the first to make this attempt. Independently of 
him and of each other, Mr. G. J. Stoney (Phil. Mag. Aug. 
1868), and Sir W. Thomson (NATURE, March 31, 1870), 
have made similar calculations. We shall follow the 
track of Prof. Loschmidt. 
The volume of a spherical molecule is 5% where s 
(7) 
is its diameter. Hence if Vis the number of molecules 
in unit of volume, the space actually filled by the mole- 
cules is = Ns. 
This, then, would be the volume to which a cubic 
centimetre of the gas would be reduced if it could be so 
compressed as to leave no room whatever between the 
molecules. This, of course, is impossible ; but we may, 
for the sake of clearness, call the quantity— ~ 
* The difference between this value and that given by M. Clausius in his 
paper of 1858, arises from his assuming that all the molecules have equal 
velocities, while I suppose the velocities to be distributed accurding to the 
“Jaw of errors,” 
e= 4 Ns3 (8) 
the ideal coefficient of condensation. The actual coeffi- 
cient of condensation, when the gas is reduced to the 
liquid or even the solid form, and exposed to the greatest 
degree of cold and pressure, is of course greater than e. 
Multiplying equations 7 and 8, we find— 
s=6/2¢/ (9) 
where s is the diameter of a molecule, e the coefficient 
of condensation, and Z the mean path of a molecule. 
Of these quantities, we know Z approximately already, 
but with respect to € we only know its superior limit. It 
is only by ascertaining whether calculations of this kind, 
made with respect to different substances, lead to con- 
sistent results, that we ¢an obtain any confidence in our 
estimates of «. 
M, Lorenz Meyer* has compared the “ molecular 
volumes” of different substances, as estimated by Kopp 
from measurements of the density of these substances 
and their compounds, with the values of s? as deduced 
from experiments on the viscosity of gases, and has 
shown that there is a considerable degree of correspon- 
dence between the two sets of numbers. 
The “ molecular volume” of a substance here spoken 
of is the volume in cubic centimetres of as much of the 
substance in the liquid state as contains as many mole- 
cules as one gramme of hydrogen. Hence if po denote 
the density of hydrogen, and » the molecular volume 
of asubstance, the actual coefficient of condensation is— 
e— pat (10) 
These “ molecular volumes” of liquids are estimated at 
the boiling-points of the liquids, a very arbitrary condition, 
for this depends on the pressure, and there is no reason 
in the nature of things for fixing on 760mm. B, as a 
standard pressure merely because it roughly represents 
the ordinary pressure of our atmosphere. What would 
be better, if it were not impossible to obtain it, would be 
the volume at — 273° C. and oB. 
But the volume relations of potassium with its oxide 
and its hydrated oxide as described by Faraday seem to 
indicate that we have a good deal yet to learn about the 
volumes of atoms. 
If, however, for our immediate purpose, we assume the 
smallest molecular volume of oxygen given by Kopp as 
derived from a comparison of the volume of tin with that 
of its oxide and put 
(Gl 16) = "27 
we find for the diameters of the molecules— 
TABLE IV. 
Hydrogen. . . . 5'8 tenth-metres, 
Oxygen. 2.94 . 76 
Carbonic Oxide. . 
Carbonic Acid®. . 9°3 
The mass of a molecule of hydrogen on this assump- 
tion is 
4°6 X 10-4 gramme. 
The number of molecules in a cubic centimetre of any 
gas at o° C. and 760 mm. B. is 
N= 19 X 1038, 
Hence the side of a cube which, on an average, would 
contain one molecule would be 
JV —- = 37 tenth-metres, : 
J. CLERK-MaXWELL 
Annalen d, Chemie u Pharmacie V; Supp, bd. 2, Heft (1867). 
