March 31, 1870] 
NA RORLS 
553 
collision to collision would be inversely as the average 
velocity of the particles. But Maxwell’s experiments 
on the variation of the viscosities of gases with change 
of temperature prove that the mean time from col- 
lision to collision is independent of the velocity, if we 
give the name collision to those mutual actions 
only which produce something more than a certain 
specified degree of deflection of the line of motion. This 
law could be fulfilled by soft elastic particles (globular or 
not globular) ; but, as we have seen, not by hard elastic 
globes. Such details, however, are beyond the scope of 
our present argument. What we want now is rough 
approximations to absolute values, whether of time or 
space or mass—not delicate differential results. By Joule, 
Maxwell, and Clausius we know that the average velocity 
of the molecules of oxygen or nitrogen or common air, at 
ordinary atmospheric temperature and pressure, is about 
50,000 centimetres per second, and the average time from 
collision to collision a five-thousand-millionth of a second. 
Hence the average length of path of each molecule 
beween collisions is about ;gg/gp5 Of a centimetre. Now, 
having left the idea of hard globes, according to which 
the dimensions of a molecule and the distinction between 
collision and no collision are perfectly sharp, something of 
apparent circumlocution must take the place of these 
simple terms. 
First, it is to be remarked that two molecules in col- 
lision will exercise a mutual repulsion in virtue of which 
the distance between their centres, after being diminished 
to a minimum, will begin to increase as the molecules 
leave one another. This minimum distance would be 
equal to the sum of the radii, if the molecules were infi- 
nitely hard elastic spheres ; but in reality we must sup- 
pose it to be very different in different collisions. Con- 
sidering only the case of equal molecules, we might, then, 
define the radius of a molecule as half the average shortest 
distance reached in a vast number of collisions. The 
definition I adopt for the present is not precisely this, 
but is chosen so as to make as simple as possible the 
statement I have to make of a combination of the results 
of Clausius and Maxwell. Having defined the radius of 
a gaseous molecule, I call the double of the radius the 
diameter ; and the volume of a globe of the same radius 
or diameter I call the volume of the molecule. 
The experiments of Cagniard de la Tour, Faraday, 
Regnault, and Andrews, on the condensation of gases do 
not allow us to believe that any of the ordinary gases 
could be made forty thousand times denser than at ordi- 
nary atmospheric pressure and temperature, without re- 
ducing the whole volume to something less than the sum 
of the volume of the gaseous molecules, as now defined. 
Hence, according to the grand theorem of Clausius 
quoted above, the average length of path from collision to 
collision cannot be more than five thousand times the 
diameter of the gaseous molecule ; and the number of 
molecules in unit of volume cannot exceed 25,000,000 
divided by the volume of a globe whose radius is that 
average length of path. Taking now the preceding esti- 
mate, zo000 Of a centimetre, for the average length of 
path from collision to collision, we conclude that the 
diameter of the gaseous molecule cannot be less than 
soo0b0000 Of a centimetre ; nor the number of molecules 
in a cubic centimetre of the gas (at ordinary density) 
greater than 6 X 1o** (or six thousand million million 
million). 
The densities of known liquids and solids are from five 
hundred to sixteen theusand times that of atmospheric air 
at ordinary pressure and temperature; and, therefore, the 
number of molecules in a cubic centimetre may be from 
3 X 10% to 10” (that is, from three million million mil- 
lion million to a hundred million million million million). 
From this (if we assume for a moment a cubic arrange- 
ment of molecules), the distance from centre to nearest 
centre in solids and liquids may be estimated at from 
1 “ ak 
Tro0b0000 tO zeGodooo0 Of a centimetre. 
The four lines of argument which I have now indicated, 
lead all to substantially the same estimate of the dimen- 
sions of molecular structure. Jointly they establish with 
what we cannot but regard as a very high degree of pro- 
bability the conclusion that, in any ordinary liquid, trans- 
parent solid, or seemingly opaque solid, the mean distance 
between the centres of contiguous molecules is less than 
the hundred-millionth, and greater than the two thousand- 
millionth of a centimetre. 
To form some conception of the degree of coarse- 
grainedness indicated by this conclusion, imagine a rain 
drop, or a globe of glass as large as a pea, to be magnified 
up to the size of the earth, each constituent molecule 
being magnified in the same proportion. The magnified 
structure would be coarser grained than a heap of small 
shot, but probably less coarse grained than a heap of 
cricket-balls. W. T. 
FRESENIUS’S ANALYSIS 
Qualitative Chemical Analysis. By Dr. C. Remigius 
Fresenius. Seventh Edition, Edited by Arthur 
Vacher. 8vo., pp. vill. and 264. (London : Churchill, 
1869.) 
Quantitative Chemical Analysis. By Dr. C. Remigius 
Fresenius, “Fifth edition. Edited by Arthur Vacher. 
8vo., pp. viii. and 377. (London: Churchill, 1870.) 
Antlettung zur qualitativen chemischen Analyse. By 
Dr. C. Remigius Fresenius. $vo., pp. xii. and 240, with 
43 woodcuts ; price 4s. (Brunswick, 1869. London: 
Williams and Norgate.) 
IN no branch of chemistry, perhaps, has more useful pro- 
gress been made of late years than in analysis. The other 
departments of the science, technical and organic che- 
mistry, for instance, have been cultivated with assiduity and 
even ostentation ; while the study of analysis, invaluable 
and necessary as it is, has been comparatively neglected 
as humble and unadorned. Much of this apathy has no 
doubt arisen from the mechanical nature of the task of 
analytical discovery, which commonly requires a greater 
share of industry than intellectual effort. The gradual 
introduction of refined physical methods has, however, 
commenced, and will no doubt complete an entire change 
in the aspect of this subject. 
Chemists will not need to be reminded of the obligations 
they owe to Fresenius, whose analytical manuals are 
deservedly known, and in common use in almost every 
laboratory. The enormous amount of special results they 
contain is hardly conceivable to an outsider, who will not 
readily appreciate the respect paid to them by grateful 
