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' Ztschr.f. ■phyRikal. Chem., Leipzig, 1887, VA. i. S. 631.



OSMOSIS. 269

Blagden ^ discovered the fact that the freezing-point of a solution is
lower than that of the solvent, and that the lowering of freezing-point
is proportional to the concentration of the solution. Eiidorff,^ Coppet/^'
and Eaoult '^ have since more thoroughly investigated the matter. If,
therefore, we know the lowering of the freezing-point of water, produced by
the addition of a gramme-molecule to the litre (1°"<S9 C), and the osmotic
(or gas) pressure at 0' C. corresponding to this (22'35 atmospheres), it is
merely a matter of simple proportion to calculate the pressure at 0° C.
corresponding to any given lowering of freezing-point, and from that to
obtain the pressure at any other temperature by the law of Charles.

Many pieces of apparatus have been devised for measuring the
lowering of the freezing-point, but that of Beckmann ^ is in most
general use. Unfortunately, the method does not yield concordant
results in the hands of different observers (when aqueous solutions
are used) within about 005° C, which corresponds to an osmotic pressure
of about 50 mm. of mercury at the temperature of the body (37° C), and
is hence of little value for the correct estimation of small differences of
osmotic pressure in the aqueous solutions to which the physiologist
confines his attention.''

An optical method has been used by Tamman.'' If a drop of
solution of potassium ferrocyanide is allowed to fall into a solution
of copper sulphate, a so-called " Traube cell " is formed, the ferrocyanide
solution within which is separated from the copper sulphate solution
outside by a precipitation membrane of copper ferrocyanide, through
which osmotic interchange can take place.

If the internal solution be of higher osmotic pressure than the
external, water passes from the copper solution outside into the
cell, and the copper solution immediately round about the cell, being
raised in concentration, tends to sink. In the reverse case, by dilution
of the layer round the cell, an upward current is started. There are
thus produced differences in the refractive index of the layer of solution
against the outside of the cell, in contrast to the rest of the copper
solution. These are easily detected by the Topler Schlierena'pi^arat}
If the ferrocyanide solution have the same osmotic pressure as the
copper solution, no schlieren will be produced, and there will be no
change in refraction. Now, since the total osmotic pressure is the sum
of the partial pressures, a third substance, not reacting with the
membranogens, may be added to the solution of one of them, and the
concentration of the other, isosmotic with the mixture, determined by the
method. Since the osmotic pressure of the solution of the mem-
branogens, to which the third substance was added, is directly
measurable, it is obvious that the partial pressure of the added
substance can be measured.

'^ Phil. Trans., London, 1788, vol. Ixxviii. p. 277.

- Ann. d. Phys. u. Chem., Leipzig, 1861, Bd. cxiv. S. 63 ; 1862, Bd. cxvi. S. 55 ; 1871,
Bd._^ cxlv. S. 599.

^ Ann. de chim., Paris, 1871, Ser. 4, tome xxiii. p. 366 ; 1872, tome, xxv. p. 502 ; 1872,
tome xxvi. p. 98.

'^Ibid., Paris, 1884, S^r. 6, tome ii. p. 66; ComjM. rend. Acad. d. sc, Paris, 1882,
tome xcv. p. 1030.

^ Ztsclir . f . liJiysikal. Chem., Leipzig, 1888, Bd. ii. S. 638.

'^ Loomis, Ann. d. Phys. u. Chem., Leipzig, 1894, Bd. Ii. S. 500; Jones, Ztschr. f.
•physikal. Chem., Leipzig, 1893, Bd. xi. S. 110 ; Raoult, ibid., 1892, Bd. ix. S. 343.

"^ Ztschr. f. physikal. Chem., Leipzig, 1888, Bd. ii. S. 415.

^ Ann. d. Phys. u. Chem., Leipzig, 1867, Bd. exxxi. S. 33.



2 70 DIFFUSION, OSMOSIS, AND FILTRATION.

Physiological methods of estimating osmotic pressure have also been
devised. The method of de Aeries ^ is based upon the plasmolysis of the
protoplasts of vegetable cells. The cells filled with coloured sap from
the middle nervure of the leaf of Trculescantia discolor are useful
for the purpose, sections of this part being allowed to soak for three to
five hours in the solutions whose osmotic pressures are to be determined.
If the cells are plasmolysed, i.e. if the protoplasts are found on
examination to have shrunk from the cell walls, the osmotic pressure
of the solution producing this effect is above that of the cell sap, for
water has passed from the latter to the former, as evidenced by the
diminution in volume. By investigating a series of solutions with
sections from the same leaf, it is of course possible to find two of
slightly differing concentration of the suljstance under investigation,
one of which just causes plasmolysis, while the other (weaker) does
not. A solution of concentration equal to the mean of these two is
said to be isotonic with the cell sap.

De Vries, on preparing a number of solutions of different substances,
all isotonic with the same batch of cells, and expressing their
concentrations in gramme-molecules to the litre, found that it required
a lower gramme -molecular concentration of some substances than of
others to obtain isotony. The term " water extracting power "
( Wasseranziehungsvcrmogeii) was used to express this peculiarity which
is obviously related to what has above been termed dissociation.
Taking O'l grm. molecule to the litre of saltpetre as a standard, and
giving it a magnitude of 3, the relative value (as regards plasmolysis
of vegetable cells) of a. molecule of a number of substances was
expressed in terms of that of a molecule of saltpetre, and the numbers
expressing this ratio called isotonic coefficients of the substances.

Thus, to barium chloride (BaCla + 2Aq = 244) is given the
isotonic coefficient 4, which means that f244 parts by weight of
barium chloride in aqueous solution exert the same plasmolysing
action as 101(KNO3= 101) parts by weight of saltpetre i.e. a 1'83
per cent, solution of crystallised barium chloride is isotonic by the
method, with a I'Ol per cent, solution of potassiiun nitrate.

Since cane sugar on this system is given the value of 2 for its
isotonic coefficient, and since, being a non-electrolyte, it is not
dissociated in solution, it is merely necessary to divide the isotonic
coefficients of de Vries by 2, in order to obtain ordinary dissociation
coefficients.

It is obvious that the substances in solution must exert no
deleterious action on the protoplast of the cell, and must, moreover,
be quite unable to diffuse through it, if the method is to be exact.

Here, again, we are met with the difficulty, that the protoplast is
not a strictly semipermeable membrane. It must let certain substances
pass, otherwise the cell sap could not have any other constituent than
water ; and it is only because the permeal)ility to certain sul:)stances is
so far below that to water, that it is possible to obtain fairly approximate
measures of osmotic pressure by this method. With other sul^stances
the permeability is so great that the values are far too low.

Thus with sodium cliloride, by this method, the dissociation coefficient
is reckoned as 1"5 (de Vries' isotonic coefficient 3), but by lowering of

^ Jahrh f. wiss. Bolanik, 1884, Bd. xiv. S. 427; Ztscltr. f. phyHikal. Chcm., Leipzig,
1888, Bd. ii'. S. 415.



OSMOSIS. 271

freezing-point method, it is found to be higher (about 1'89). Other
indices of " isotony " than the plasmolysis of tlie vegetable cell have
been used by physiologists.

Hamburger ^ has used red blood corpuscles. If these are placed
in solutions of substances which do not penetrate, and which do not
act chemically upon them, an index of the entrance of water into
the substance of the corpuscle is presented by the setting free of
haemoglobin, which is recognisable in the solution. In a solution of lower
osmotic pressure than the corpuscle-contents (hypoisotonic solution),
water enters the corpuscles and the solution is reddened. In a solution
of higher osmotic pressure than the contents (hyperisotonic solution),
water is extracted from the corpuscles, they shrivel and sink, and the
solution retains its original colour. Two limiting solutions are thus
obtainable, and the mean concentration of the two is taken as that
isosmotic with the contents of the corpuscle.

The method has very considerable limits in practice, for not only
is it obviously restricted to colourless solutions, but it can also only
give results approaching the truth, in cases where the substance in
solution does not penetrate ; and, as indicated by Gryns,'^ who has
criticised the method very severely, the red corpuscles are penetrable
by a very large number of substances.'^

Another blood corpuscle method is that of the hsematokrit.* Here
the gauge of entrance or exit of water from the corpuscles is the volume
they occupy, in a graduated capillary tube, after having been centrifu-
galised with the solution. The volume of the corpuscles is dependent
on the osmotic pressure of the solution in which they are placed (provided
the dissolved substance does not penetrate), and if equal volumes of the
same blood specimen, contemporaneously centrif ugalised in two solutions
of different substances, give the same volume of corpuscles, those solutions
have the same osmotic pressure. By centrifugalising a given volume
of a blood sample in a series of solutions of a substance not jDenetrating
corpuscles (cane sugar), of different and known osmotic pressure, in
separate tubes, at the same time as an equal volume of the same blood
treated with the solution of the substance to be investigated, a final
comparison of the length of the " threads " of corpuscles in the tubes
gives a gauge of the osmotic pressure of the solution.

By centrifugalising blood in a pipette, previously oiled (cedar oil)
to prevent clotting, measuring the length of the " thread," and
comparing with the same, blood treated with sugar solutions of known
osmotic pressure, the pressure of the plasma is determinable and is
found to vary, rising after meals, and especially after the ingestion
of solutions of salt (Koeppe).

A bacterial method even has been used by Wladimiroff,-^ who has

^ Arch. f. Anat. u. Physiol.,^ Leipzig, 1SS6, Phys. Abth., S. 476; 1887. S. 31;
Ztschr.f. physikal. Chem., Leipzig, 1890, Bd. vi. S. 319.

■■^ Arch./, d. ges. Physiol., Bonn, 1896, Bd. L-ciii. S. 86.

^Hanibui-ger liimself {Ztschr. f. lohysikal. Chem., Leipzig, 1890, Bd. vi. S. 319)
maintained tliat permeability did not affect liis method, since, by a "vital act"
(" Lebenserscheinung"), S. 331, the corpuscles give up to the solution from their juice
an amount of some other substance exactly equivalent to that Avhich pienetrates from
without, so that the total osmotic pressure of the juice is unaltered !

■^Hedin, Skandin. Arch. f. Physiol., Leipzig, 1890 ; Gaertner, Berl. klin. Wchnsdir.,
1892, Bd. xxix. S. 36 ; Koeppe, Arch. f. Physiol., Leip/;ig, 1895, S. 154 ; Arch. f. d. ges.
Physiol., Bonn, 1896, Bd. Ixii. S. 567 ; Munchen. med. JVchnschr. , 1893, No. 24.

^ Ztschr. f. 2}hysikal. Chem., Leipzig, 1891, Bd. vii. S. 529.



2 72 DIFFUSION, OSMOSIS, AND FIITRATION.

maintained that cessation of motion of bacteria placed in solutions
indicates that the solution is isosmotic with the cell sap, in cases
where poisonous action can be excluded.

The above physiological methods of measuring osmotic pressure are
of considerable interest, but, as already stated, their application is
decidedly limited ; and though, as will appear below, often of indirect
value, as giving information bearing on the permeability of cells and
membranes, they are not to be classed with the more accurate methods
of experimental physics.

In the case of colloid solutions, it is not necessary to use pre-
cipitation membranes for the direct measurement of osmotic pressure,
for such material as vegetable parchment is, as a rule, impermeable to
colloids, and it moreover presents certain advantages in particular
cases, namely, those in which the colloidal substance is contaminated
by salts {e.g. albuminous solutions), since the salts can pass out, and
the determination is freer from the error of inclusion of the partial
pressure of these, unavoidable by a direct measurement by a copper
ferrocyanide membrane, or an indirect determination by lowering of
freezing-point.

It is known that solutions of colloids of considerable concentration
exert very low osmotic pressure, though their exact measurement is
difficult. Picton and Linder,i in a direct measurement (by a copper
ferrocyanide membrane) of the pressure of a 4 per cent, solution
of colloidal arsenious sulphide, obtained a pressure of only 17 mm. of
water. Sabanejew ^ states that the lowering of freezing-point by silicic
acid is so small as to be within the limits of the method. With
albuminous solutions the difficulty of contaminating salts is almost
insuperable, and since the molecular weight of albumin is not known,
calculation is excluded.

Sabanejew ^ investigated the lowering of freezing-point of water by
solution of egg albumin, and quotes a lowering of '02° C. for a 15"6 per
cent, solution, and "042° C. for a 30'35 per cent, solution, but since the
specimens held "4 to '6 6 per cent, of ash, the numbers are of no value.
Tamman* gives the difference in lowering of freezing-point of horses'
serum, produced by coagulation of the proteids by heat and removing
them, as only '006° C, which is in the region of the error of the method.^
Dreser^ and Koeppe'^ also state that the removal of proteid from
albuminous solutions does not affect the osmotic pressure, while
Liideking^ maintains that the boiling point of 40 per cent, solution
of gelatin is 100° C.^ It is therefore uncertain whetlier proteids in

'^ Jour 11. Chem. Soc, London, 1895, vol. Ixvii. p. 63.

- Be7'. d. deutsch. chem. Gcsellsch., Berlin, 1890, Bd. xxiii. S. 87.

'^Ihid., 1891, Bd. xxiv. S. 558.

^ Ztschr. f. physikal. Chem., Leipzig, 1896, Bd. xx. S. 180.

■■^ Starling, on the other hand, quotes two experiments to prove that the osmotic
pressure of the proteids of serum can be directly measured. It is stated to be from 30 to
40 mm. of Hg. Journ. Physiol., Cambridge and London, 1895, vol. xix. p. 323. Cf. also
next article, p. 308.

^ Arch. f. exper. Path. u. PharmakoL, Leipzig, 1892, Bd. xxix. S. 314.

"^ Arch. f. d. ges. Physiol., Bonn, 1896, Bd. Ixii. S. 571 (footnote).

^ Ann. d. Phys. u. Chem., Leipzig, 1888, Bd. xxxv. S. 552.

^ A lowering of vapour pressure (raising of boiling point) is produced by solution
of a substance in a solvent, and the lowering of vapour pressure, like that of the
freezing-point, is pro]>ortional to the concentration. WilUner, Ann. d. Phys. u. Chem.,
Leipzig, 1858, Bd. ciii. S. 529 ; 1858, Bd. cv. S. 85 ; 1860, Bd. ex. S. 564 ; Taniman,
Ann. d. Phys. u. Chem., Leipzig, 1888, Bd. xxxiv. S. 299.



OSMOSIS. 273

colloidal solution exert an osmotic pressure capable of measurement
by our present methods.

From the above account of osmotic pressure, it is evident that,
since it is present in high or low degree in all true solutions, as a result
of the kinetic energy of the dissolved molecules, the phenomena of
diffusion are most satisfactorily accounted for as directly dependent
on the osmotic pressure exerted by the diffusing substance.^ Substances
diffuse from places of higher to those of lower partial pressure, and
the differences in rapidity of diffusion of different substances, though
present in concentrations exerting the same osmotic pressure, must be
accounted for by differences in the resistance met in their passage
among the molecules of the solvent.

When we now turn to the consideration of the interchange of the
constituents of solutions through animal membranes, we at once find
that, since these membranes are never strictly semipermeable, and are
frequently very permeable for dissolved substances, the phenomena are
neither those of pure osmose nor pure diffusion, but a complex of
the two, in which the relative permeability of the membrane to solvent
and dissolved substance is of paramount importance, but, unfortunately,
a variable factor with different membranes.^ All the earher work upon
osmosis was carried out with membranes not fulfilling the condition of
semipermeability, so that a double stream of solvent into solution
(endosmose) and dissolved substance into solvent (exosmose) was con-
sidered as a necessary feature of the process until Traube's discovery of
precipitation membranes.

The first osmose experiment was probably that of the Abbe JSToUet,^
in which it was observed that a bladder tied over a vessel of spirits of
wine became distended, or even burst, when vessel and membrane were
under water. Parrot^ again called attention to the fact, which
had been forgotten, and ascribed the process to " affinity of the first
order," which causes all miscible fluids to " wander " into one another.
Fischer^ in Grermany and Dutrochet^ in France again rediscovered
the prime fact, and commenced its systematic study. Certainly the
main stimulus to subsequent study of the phenomena was given
by the work of Dutrochet.'' Dutrochet's endosmometer was a funnel
closed by membrane and provided with a long stem. The body
of the funnel was filled with the solution, and the whole immersed
in water. The height to which the fluid rose in the stem was the
gauge of the osmotic action of the solution. Dutrochet recognised
that the concentration of the solution and the temperature affected
the results.

Vierordt ^ improved upon the arrangement used by Dutrochet, by
setting the membrane vertical and the stem horizontal, so that filtration
error was avoided, and also concluded that the stream of water into the

1 Nernst, Ztschr. f. pliysikal. Chem., Leipzig, 1888, Bd. ii. S. 611.

" In this connection see a paper by Lazarus Barlow, Journ, Physiol., Cambriclge and
London, 1895, vol. xix. p. 140.

^ " Histoire de I'Academie royale des sciences," 1748, p. 101.

* Ann. d. Pliys. u. Clvejn., Leipzig, 1815, Bd. li. S. 318.

^Ibid., 1822, Bd. Ixxii. S. 300.

^ Ann. de chim., Paris, 1827, tome xxxv. p. 393 ; "Agent immediat dn mouvement
vital," Paris, 1826.

^ See also ' ' Memoires pour servir a, I'histoire anatomique et physiologique des vegetans
et des animaux, " Bruxelles, 1837.

^ Ann. d. Phys. u. Chem., Leipzig, 1848, Bd. Ixxiii. S. 519.

VOL. I. — 18



^74 DIFFUSION, OSMOSIS, AND FIITRATION.

funnel was proportional to the difference of concentration of the solu-
tions on either side of the membrane.

Jolly ^ specially studied the ratio between the amount of water
passing into the solution and the amount of dissolved substance passing
out, using salts with pig's bladder as membrane. This ratio he termed
the endosmotic equivalent of the salt, and maintained that it is constant
for the same membrane, concentration of the salt solution, and tem-
perature. For some years after this the whole attention of those interested
in the matter of osmosis was directed to a fuller study of this ratio in
the case of different substances.^

As a result of these researches, it was seen that even with the same
membrane it was only within slight changes of concentration of the
solution that constancy of the endosmotic equivalent was obtainable, a
result in accordance with expectation, seeing that the physical nature of
an animal membrane must necessarily undergo change with the amount
of water imbibed, a quantity variable with the concentration of the solu-
tions in which it is in contact. With a strictly semipermeable membrane,
the endosmotic equivalent is evidently infinite, while the more permeable
the membrane to dissolved substance the lower will be the equivalent
Thus, according to Harzer,^ the endosmotic equivalent for sodium chloride
is with fish-swim-bladder, 2-9 ; ox-]3ericardium, 4-0 ; ox-bladder, 6 •4.

It must therefore be admitted that, in spite of the great labour that
has been expended on the determination of endosmotic equivalents of
different substances with different membranes, the results obtained are
of little value to the practical physiologist, who deals with membranes
in the living body, whose physical characters are by no means necessarily
those of the structures used in such experiments. The only value that can
be attached to these determinations is an orienting one, as to the diffusi-
bility of the substances into water, through dead animal membranes,
under the conditions of the experiments.

Before we can attempt to answer the question. How is the process of
diffusion modified when in an osmose experiment an animal membrane
is placed between solution and solvent ? it is obviously necessary to
know the physical structure of the membrane. Of this we must admit
great ignorance. To Briicke-* we owe a theory of "pore diffusion."
Assuming capillary pores in the membrane, it maintains that, by
attraction, a layer of pure water lines these, while an axis of salt solu-
tion, whose concentration falls from axis to mantle of the cyhndrical
pore, lies centrally. The highest concentration in the axis must be that
of the salt solution in the experiment, and along the axis ordinary
hydrodiffusion takes place, water entering the salt solution and salt
entering the water. Along the mantle, however, only water can pass
into the salt solution, so that the stream of water exceeds that of salt.
If the pores are very narrow, it is conceivable that there is no central
core of salt solution, in fact the membrane becomes semipermeable.

1 Ztschr. f. rat. Med., 1849, Bd. vii. p. S3 ; Ann. d. Phys. u. Chem., Leipzig, 1849,
Bd. Ixxviii. S. 261.

2 Fick, Untersuch. z. Naturl. d. Mensch. u. d. Thiere, 1857, Bd. iii. S. 294 ; W. Sclimidt,
Ann. d. Phys. u. Chem., Leipzig, 1857, Bd. cii. S. 122 ; Beitr. z. Anat. u. Physiol.
{Eckhard), Giesseu, 1855, Bd. i. S. 97 ; 1860, Bd. ii. S. 1, 31, 147 ; Hoffmann, ihid.,
1860, Bd. ii. S. 59.

^ Arch, f.jjh-ysiol. Heilk., Stuttgart, 1856, Bd. xv. S. 194.

■* " De ditiusioiie liunioruin ])er septa niortua et viva," Berlin, 1842 ; Ann. d. Phys, m.
Chcm., Leipzig, 1843, Bd. Iviii. S. 77.



OSMOSIS. 275

The attraction of the substance of the membrane for water, at any
rate, may then be a factor in the case. Ludwig ^ demonstrated, indeed,
that the concentration of the solution imbibed by an animal membrane
may be lower than that of the solution in which it is soaked.

Tick 2 distinguished between two possibilities for diffusion through an
animal membrane — a " pore diffusion " in Brlicke's sense, and a
diffusion occurring through the spaces between the molecular aggregates
of which the membrane may be considered to be built. The latter idea
is somewhat of the nature of that formed of the diffusion of a gas
through a film of liquid in which it is soluble, or is perhaps better
illustrated in the experiment of L'Hermite/^ in which, when water
separates chloroform from ether in a tube, the chloroform increases at
the expense of the ether. Fick's " homogeneous " membranes were
made of collodion ; but his results show that such a membrane is not
unalterable, since the amount of salt passing through increases with
time, and it is difficult to escape the conclusion that in many cases
some interaction of chemical nature takes place between the membrane
and the substances to which it is permeable.^

The property possessed by certain substances of imbibing certain Kquids
(apart from capillary action), must be borne in mind in all considerations of the
essential nature of the processes involved in the passage of fluids through
membranes. This property can only be ascribed to some '' affinity " between
the molecules of the imbibing substance and that imbibed; thus gelatin
swells in water but not in ether, while the reverse is true of caoutchouc. The
retention of a gas, or a colouring matter by charcoal, of water by the silica
of the opal, or that of pepsin by fibrin, are instances of the class of phenomena
to which attention is here called, and to which the name of adsorption is often,
applied. When a homogeneous substance imbibes a solution, compounds of
the imbibed with the imbibing substance may be formed, which may have a
greater affinity for the solvent than the original imbibing substance, but at the
same time the osmotic pressure of the solution tends to retard the imbibition
of the solvent; hence, with a given pair of substances, the amount of the
solution of one taken up by the other will reach a maximum at a certain con-
centration, a maximum, however, which may be well above that for imbibition
of the pure solvent.

The "affinity" of the imbibing substance for the solvent and dissolved



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