254 
NATURE 
[JANUARY 14, 1897 
are accordingly difficult to follow. Perhaps this remark 
applies especially to his treatment of the central theorem, 
viz. the identification of the osmotic pressure of a dis- 
solved gas with the pressure which would be exercised 
by the gas alone if it occupied the same total volume in 
the absence of the solvent. From this follows the formal 
extension of Avogadro’s law to the osmotic pressure of 
dissolved gases, and thence bya natural hypothesis to the 
osmotic pressure of other dissolved substances, even 
although they may not be capable of existing in the 
gaseous condition. If I suggest a somewhat modified 
treatment, it is not that I see any unsoundness in van 
t Hoffs argument, but because of the importance of 
regarding a matter of this kind from various points of 
view. 
Let us suppose that we have to deal with an involatile 
liquid solvent, and that its volume, at the constant tem- 
perature of our operations, is unaltered by the dissolved 
gas—a question to which we shall return. We start with 
a volume v of gas under pressure #y, and with a volume 
V of liquid just sufficient to dissolve the gas under the 
same pressure, and we propose to find what amount of 
work (positive or negative) must be done in order to bring 
the gas into solution reversibly. If we bring the gas 
at pressure Zp) Into contact with the liquid, solution 
takes place irreversibly, but this difficulty may be over- 
come by a.method which I employed for a similar purpose 
many years ago.!. We begin by expanding the gas until 
its rarity is such that no sensible dissipation of energy 
occurs when contact with the liquid is established. The 
gas is then compressed and solution progresses under 
rising pressure until just as the gas disappears the 
pressure rises to fy. The operations are to be conducted 
at constant temperature. and so slowly that the condition 
never deviates sensibly from that of equilibrium. The 
process is accordingly reversible. 
In order to calculate the amount of work involved in 
accordance with the laws of Boyle and Henry, we may 
conveniently imagine the liquid and gas to be confined 
under a piston in a cylinder of unit cross-section. During 
the first stage contact is prevented by a partition inserted 
at the surface of the liquid. If the distance of the piston 
from this surface be x, we have initially x=v. At any 
stage of the expansion (7) the pressure # is given by 
~=fou/x, and the work gained during the expansion is 
represented by 
ahs 
Pe’ | Ler 
x being a very large multiple of v. During the con- 
densation, after the partition has been removed, the pres- 
sure upon the piston in a given position -r is less than 
before. For the gas which was previously confined to 
the space x is now partly in solution. If s denote the 
solubility, the available volume is practically increased 
in the ratio x : x + sV, so that the pressure in position + 
is now given by 
B= pul +sV), 
and the work required to be done during the com- 
pression 1s 
= po log 
rz dx 1 t+SV 
Po a a+sV eae: sV 
On the whole the work lost during the double opera- 
tion is 
SV uv ) 
Dov log ~~ + log - ae 
and of this the first part must be omitted, as + is indefin- 
itely great. As regards the second part, we see that it is 
zero, since by supposition the quantity of liquid is such 
as to be just capable of dissolving the gas, so that sV=v. 
The conclusion then is that, upon the whole, there is no 
1 “On the Work that may be gained during the Mixing of Gases,’ Phi. 
Mag. vol. xlix. p. 311, 1875. 
0. 1420, VOL. 55] 
gain or loss of work in passing reversibly from the initial 
to the final state of things. 
The remainder of the cycle, in which the gas is 
removed from solution and restored to its original state, 
may now be effected by the osmotic process of van 
 Hoff.t For this purpose one “‘semi-permeable mem- 
brane,” permeable to gas but not to liquid, is introduced 
just under the piston which rests at the surface of the 
liquid. A second, permeable to liquid but not to gas, is 
substituted as a piston for the bottom of the cylinder, and 
may be backed upon its lower side by pure solvent. By 
suitable proportional motions of the two pistons, the 
upper one being raised through the space v, and the 
lower through the space V, the gas may be expelled, the 
pressure of the gas retaining the constant value Zo, and 
the liquid (which has not yet been expelled) retaining a 
constant strength, and therefore a constant osmotic 
pressure P. When the expulsion is complete, the work 
done upon the lower piston is PV, and that recovered 
from the gas is Zyv, upon the whole PV-f wv. Since 
this process, as well as the first, is reversible, and since 
the whole cycle has been conducted at constant tempera- 
ture, it follows from the secozd law of thermo-dynamics 
that no work is lost or gained during the cycle, or that 
=p: 
The osmotic pressure P is thus determined, and it is 
evident that its value is that of the pressure which the 
gas, as a gas, would exert in space V. 
The objection may perhaps be taken that the assump- 
tion of unaltered volume of the liquid as the gas dissolves 
in it unduly limits the application of the argument. It 
is true that when finite pressures are in question, an 
expansion (or contraction) of the liquid would complicate 
the results ; but we are concerned only, or at any rate 
primarily, with the osmotic pressure of @/u¢e solutions. 
In this case the complications spoken of relate only to 
the second order of small quantities, and in our theory 
are accordingly to be dismissed. 
January 8. RAYLEIGH. 
THE BOG-SLIDE OF KNOCKNAGEEHA,. IN 
THE COUNTY OF KERRY. 
T about three a.m. on Monday, December 28, 1896, 
a catastrophe occurred some twelve miles north- 
east of Killarney, of which mention has been already 
made in these columns (NATURE, vol. lv. p. 205). A 
bog gave way at its lower edge, and precipitated itself as 
a black peaty flood into the valley of the Ownacree 
River. In the upper part of its course it unfortunately 
overwhelmed the cottage of Cornelius Donnelly, carrying 
away the structure and its eight occupants. Five of the 
bodies were recovered, with considerable difficulty, by 
January 3, when the mass had come practically to a 
standstill. In the lower part of its course, it flooded a 
number of farm-lands upon the slopes of the valley, and 
seriously threatened the cottage of Jeremiah Lyne, rising 
some five feet against its wall. Even at the junction of 
the Ownacree and the Flesk, one of the great feeders of 
the Lower Lake of Killarney, the banks were smeared 
over with a peaty mud, ten miles from the point of 
origin of the bog-slide ; while a quantity of the material. 
was carried another nine miles west into the Lower Lake 
itself. 
While the first accounts of the disaster were naturally 
exaggerated, and even contradictory, coming as they did 
from places on opposite sides of the peaty watershed, 
an inspection of the area leaves no doubt as to 
the magnitude of the bog-slide. Such phenomena 
are not unknown in Ireland, one being recorded 
from the County of Galway in 1745, and another 
1 Phil. Mag., vol. xxvi. p. 88, 1888. 
