272 
fish, &c., I cannot help thinking that Lilienthal’s central and 
superposed aeroplanes were a mistake ; and that instead of that 
type, while the weight must be central, the sustaining aeroplanes 
should, like the birds, have great lateral extension. 
You will observe in the diagram that the wing planes can each 
be divided into two portions, having quite distinct functions. 
The outer extremities are the sustaining aeroplanes, marked by 
the arrows, while the inner portion of each wing, A to W, is 
that which assists the bird when it is alighting, by offering a 
fixed passive resistance to a fall when the speed is slackened 
down. W is the central weight. 
—— 
— 
faa 
rF : 
— 
= 
— 
ss 
Observe also that in the bird, the sustaining mechanism is 
so far structurally subdivided that the loss of a primary feather 
is not fatal to flight ; each primary lies, and acts, in a distinct 
plane, and has its attachment distinct from the others. 
Now, it seems to me that Mr. Maxim’s central aeroplane and 
twin screws, situated so far apart, are hardly a safe plan, for if 
accident happen to one screw, the other must at once stop, and 
the whole thing, zo/ens volens, come down. 
It is not like the twin-screw steamer, where the water sus- 
tains the hull, and progress by one screw is still possible. In 
the aerial ship translation is the support, and it only. 
In the bird, when sailing, we see no screw at work: the 
aeroplanes are there plain enough, lifting the 16-pound bird 
higher and higher as we watch it; but propeller there is none. 
This propulsion, as I before stated, must be got from an out- 
side source. The bird can only soar 27 a wznd, and then, to rise, 
must go in spirals, passing to leeward a little at each lap. Of 
course the wing planes are not horizontal, but inclined thus in 
passing round the centre of spiral C ; and there is necessarily 
great centripetal reaction at such a high speed of translation 
as fifty or sixty miles per hour. 
I think Mr. Maxim will find the bird arrangement of aero- 
planes to weight, and a central screw, the best and safest. Ifa 
large central overhead aeroplane is needed, it would be for 
safety in alighting only. S. E. PEAL. 
Sibsagar, Asam, December 13, 1896. 
OSMOTIC PRESSURE. 
N last week’s NaTuRR, Lord Rayleigh gave, for an 
tnvolatile liguid, a rigorous and clear proof of “the 
Central Theorem” of osmotics. But this theorem, though 
highly interesting in itself, is not, so faras I can see, 
useful as a guide for experiment. Consider for example 
the typical cases of sugar, and of common salt, dissolved 
in water. 
Tf water were absolutely non-volatile, the osmotic pres- 
sure of eachsolution against anideal semi-permeable mem- 
brane separating it from pure water, would, according to 
the theorem, be equal to the calculable pressure of the 
ideal gas of the dissolved substance supposed alone in 
the space occupied by the solution. Zhzs would be true 
whatever be the molecular grouping of the sugar or of 
the saltin the solution. It is believed that experiment 
has verified the theorem, extended to volatile solvents, 
as approximately true for sugar and several other sub- 
stances of organic origin, and of highly complex atomic 
NO. 1421, VOL. 55] 
WATRORE 
[ JANUARY 21, 1897 
structure ; but has proved it to vastly under-estimate the 
osmotic pressure for common salt. and many other sub- 
stances of similarly simple composition. KELVIN. 
Belfast, January 19. 
ON OSMOTIC PRESSURE AGAINST AN IDEAL SEMI- 
PERMEABLE MEMBRANE.! 
To approach the subject of osmotic pressure against 
an ideal impermeable membrane by the easiest 
way, consider first a vessel filled with any particular 
fluid divided into two parts, A and B, by an ideal sur- 
face, MM. Let a certain number of individual mole- 
cules of the fluid in A, any one of which we shall call 
D (the dissolved substance), be endowed with the property 
that they cannot cross the surface M M (the semi-permeable 
membrane) ; but let them continue to be in other respects 
exactly similar to every other molecule 
of the fluid in A, and to all the mole- 
cules of the fluid in B, any one of 
which we shall call S (the solvent), 
each of which can freely cross the 
membrane. Suppose now the con- 
taining vessel and the dividing mem- 
brane all perfectly rigid.* Let the 
apparatus be left to itself for so long 
time that no further change is _per- 
ceptible in the progress towards final 
equilibrium of temperature and pres- 
sure. The pressures in A and B will 
be exactly the same as they would 
be with the same densities of the 
fluid if MM were perfectly imperme- 
able, and all the molecules of the 
fluid were homogeneous in all quali- 
ties ; and MM will be pressed on one 
side only, the side next A, with a 
force equal to the excess of the 
pressure in A above the pressure in 
B, and due solely to the impacts of 
D molecules striking it and rebounding 
from it. 
If now, for a moment, we suppose 
the fluid to be “perfect gas,” we should 
find the pressure on MM to be equal 
to that which would be produced ,by 
the D molecules if they were alone in 
the space A ; and this is, in fact, very 
approximately what the osmotic pres- 
sure would be with two ordinary 
gases at moderate pressures, one of 
which is confined to the space A by 
a membrane freely permeable by the 
other. On this supposition the number 
of the S molecules per unit bulk would be the same on 
the two sides of the membrane. And if, for example, 
there are 1000 S molecules to one D molecule in the 
space A, the pressure on the piston P would be too! 
times the osmotic pressure, and on Q 1000 times the 
osmotic pressure. But if the fluid be “liquid” on both 
sides of the membrane, we may annul the pressure on Q 
and reduce the pressure on P to equality with the 
osmotic pressure, by placing the apparatus under the 
receiver of an air-pump, or by pulling Q outwards 
with a force equal and opposite to the atmospheric 
pressure on it. When we do this, the annulment of 
the integral pressure of the liquid on the piston Q is 
effected through balancing by attraction, of pressure due 
SSS 
NNSA AAA 
: ; 
1 Communicated to the Royal Society of Edinburgh, January 18, by Lord 
Kelvin. 
2 In the drawing, the vessel is represented by a cylinder closed at each 
end by a pistonito facilitate the consideration of what will happen if, instead 
of supposing it rigid, any arbitrary condition as to the pressures on the two 
sides of the membrane be imposed. 
