46 
where signify 
7 the See of the cylinder. 
¢ the time of the experiment. 
¢, the concentration of the salt solution before the experiment. 
¢, the mean concentration of the solution after the experiment. 
D the coefficient of diffusion. 
§ 2.,—Chloride of sodium was the substance experimented 
with to test the method, Three solutions were prepared, of 
which the first contained 0°66487, the second 5°8506, and the 
third 17°695 parts by weight of the anhydrous salt in 100 parts 
of the solution. The cylinders employed were 2 to 8 cm, iu 
diameter, and 3°45 to 5°036 cm. in depth. The experiments 
were conducted either in such a way that all the cylinders were 
filled with the same solution, and the observation made if the 
cross-cut and the depth of the cylinder had influenced the final 
result ; or else differently concentrated solutions were taken, and 
the experiment carried out at exactly the same temperature and 
under the same other conditions. The method was found to be 
sensitive and accurate. The temperature being 8°5° C., and the 
duration of the experiment 6°5 hours, the coefficient found 
was :— 
With a solution of 0°66487 per cent.... 768 ae 
” ” 58506 ” . 808 > x 10-8 — 
” 9» 177695 ” 889 esc 
The conclusion to be drawn from these numbers is that co- 
efficient of diffusion within the limits of time and concentration 
indicated decreases according to the law of the straight line as 
the quantity of salt in solution, 
From this result follow :— 
1, The numerical value of the coefficient at the same tempe- 
rature, and the same initial concentration depends upon the 
duration of the experiment. 
2, A fixed state, in which the concentrations in the fluid 
decrease from bottom to top, according to the law of the straight 
line, is impossible. Fick’s method, which presupposes this state, 
cannot therefore give correct results. 
From the above-mentioned law of the dependence of the co- 
efficient of diffusion on the quantity of salt in solution, and from 
the first conclusion, it follows that at one and the same tempera 
ture the value of the coefficient may vary between two widely 
separated limits. An experiment performed with a saturated 
solution during the shortest possible time would furnish the one 
limit, another with a solution containing a quantity of salt 
approximating to zero would give the other. 
‘The physical cause and the necessity for the mentioned depen- 
dence is very simple. If a volume of water be mixed with one 
volume of concentrated salt-solution, and if a volume of water 
be mixed with a volume of dilute salt-solution, the resulting con- 
traction in the first instance is greater than in the second. The 
diffusion of a salt-solution in water has been up to the present 
considered from a very one-sided point of view. Berthollet and 
Fick ascribe the diffusion to the forces alone which act between 
water and salt-solution ; modern investigators ascribe it solely to 
the molecular velocity of the fluid molecules. The experiment 
shows that the diffusion depends on both, and therefore supports 
neither of these views entirely. When the cylinder has been 
filled with concentrated solution the participation of the mole- 
cular forces is greater than in the case of weak solution, The 
numerical value of the coefficient of diffusion, which expresses the 
result of the experiment, must necessarily be greater in the first 
case than in the latter. It is therefore in our power to regulate 
the phenomena of diffusion ina salt solution according to our 
will ; thus when we experiment with concentrated solutions the 
principal agents at work are the molecular forces, whilst the 
velocity of the molecules plays the chief part in dilute solutions. 
The coefficient of diffusion of a salt-solution loses, therefore, 
entirely the signification of a constant, because in every special 
case it has another value. 
§ 3. The coefficients of diffusion of salt solutions in water at 
the temperature of 10° C,, determined by Graham, Fick, Weber, 
and Schuhmeister, form a group of numbers which lie between 
cm? 
0’000010 and 0’000002 
c. 
It was of great interest to ascertain the value of the coeffi- 
cient of diffusion when the quantity of salt is so small that it can 
neither be estimated with the balance nor with chemical means ; 
when, in short, the solution differs hardly at all from pure water, 
and when the participation of molecular forces has been brought 
toaminimum, Such an experiment may be made by tinting 
ae a Sar 
[Wov. 10, 1881 
water with a salt of great tinctorial power and observing the dif- 
fusion of the coloured water into the pure. It is much more 
difficult to follow these experiments quantitatively, as very small 
quantities have to be determined. Colorimetrical methods are 
not sensitive enough. 
I therefore tried to measure the concentration photometrically, — 
Nigrosin, which is sufficiently stable towards sunlight, was the - 
colouring matter chosen for the purpose. Hiifner’s spectro-pho- 
tometer was employed. The water was coloured with nigrosin 
to such an extent that its coefficient of extinction for sodium light 
amounted to 1°343. The quantity of colouring matter used was 
so small that the change of specific gravity in the water through 
its addition could not be ascertained. 
A full report of the many difficulties which were encountered ~ 
and a detailed description of how the experiments were conducted 
will be found in the above-mentioned Wredemann’s Annalen, 
It was discovered that the coefficient of diffusion was smaller 
by one decimal place than the smallest :known coefficient of a 
salt. == Bess 
The method here described urges the investigation of a series 
of new problems. 
In the first place the value of the coefficient must be ascer- 
tained for different salts when the salt in solution approximates 
zero. When these values have been found, only then it will be 
possible to define in what way the coefficient of diffusion depends 
on the nature of the salt. 
Secondly, it is necessary to find out if it is not possible, by 
tinting water with different colouring-matters, to obtain a con- 
stant, which I propose — analogously to a case already considered 
by J. Clerk Maxwell—to call the coefficient of diffusion of a 
fluid into ttself. 
If we suppose a room -to be divided into two parts by a 
movable wall and filled with the same gas at the same pressure 
and temperature, and we then remove the wall, a diffusion of 
the gas takes place from the one half of the room to the other, 
and vice versd, in consequence of molecular velocity. The co- 
efficient of the diffusion which takes place here, Maxwell calls 
the coefficient of diffusion of a gas into itself. Tt is not measur- 
able, as the molecules of a gas cannot be marked. It can how- 
ever be calculated from the coefficient of viscosity of this par- 
ticular gas kinematically measured by multiplying by 175435. 
When salt-solution diffuses, it is not the salt, but the salt- 
solution, which diffuses into water. The more dilute the solution, 
the nearer that state is approached in which pure water diffuses 
into pure water. How near I have approached this state in my 
experiments with nigrosin I have no means at present to judge. 
I have no doubt however that this is the only method of ascer- 
taining the coefficient, which, if once determined in similar 
manner for every fluid, will be of eminent importance to a 
kinetic theory of fluids, which has yet to be built up. It is 
only necessary to bear in mind the assistance rendered to Max- 
well by the determination of the coefficients of diffusion of gases 
by Loschmidt. S. WROBLEWSKI 
THE ROTATIONAL CO-EFFICIENT IN 
VARIOUS METALS 
‘THE following is an abstract of: a Note on the above subject 
read by Prof. E. H. Hall at the meeting of the British 
Association at York. 
Tt was discovered two years ago in Johns Hopkins University 
that when a conductor carrying a current is placed in a magnetic 
field, the direction of whose force is perpendicular to the current, 
the current is deflected at right angles to the force and to the 
original direction of the current. A slip of gold leaf on glass 
was placed between the poles of Faraday’s electro-magnet, with 
the faces of the gold-leaf perpendicular to the lines of force. 
Wires were attached one at each end of the strip, for the pur- 
pose of transmitting a current through it, and two other wires 
were led from the middle points of the sides of the strip toa 
Thomson’s galvanometer. When the electro-magnet was not 
made this galvanometer showed no deflection, but on sending a 
current through the coil of the electro-magnet a deflection was 
obtained, and on reversing the direction of this current the 
deflection was reversed. ‘ 
Dr. Hopkinson has pointed out that Maxwell, in the first part 
of his book, treating this subject in the most general way, allows 
the possibility that something of this kind may take place. 
Maxwell suggests the name ‘‘rotational coefficient” ; so the 
j 
i 
d 
’ 
