Cryoscopy.—The usual method employed for the determination of the molecular concentration and osmotic pressure of a solution is by cryoscopy—the measurement of its temperature of congelation. A very sensitive thermometer is used, the scale of which extends over only 5° and is divided into hundredths of a degree. The liquid under examination is placed in a test tube, in which the bulb of the thermometer is plunged, and this is supported in a second tube with an air space all round it. The whole is then suspended to the under side of the cover of the refrigerating vessel, which may be cooled either by filling it with a freezing mixture, or by the evaporation of ether. During the whole of the operation the liquid is agitated by a mechanical stirrer. The first step is to determine the freezing point of distilled water. As the water cools the mercury gradually descends in the stem of the thermometer till it reaches a point below the zero mark at 0° C. As soon as ice begins to form the mercury rises, at first rapidly and then more slowly, reaches a maximum, and finally descends again. This maximum reading is the true point of congelation. The inner tube is then emptied, care being taken to leave a few small ice crystals to serve as centres of congelation for the subsequent experiment, thus avoiding supercooling of the solution. The process is then repeated with the solution under examination. The difference between the two freezing points is the required "lowering of the freezing point."

Cryoscopy is the method most used in biological research to determine molecular concentration. It has, however, some grave defects. It necessitates several cubic centimetres of the liquid under examination. It gives us the constants of the solution at the temperature of freezing, which is far below that of life. Organic liquids are easily altered and are extremely sensible to minute differences of temperature, cryoscopy therefore gives us no information as to the constitution of solutions under normal conditions. It is desirable to have some other method of determining molecular concentration and the other interdependent constants at the normal temperature of life. A much better method, were it possible, would be the direct determination of the vapour tension of the solutions under normal conditions of temperature and pressure.

Molecular Lowering of the Freezing Point.—For every substance whose solution is not ionized and therefore does not conduct electricity, the lowering of the freezing point is the same, viz. 1.85° C. for each gramme-molecule of the solute per litre of the solution.

Determination of the Molecular Concentration.—In order to obtain the molecular concentration of a non-ionizable substance, we have only to determine the lowering of the freezing point. Let A be the lowering of the freezing point of any solution. On dividing it by 1.85 (the lowering of the freezing point for a normal solution), we obtain the number of gramme-molecules in a litre of the solution. If n be the number of gramme-molecules per litre, then n = A / 1.85.

Determination of the Osmotic Pressure.—The osmotic pressure P of a solution may be obtained by multiplying its molecular concentration n by 22.35 atmospheres. P = n × 22.35 = A / 1.85 × 22.35.

Determination of Molecular Weight.—The lowering of the freezing point also enables us to calculate the molecular weight of any non-ionizable solute. Thus Bouchard has been able to determine by means of cryoscopy the mean molecular weight of the substances eliminated by the urine. A weight x of the substance is dissolved in a litre of water, and the lowering of the freezing point is observed. The value thus found divided by 1.85 gives us n, the number of gramme-molecules per litre. The molecular weight M may be determined by dividing the original weight x by n.

The study of osmotic pressure was begun by the Abbé Nollet; and one of his disciples, Parrot, at an early date thus described its importance: "It is a force analogous in all respects to the mechanical forces, a force able to set matter in motion, or to act as a static force in producing pressure. It is this force which causes the circulation of heterogeneous matter in the liquids which serve as its vehicle. It is this force which produces those actions which escape our notice by their minuteness and bewilder us by their results. It is for the infinitely small particles of matter what gravitation is for heavy masses. It can displace matter in solution upwards against gravity as easily as downwards or in a horizontal direction."

Thus the recognition of the fact that a substance in solution is really a gas, has at a single stroke put us in possession of the laws of osmotic pressure—laws slowly and laboriously discovered by the long series of investigations on the pressure of gases.

Osmotic pressure plays a most important rôle in the arena of life. It is found at work in all the phenomena of life. When osmotic pressure fails, life itself ceases.

CHAPTER III

ELECTROLYTIC SOLUTIONS

Solutions which conduct Electricity.—The laws of solution which we have studied in the previous chapter apply only to those solutions, chiefly of organic origin, which do not conduct electricity. Solutions of electrolytes such as the ordinary salts, acids, and bases, which are ionized on solution, give values for the various constants of solution which do not accord with those required by theory. If, for instance, we take a gramme-molecule of an electrolyte such as chloride of sodium, and dissolve it in a litre of water, we find that the lowering of the freezing point is nearly double the theoretical value of 1.85°. The same holds good for the osmotic pressure, and for all the constants which are proportional to the molecular concentration of the solute. The solution behaves, in each case, as if it contained more than one gramme-molecule of sodium chloride per litre. It behaves, in fact, as if it contained i times the number of molecules of solute originally introduced into it. If n be the original number of molecules, then it will apparently contain n′ = in molecules. This law is universal for all electrolytic solutions; the theoretical value for their concentration, osmotic pressure, and all the proportional physical constants must be multiplied by this quantity, i = n′/n, which is the ratio of the apparent number of the molecules present to the number originally introduced.

A similar dissociation of the molecule is observed in the case of many gases. The vapour of chloride of ammonium, for instance, is decomposed by heat, and it may be shown experimentally that the increase of pressure on heating above that which theory demands, is due to an increase in the number of the gaseous molecules present. Some of the vapour particles are dissociated into two or more fragments, each of which plays the part of a single molecule.

Arrhenius, in 1885, advanced the hypothesis that the apparent increase in the number of molecules of an electrolytic solution was also due to dissociation. This interpretation at once threw a flood of light on a number of phenomena hitherto obscure.

Coefficient of Dissociation.—We have seen that in order to obtain values which accord with experiment we have to multiply the number of gramme-molecules of the solute by the coefficient i, which is called the Coefficient of Dissociation.

This coefficient of dissociation, i, may be found by observing the lowering of the freezing point of a normal solution, and dividing it by 1.85. i = t/1.85.

The coefficient of dissociation varies with the degree of concentration of the solution, rising to a maximum when the solution is sufficiently diluted.

If we know i, the coefficient of dissociation for a given solute, contained in a solution of a definite concentration, we can find n′, the number of particles present in a solution containing n gramme-molecules of the solute per litre, since n′ = in. On the other hand, if from a consideration of its freezing point and other constants we find that an electrolytic solution appears to contain n′ gramme-molecules per litre, the real number of chemical gramme-molecules in one litre of the solution will be only n′ / i = n.

Very concentrated solutions do not conform to these laws. In this they resemble gases, which as they approach their point of condensation tend less and less to conform to the laws of gaseous pressure.

Electrolysis.—If we take a solution of an acid, a salt, or a base, and dip into it two metallic rods, one connected to the positive and the other to the negative pole of a battery, we find that the metals or metallic radicals of the solution are liberated at the negative pole, while the acid radicals of the salts and acids and the hydroxyl of the bases are liberated at the positive pole. The liberated substances may either be discharged unchanged, or they may enter into new combinations, causing a series of secondary reactions.

Electrolytes.—Solutions which conduct electricity are called Electrolytes, and the conducting metallic rods dipping into the solution are the Electrodes. Faraday gave the names of Ions to the atoms or atom-groups liberated at either electrode. The ions liberated at the positive electrode are the Anions, and those at the negative electrode are the Cations. The only solutions which possess any notable degree of electrical conductivity are the aqueous solutions of the various salts, acids, and bases, and in these solutions only do we meet with those phenomena of dissociation which are evidenced by anomalies of osmotic pressure, freezing point and the like,—anomalies which show that the solution contains a greater number of molecules than that indicated by its molecular concentration. These anomalies are due to dissociation, the division of some of the molecules into fragments, each of which plays the part of a separate molecule, contributing its quota to the osmotic tension and vapour pressure of the solution, in fact to all the phenomena which are dependent on the degree of molecular concentration. The electrical conductivity of a solution is therefore proved to be dependent on its molecular dissociation.

Arrhenius' Theory of Electrolysis.—In 1885, Arrhenius brought forward his theory of the transport of electricity by an electrolyte. According to this hypothesis, the electric current is carried by the ions, the positive charges by the cations, and the negative charges by the anions. In virtue of the attraction between charges of different sign, and repulsion between charges of like sign, the cations are repelled by the positive charge on the anode, and attracted by the negative charge on the cathode. Similarly the anions are repelled by the cathode and attracted by the anode.

An electrolytic solution contains three varieties of particles, positive ions or cations, negative ions or anions, and undissociated neutral molecules. The molecular concentration of such a solution, with the corresponding constants, depends on the total number of these particles, i.e. the sum of the ions and the undissociated neutral molecules. We may indicate an ion by placing above it the sign of its electrical charge, one sign for each valency. Thus Na⁺ and Cl^- indicate the two ions of a salt solution; Cu⁺⁺ and SO₄^-- the two ions of a solution of sulphate of copper. A point is sometimes substituted for the + sign, and a comma for the - sign. Thus Na^. and Cl^,; Cu^.. and SO₄^,,.

My friend Dr. Lewis Jones has given a very vivid picture of the processes which go on in an electrolytic solution when an electric current is passing. He compares an electrolytic cell to a ballroom, in which are gyrating a number of dancing couples, representing the neutral molecules, and a number of isolated ladies and gentlemen representing the anions and cations respectively. If we suppose a mirror at one end of the ballroom and a buffet at the other, the ladies will gradually accumulate around the mirror, and the gentlemen around the buffet. Moreover, the dancing couples will gradually be dissociated in order to follow this movement.

Degree of Dissociation.—The degree of dissociation is the fraction of the molecules in the solution which have undergone dissociation. Let n be the total number of molecules of the solute, and n″ the number of dissociated molecules. Then n″ / n = a will represent the degree of dissociation. Let k be the number of ions into which each molecule is split. Then a = n″k / nk, i.e. the degree of dissociation is the ratio of the number of ions actually present in a solution to the number which would be present if all the molecules of the solute were dissociated.

Let n′ be the total number of particles present in a solution containing n molecules, each of which is composed of k ions. Then if a is the degree of dissociation,

We thus obtain i the coefficient of dissociation, in terms of the degree of dissociation a and the number of ions in each molecule k.

If there is no dissociation, i.e. if a = 0, then n′ = n, and i = 1. If all the molecules are dissociated, a = 1, and i = k.

Faraday's Law.—Faraday found that the quantity of electricity required to liberate one gramme-molecule of any radical is 96.537 coulombs for each valency of the radical.

Electrochemical Equivalent.—The electrochemical equivalent of a radical is the weight liberated by one coulomb of electricity. It is equal to the molecular weight of the ion, divided by 96.537 times its valency.

Electrolytic Conductivity.—The conductivity of an electrolyte is the inverse of its resistance. C = 1/R.

For a given difference of potential the conductivity of an electrolyte is proportional to the number of ions in unit volume, the electrical charge on each ion, and the velocity of the ions.

The specific conductivity Δ of an electrolyte is the conductivity of a cube of the solution, each face of which is one square centimetre in area. The molecular conductivity of an electrolyte is the conductivity of a solution containing one gramme-molecule of the substance placed between two parallel conducting plates, one centimetre apart. The molecular conductivity is independent of the volume occupied by the gramme-molecule of the solute, depending only on the degree of dissociation. The molecular conductivity U is equal to the product of V, the volume of the molecule, by Δ, its specific conductivity. U = VΔ. Whence Δ = U / V, i.e. the specific conductivity equals the molecular conductivity divided by the volume.

The conductivity of an electrolyte is proportional to the number of ions in a volume of the solution containing one gramme-molecule. Let M_∞ be the conductivity for complete dissociation and M_v the molecular conductivity at the volume V. Then

the degree of dissociation. This is Ostwald's law, which says that the degree of dissociation is equal to the ratio of conductivity when the gramme-molecule occupies a volume V, to its conductivity when the solution is so dilute that dissociation is complete. Hence the degree of dissociation may also be determined by comparing the electrical conductivities of two solutions of different degrees of concentration.

Velocity of the Ions.—If the electrolytic cell is divided into two segments by means of a porous diaphragm, we shall find after a time an unequal distribution of the solute on the two sides. For instance, with a solution of sulphate of copper, after the current has passed for some time there will be a diminution of concentration in the liquid on both sides of the diaphragm, but the loss will be very unequally divided. Two-thirds of the loss of concentration will be on the side of the negative electrode and only one-third on the positive side. In 1853, Hittorf gave the following ingenious explanation of this phenomenon:—

Fig. 1 represents an electrolytic vessel containing a solution of sulphate of copper, the vertical line indicating a porous partition separating the vessel into two parts. Fig. 2 shows the same vessel after the passage of the current. The acid radical has travelled twice as fast as the metal. For each copper ion which has passed through the porous plate towards the cathode two acid radicals have passed through it towards the anode. Three ions have been liberated at either electrode, but in consequence of the difference of velocity with which the positive and the negative ions have travelled, the negative side of the vessel contains only one molecule of copper sulphate and has lost two-thirds of its molecular concentration, while the positive side contains two molecules of copper sulphate and has only lost one-third of its concentration. This proves clearly that the ions move in different directions with different velocities. Let u be the velocity of the anions, and v the velocity of the cations. Let n be the loss of concentration at the cathode, and 1 - n the loss of concentration at the anode. Then

i.e. the loss of concentration at the cathode is to the loss of concentration at the anode as the velocity of the anions is to that of the cations. Hence by measuring the loss of concentration at the two electrodes, we have an easy means of determining the comparative velocity of different ions.

In 1876, Kohlrausch compared the conductivity of the chlorides, bromides, and iodides of potassium, sodium, and ammonium respectively. He found that altering the cation did not affect the differences of conductivity between the three salts, thus showing that these differences of conductivity were dependent on the nature of the anion only, and not on the particular base with which it was combined. The difference of conductivity between an iodide and a bromide, for example, is the same whether potassium, sodium, or ammonium salts are compared. A similar experiment has been made with a series of cations combined with various anions. The difference of conductivity of the salts in the series is the same whichever anion is used, i.e. the difference of conductivity between potassium chloride and sodium chloride is the same as that between potassium bromide and sodium bromide. Hence we may conclude that the conductivity of any salt is an ionic property.

Kohlrausch's law may be expressed by the formula c = d(u + v), where c is the conductivity of the salt, d the degree of dissociation, i.e. the fraction of the electrolyte broken up into ions, and u and v the velocity of the anions and cations respectively. When all the molecules of the electrolyte are dissociated, d = 1, and the formula becomes c_∞ = u + v.

As we have already seen, a salt is formed by the union of a metal M with an acid radical R. Potassium sulphate, K₂SO₄, consists of the metal K₂ and the acid radical SO₄. Ammonium chloride, NH₄Cl, consists of the basic radical NH₄ and the acid radical Cl. The various acids may be considered as salts of the metal hydrogen. Thus sulphuric acid, H₂SO₄, is the sulphate of hydrogen. Bases may be considered as salts with the hydroxyl group, OH, replacing the acid radical. Thus potash, KOH, is the hydroxyl of potassium. The various electrolytic combinations may be represented by the following symbols:—

The various chemical reactions of an electrolyte are all ionic reactions, the chemical activity of an electrolytic solution being proportional to its electric conductivity, i.e. the degree of dissociation of its ions. The acidity of an electrolytic solution is due to the presence of the dissociated ion H⁺, and its strength is determined by the concentration of these free hydrogen ions. Hence the greater the degree of dissociation the stronger the acid.

The basic character of a solution is determined by the presence of the hydroxyl radical OH^-. The greater the concentration of the hydroxyl ions, i.e. the greater the dissociation, the stronger is the base.

The ions H⁺ and OH^- are of special importance, since they are the ions of water, H₂O = H⁺ + OH^-. The degree of dissociation of pure water is but small. Water is, however, the most important of all the various agents in the chemical reactions of life, since a large number of organic substances are decomposed by water by a process of hydrolysis, and a vast number of organic substances are but combinations of carbon with the ions H⁺ and OH^-, their diversity being due to variations in the relative proportions and grouping.

The Chemical, Therapeutic, and Toxic Actions of Ions.—The chemical, therapeutic, antiseptic, and toxic actions of electrolytic solutions are almost exclusively due to ionization. Take, for instance, a solution of nitrate of silver in which the addition of chlorine produces a white precipitate of chloride of silver. This precipitate occurs only when the solution added is one such as NaCl, where the chlorine is present as the free ion Cl^-. No such precipitate is produced in a solution of chlorate of potassium or chloracetic acid, where the chlorine is entangled in the complex ion ClO₃ or C₂H₃ClO₂.

Since, then, the toxic and pharmacological properties of an electrolyte depend entirely on the ionic grouping, it behoves the physician and the biologist to study the structure and grouping of the ions in a molecule, rather than that of the atoms. Consider for a moment the totally different properties of the phosphides and the phosphates. The former are extremely toxic, while the latter are perfectly harmless. There is not the slightest analogy between their actions on the living organism. On the other hand, all the phosphides produce the same toxic and therapeutic effects, whatever the cation with which they are united. Their toxic properties are derived from the presence of the free phosphorus ion P^---. The phosphates contain phosphorus in the same proportion as the phosphides, but this phosphorus is harmlessly entangled in the complex ion PO₄^---, whose properties are absolutely different from those of the ion P^---.

The above considerations apply equally to the chlorides and chlorates, the iodides and iodates, the sulphides and sulphates, and in general to all chemical salts.

The question has an intimate bearing on practical pharmacology. When we prescribe a cacodylate or an amylarsinate, we are not prescribing an arsenical treatment whose effects can be compared with those of an arsenide, an arsenite, or an arsenate. This fact is sufficiently indicated by the difference in the toxic doses of the different salts. Each variety of arsenical ion has its own special physiological and therapeutic properties. We do not expect to obtain the results of a ferruginous treatment from the administration of a ferrocyanide or a ferricyanide. Both contain iron, it is true, but neither possess the properties of the cation Fe⁺⁺⁺, but rather those of the complex anion of which they form a part.

We have already said that most of the therapeutic, toxic, and caustic actions of an electrolyte are due to ionic action, and the substances can therefore have no toxic action unless they are dissociated. Many of the solvents employed in medicine, such as alcohol, glycerine, vaseline, and chloroform dissolve the electrolytes but do not dissociate them into ions, and these solutions therefore do not conduct electricity. Such solutions have no therapeutic action. With the absence of dissociation all the ionic toxic and caustic effects also disappear entirely, and only re-appear as the water of the tissue is able slowly to effect the necessary dissociation.

Carbolic acid dissolved in glycerine is hardly caustic and but very slightly toxic. We have met with several instances in which a tablespoonful of carbolized glycerine, in equal parts, has been swallowed without any ill effect, either caustic or toxic, whereas the same dose dissolved in water would have been fatal. This absence of dissociation has enabled the surgeon Mencière to inject carbolic and glycerine in equal proportions into the larger joints, the part being subsequently washed out with pure alcohol. Thus by employing vaseline, oil, or glycerine as a solvent, and avoiding the access of water, we are able to use electrolytic antiseptics in very concentrated form. Their action is brought out very slowly, as the water of the organism effects the necessary dissociation of the electrolyte.

Since all chemical, toxic, and therapeutic actions are ionic, they are proportional to the degree of ionic concentration, i.e. to the number of ions in a given volume. The only point of importance, that which determines their activity, whether chemical or therapeutic, is the degree of ionization or dissociation. For example, all acids have the same cation H⁺. They have all identical properties, but they differ widely in the intensity of their action. There are weak acids such as acetic acid, and strong acids like sulphuric acid. The stronger acids are those which are more thoroughly dissociated, and in which the ion H⁺ is very concentrated; whereas the feeble acids are but slightly dissociated, so that the ion H⁺ is less concentrated.

Paul and Krönig have shown that the bactericidal action of different salts also varies with their degree of dissociation, i.e. with the concentration of the active ions. They made a series of observations on the bactericidal action of various salts of mercury, the bichloride, the bibromide, and the bicyanide, on the spores of Bacillus anthracis. The following results were obtained from a comparison of solutions containing 1 gramme-molecule of the salt in 64 litres of water. With the bichloride solution, after exposure to the solution for twenty minutes, only 7 colonies of the bacillus were developed. After exposure to a similar solution of the bibromide the number of colonies was 34. The antiseptic action of the bichloride was therefore five times as great as that of the bibromide. The bicyanide of mercury, however, even when four times as concentrated, permitted the growth of an enormous number of colonies, showing that it had no appreciable antiseptic action whatever. Nevertheless, the proportion of Hg is the same in all the solutions, and if there were any difference one would naturally expect that the ion Cy^- would be more toxic than Cl^- or Br^-. The real condition which varies in these solutions and determines their activity is the degree of dissociation. The whole of the antiseptic property resides in the ion Hg⁺⁺. This ion is very concentrated in the highly dissociated solution HgCl₂, less concentrated in the less ionized solution HgBr₂, and exceedingly dilute in the HgCy₂, which is hardly ionized at all.

What is true of the bactericidal action of the salts of mercury is equally true of their therapeutic effect. It is a great mistake to estimate the medicinal activity of a solution of a salt of mercury, or indeed of any electrolytic solution, simply by its degree of molecular concentration. The important point is the degree of dissociation, which is the only true measure of its activity. In the intramuscular injection of mercury salts it is by no means a matter of indifference what salt we employ. A salt should be used such as the bichloride or the biniodide, which is easily dissociated. Other salts are often employed because they occasion less pain at the site of injection; but the pain is a sign of the degree of activity of the preparation. The pain, it is true, may be avoided by using a salt which is less easily dissociated, or in which the mercury is bound up in a complex ion, but by so doing we diminish the efficacy of the remedy. It is moreover quite easy to diminish, or even entirely to suppress, the pain, by using a very dilute solution of an active ionized salt. A one-half per cent. or even one-quarter per cent. solution of the bichloride or biniodide of mercury may be injected very slowly in sufficient quantity without producing the slightest discomfort. Local action depends entirely on ionic concentration. One drop of pure sulphuric acid will destroy the skin, whereas the same amount if diluted in a tumblerful of water will furnish a refreshing drink.

CHAPTER IV

COLLOIDS

As we have already seen, living organisms are formed essentially of liquids. These liquids are solutions of crystallizable substances or crystalloids, and non-crystallizable substances or colloids—a classification which we owe to Graham.

The liquids are the most important constituents of a living organism, since they are the seat of all the chemical and physical phenomena of life. The junction of two liquids of different concentration is the arena in which takes place both the chemical transformation of matter and the correlative transformation of energy. In a former chapter we have passed in review the class of crystalloids, we will now turn our attention to the characteristic properties of colloids.

Colloids.—Colloids differ from crystalloids in that they do not form crystals from solution, being completely amorphous when in the solid state. The solution of a colloid solidifies in the same form which it possessed in the liquid state, the solvent being enclosed in the meshes of a sort of network formed by the solute. This form is approximately retained even after the water has evaporated by drying, the passage from the liquid state of solution to the solid state being effected through a series of intermediary states, such as a clot, coagulum, or jelly. This passage from the state of solution into a state of jelly is called coagulation. Some colloids, such as gelatine, coagulate with cold; while others, such as egg-albumin, coagulate with heat. Some, like the caseine of milk, require the addition of certain chemical substances to set up coagulation; while still others, such as the fibrin of blood, appear to coagulate spontaneously. The physical phenomena of coagulation are still but little understood. In some cases it is a reversible phenomenon, thus gelatine coagulated by cold is redissolved by heat; whereas with other colloids the process is irreversible, albumin coagulated by heat is not redissolved on cooling.

Colloids in a state of coagulation have a vacuolar or sponge-like structure. The solvent is imprisoned in the vacuoles of the clot, and is expelled little by little by its retraction. Colloids diffused in water are usually called colloidal solutions, but they are not true solutions. Such a pseudo-solution of a colloid is called a "sol," while a colloid in a state of coagulation is called a "gel." Colloidal solutions spread but little, diffuse very slowly in the liquids of the body, and cannot penetrate organic membranes.

Colloidal solutions diffuse light, unlike crystalloid solutions, which are transparent. We all know how the trajectory of a beam of sunlight through a darkened room is rendered visible by the particles of dust. In the same way if a colloidal solution is illuminated by a transverse ray of light, the light is diffused by the molecules of the colloid in semi-solution, and the liquid appears faintly illuminated on a dark background. The light diffused by a colloidal solution is polarized, which shows that it is reflected light,

Siedentopf and Sigmondy have applied this principle of lateral illumination on a dark background to the construction of the ultra-microscope. With the aid of this instrument we may not only see, but count the particles in a colloidal solution, which is in reality merely a pseudo-solution or suspension, in contradistinction to the true solution of a crystalloid.

Colloidal solutions possess only a very feeble osmotic pressure. The lowering of the freezing point and the other corresponding constants are also quite insignificant. This arises from the fact that the molecules of a colloid are extremely large when compared with those of a crystalloid. For example let us take colloidal substance whose molecular weight is 2000. A solution containing 40 grammes per litre would have an osmotic pressure only one-fiftieth of that of a solution of similar strength of a crystalloid whose molecular weight was 40.

Not only so, but on measuring the molecular concentration, the osmotic pressure, and the other constants of a colloidal solution, we find values even lower than those which we should expect from a consideration of its molecular weight. This is probably due to the tendency of a colloid to polymerization, i.e. to form groups or associations of molecules. Suppose, for instance, that the molecules of a colloidal solution are aggregated into groups of ten. Since each group plays the part of a simple molecule, the osmotic pressure will be ten times less than that corresponding to the quantity of the solute present. Such a group of molecules is called by Naegeli a "micella."

Similar phenomena of aggregation may be observed in the molecules of many inorganic substances. The molecule of iodine, for example, is monatomic at 1200° C., but becomes diatomic at the ordinary temperature. Sulphur at 860° C. is a gas with a vapour density of 2.2, while at 500° C. its vapour density rises to 6.6. In both of these cases two or more molecules of the element have been condensed into one as a result of the fall of temperature.

We frequently find that two successive cryoscopic observations on the freezing point of the same colloidal solution will vary. This is due to the extreme sensitiveness of the micellæ, which absorb or abandon their extra molecules under the slightest influence. This mobility in the constitution of the micellæ appears to be one of the principal causes of the peculiar properties of colloidal solutions.

The phenomenon of polymerization appears to be reversible. The micellæ are formed under certain conditions, and are disintegrated when these conditions are removed. The osmotic pressure varies in the same manner, diminishing with polymerization and augmenting with the disintegration of the micellæ. One may easily understand what an important rôle is played by this alternate polymerization and disintegration in the phenomena of life.

Most colloidal substances are precipitated from their solutions by the addition of very small quantities of electrolytic solutions. Non-electrolytic solutions do not appear to provoke this precipitation. This is not a chemical action, for an exceedingly small quantity of an electrolyte is able to precipitate an indefinite quantity of the colloid. The precipitation is probably due to the electric charges carried by the dissociated ions of the electrolytes.

When an electric current is passed through a colloid solution, the course of the molecules of the colloid is sometimes towards the cathode and sometimes towards the anode, according to the nature of the colloid and of the solvent. This displacement would appear to indicate a difference of electric potential between the molecules of the colloid and those of the solvent. Hardy has shown that in an alkaline solution the molecules of albumin travel towards the anode, while in an acid solution they travel towards the cathode.

Metallic Colloids.—Carey Lea and afterwards Credé succeeded in obtaining silver in colloidal solution by ordinary chemical means. Professor Bredig has introduced a more general method of obtaining a number of metals in colloidal solutions in a state of great purity. He causes an electric arc to pass between two rods of the metal immersed in distilled water. The cathode is thus pulverized into a very fine powder which rests in suspension in the liquid, constituting a colloidal solution. Bredig has in this way prepared sols of platinum, palladium, iridium, silver, and cadmium.

Catalytic Properties of Colloids.—Catalysis is the property possessed by certain bodies of initiating chemical reaction. The mass of the catalyzing body has no definite proportion to that of the substances entering into the reaction, and the appearance of the catalyzer is in no way altered by the reaction.

Ostwald has shown that catalysis consists essentially in the acceleration or retardation of chemical reactions which would take place without the action of the catalyzer, but more slowly.

Catalytic reactions are very numerous in chemistry. The inversion of sugar by acids, the etherization of alcohol by sulphuric acid, the decomposition of hydrogen peroxide by platinum black are all instances of catalysis. Fermentation by means of a soluble ferment or diastase, a phenomenon which may almost be called vital, is also a catalytic action. The action of pepsin, of the pancreatic ferment, of zymase, and of other similar ferments has a great analogy with the purely physical phenomenon of catalysis. The diastases are all colloids, and so are many other catalyzers.

A catalyzer is a stimulus which excites a transformation of energy. The catalyzer plays the same rôle in a chemical transformation as does the minimal exciting force which sets free the accumulation of potential energy previous to its transformation into kinetic energy. A catalyzer is the friction of the match which sets free the chemical energy of the powder magazine.

Bredig has studied the catalytic decomposition of hydrogen peroxide by metallic colloids prepared by his electric method. He found that 1 atom-gramme of colloidal platinum gives a sensible catalytic effect when diluted with 70 million litres of water. Caustic soda and other chemical substances inhibit the catalytic action of colloidal platinum in the same way as they inhibit the fermenting action of diastase. The curve of decomposition of hydrogen peroxide by colloidal platinum may be compared with the curve of fermentation by emulsin. Both are equally affected by the addition of an alkali. Many other chemical and physical agents have a similar inhibitory action on the catalysis of colloidal metals and on diastasic fermentation. Thus a mere trace of sulphuretted hydrogen or hydrocyanic acid will paralyse the action of a colloidal metal, just as it does that of a ferment. This is what Bredig calls the poisoning of metallic ferments.

We may hope that the further study of catalysis, a purely physico-chemical phenomenon, may throw more light on the mechanism of diastasic fermentation, which is essentially a vital reaction.

It must not be forgotten that all classification is artificial and arbitrary, and only to be used as long as it facilitates study. This observation is particularly applicable to the classification of substances into crystalloids and colloids. There is no sharp line between the two groups, the passage is gradual, and it is impossible to say where one group ends and the other begins. Many colloids such as hæmoglobin are crystallizable, and many crystallizable substances are coagulable. Many substances appear at one time in the crystalloid state and at another time in the colloidal state, so that instead of dividing substances into colloids and crystalloids, we should rather consider these expressions as denoting different phases assumed by the same substance.

In order to define clearly our various classes and divisions, we are apt to exaggerate slight differences of properties or composition. We say that colloids have no osmotic pressure, whereas in fact the osmotic pressure of the colloids though feeble plays a very important part in the phenomena of life.

So in other departments of science—a factor which is almost infinitesimal may yet exercise a vast influence on the results. It is by infinitesimal variations of pressure, a thousandth of a millimetre or less, that we obtain the various degrees of penetration in the Röntgen rays.

The division into solutions and pseudo-solutions or suspensions is also an arbitrary one. A true solution is also a suspension of the molecules of the solute. There is no essential difference between a solution and a suspension, but only a difference in the size of the molecules, or agglomerations of molecules, in one case so small as to be transparent, and in the other case just big enough to diffuse light. There are moreover many properties common to colloidal solutions and suspensions of fine powders, such as kaolin, mastic, charcoal, or Indian ink. These particles in suspension are precipitated by solutions of electrolytes in a manner similar to the coagulation of colloids.

The surface of every liquid is covered by a very thin layer, a sort of membrane slightly differentiated from the rest of the liquid. This membrane may be a chemical one, a pellicular precipitate like that which is formed by the contact of two membranogenous liquids. On the other hand, the membrane may not differ from the subjacent liquid in chemical composition, but only in physical properties. If we consider the molecules in the middle of a liquid, each molecule is subjected to the cohesive attraction of molecules on every side, attractions which neutralize one another. At the surface of the liquid, however, there are quite other conditions of equilibrium. There each molecule is drawn downwards towards the centre of the liquid, and there is no compensating attraction in an opposite direction. The resultant pressure is normal to the surface of the liquid, and is mechanically equivalent to an elastic membrane which tends to diminish the surface, and hence the volume of the liquid. We may therefore regard this surface tension as acting the part of a veritable physical membrane.

There is a still further differentiation of the surface of a liquid. When the liquid is not a simple one, but complex as in a solution, we find that the concentration of the solute is greater at the surface than in the interior. This is the so-called phenomenon of "adsorption," which is another cause for the production of a physical membrane covering the surface of a liquid.

Substances in a colloidal state have a great tendency to form these chemical or physical membranes at the point of contact between the colloidal solute and the solvent. This is probably the reason why the coagulum of a colloidal liquid usually presents a vacuolar or spongy structure.

CHAPTER V

DIFFUSION AND OSMOSIS

Diffusion and Osmosis.—If we place a lump of sugar in the bottom of a glass of water, it will dissolve, and spread by slow degrees equally throughout the whole volume of the liquid. If we pour a concentrated solution of sulphate of copper into the bottom of a glass vessel, and carefully pour over it a layer of clear water, the liquids, at first sharply separated by their difference of density, will gradually mix, so as to form a solution having exactly the same composition in all parts of the jar. The process whereby the sugar and the copper sulphate spread uniformly through the whole mass of the liquid in opposition to gravity is called Diffusion. This diffusion of the solute is a phenomenon exactly analogous to the expansion of a gas. It is the expression of osmotic pressure, or rather of the difference of the osmotic pressure of the solute in different parts of the vessel. The molecules of the solute move from a place where the osmotic pressure is greater towards a position where the osmotic pressure is less. The water molecules on the other hand pass from positions where the osmotic pressure of the solute is less towards positions where it is greater. As a consequence of this double circulation the osmotic pressure tends to become equalized in all parts of the vessel.

Diffusion appears to be the fundamental physical phenomenon of life. It is going on continually in the tissues of all living beings, and a study of the laws of diffusion and osmosis is therefore absolutely necessary for a just conception of vital phenomena.

Coefficient of Diffusion.—The coefficient of diffusion has been defined by Fick as the quantity of a solute which in one second traverses each square centimetre of the cross section of a column of liquid 1 centimetre long, between the opposite sides of which there is unit difference of concentration. Nernst in his definition substitutes "unit difference of osmotic pressure" for "unit difference of concentration."

Until recently it was generally believed that diffusion took place in colloids and plasmas just as in pure water. This is, however, by no means the case: the differences are considerable. When a solute is introduced into a colloidal solution, the greater the concentration of the colloid the slower will be the diffusion. This may be shown by a simple experiment. Several glass plates are prepared, by spreading on each a solution of gelatine of different concentration, to which a few drops of phenol phthalein have been added. If now a drop of an alkaline solution be placed on each plate, we can see that the drop diffuses more slowly through the more concentrated gelatine solution, since the presence of the alkali is rendered visible by the coloration of the phenol phthalein. A similar demonstration may be made by allowing drops of acid to diffuse through solutions of gelatine made slightly alkaline and coloured with phenol phthalein. In general, we find on experiment that when similar drops of any coloured or colouring solution are left for an equal time on plates of gelatine of different degrees of concentration, the greater the concentration of the gelatine the smaller will be the circle of coloration obtained.

We may show that the rapidity of diffusion diminishes as the gelatinous concentration increases, by another experiment. If we put side by side on our gelatine plate a drop of sulphate of copper and another of ferrocyanide of potassium, the point of contact of the two fluids will be sharply marked by a line of precipitate. We find that under similar conditions the time between the sowing of the drops and the formation of this line of precipitate is longer when the gelatine is more concentrated.

Osmosis.—In 1748, l'Abbé Nollet discovered that when a pig's bladder filled with alcohol was plunged into water, the water passed into the bladder more rapidly than the alcohol passed out; the bladder became distended, the internal pressure increased, and the liquid spirted out when the bladder was pricked by a pin. This passage of certain substances in solution through an animal membrane is called Osmosis, and membranes which exhibit this property are called osmotic membranes.

Precipitated Membranes.—In 1867, Traube of Breslau discovered that osmotic membranes could be made artificially. Certain chemical precipitates such as copper ferrocyanide can form membranes having properties analogous to those of osmotic membranes. With these precipitated membranes Traube made a number of interesting experiments. These have lately been collected in the volume of his memoirs published by his son.

Osmotic Membranes.—Osmotic membranes were formerly called semi-permeable membranes, being regarded as membranes which allow water to pass through them, but arrest the passage of the solute. This definition is inexact, since no membrane permeable to water is absolutely impermeable to the solutes. All we can say is that certain membranes are more permeable to water than to the substances in solution, and are moreover very unequally permeable to the various substances in solution. As a rule a membrane is much more permeable to a solute whose molecule is of small dimensions. Molecules of salt, for instance, pass through such a membrane much more quickly than do those of sugar. The term "osmotic membrane" should therefore in all cases replace that of "semi-permeable membrane."

Osmotic membranes behave exactly like colloids. The resistance which they oppose to the passage of different substances varies with the nature of the liquid or solute concerned. There is no real difference between the passage of a solution through an osmotic membrane and its diffusion through a colloid. The protoplasm of a living organism, being a colloid, acts exactly like an osmotic membrane so far as regards the distribution of solutions and substances in solution.

The diffusion of molecules through a colloid, a plasma, or a membrane is governed by laws precisely analogous to Ohm's law, which governs the transport of electricity. The intensity or rapidity of diffusion is proportional to the difference of osmotic pressure, and varies inversely with the resistance.

In the case of molecular diffusion, however, the rapidity of diffusion depends also on the size and nature of the molecules of the diffusing substance. The theory of the resistance of the various plasmas and membranes to diffusion has been but little understood; we can discover hardly any reference to it in the literature of the subject.

The laws of diffusion apply equally to the diffusion of ions. Nernst has shown that there is a difference of electric potential at the surface of contact of two electrolytic solutions of different degrees of concentration. Both the positive and negative ions of the more concentrated solution pass into the less concentrated solution, but the ions of one sign will pass more rapidly than those of the other sign, because being smaller, they meet with less resistance.

The resistance of the medium plays a most important part in all the phenomena of diffusion. When two solutions of different concentration come into contact, the interchange of molecules and ions which occurs is unequal owing to the differences in resistance. Hence both solutions become modified not only in concentration but also in composition. It has long been known that diffusion can cause the decomposition of certain easily decomposed substances, and it would appear probable that diffusion is also capable of producing new chemical combinations.

The separation of the liberated ions in consequence of the unequal resistance which they meet with in the medium they traverse often determines chemical reaction. This ionic separation is a fertile agent of chemical transformation in the living organism, and may be the determinant cause in those chemical reactions which constitute the phenomena of nutrition.

When different liquids come into contact there are two distinct series of phenomena, those due to osmotic pressure and those due to differences of chemical composition. Even with isotonic solutions there will be a transfer of the solutes if these are of different chemical constitution. Take, for instance, two isotonic solutions, one of salt and another of sugar. When these are brought into contact there is no transference of water from one solution to the other, but there is a transference of the solutes. In the salt solution the osmotic pressure of the sugar is zero. Hence the difference of osmotic pressure of the sugar in the two solutions will cause the molecules of sugar to diffuse into the salt solution. For the same reason the salt will diffuse into the sugar solution.

A disregard of this fact, that a solute will always pass from a solution where its osmotic pressure is high, into one where its osmotic pressure is low, is a frequent source of error. Thus it is said to be contrary to the laws of osmosis that solutes should pass from the blood, with its low osmotic pressure, into the urine, where the general osmotic pressure is higher; the more so because in consequence of the exchange the osmotic pressure of the urine is still further increased. Such an exchange, it is argued, is contrary to the ordinary laws of physics, and can therefore only be accomplished by some occult vital action. This, however, is not the fact, as is proved by experiment.

Consider an inextensible osmotic cell containing a solution of sugar, the walls of the cell being impermeable to sugar but permeable to salt. Let us plunge such a cell into a solution of salt, which has a lower osmotic pressure than the sugar solution. Since the walls of the cell are inextensible, the quantity of water in the cell cannot increase. The salt, however, will pass into the cell, since the osmotic pressure of the salt is greater on the outside than on the inside, and the walls are permeable to the molecules of salt. This passage will continue until the osmotic pressure of the salt is equal inside and outside the cell; at the same time the total osmotic pressure within the cell will have increased, in spite of its being originally greater than the osmotic pressure outside.

Plasmolysis.—We all know that a cut flower soon dries up and fades. When, however, we place the shrivelled flower in water, the contracted protoplasm swells up again and refills the cells, which become turgid, and the flower revives. This phenomenon is due to the fact that vegetable protoplasm holds in solution substances like sugars and salts which have a high osmotic pressure. Consequently water has a tendency to penetrate the cellular walls of plants, to distend the cells and render them turgescent. De Vries has used this phenomenon for the measurement of osmotic tension. He employs for this purpose the turgid cells of the plant Tradescantia discolor. The cells are placed under the microscope and irrigated with a solution of nitrate of soda. On gradually increasing the concentration of the solution there comes a moment when the protoplasmic mass is seen to contract and to detach itself from the walls of the cell. This phenomenon, which is known as plasmolysis, occurs at the moment when the solution of nitrate of soda begins to abstract water from the protoplasmic juice, i.e. when the osmotic tension of the nitrate of soda becomes greater than that of the protoplasmic liquid. So long as the osmotic tension of the soda solution is less than that of the protoplasm, there will be a tendency for water to penetrate the cell wall and swell the protoplasm. When the osmotic tension of the solution which bathes the cell is identical with that of the cellular juice, there is no change in the volume of the protoplasm. In this way we are able to determine the osmotic pressure of any solution. We have only to dilute the solution till it has no effect on the protoplasm of the vegetable cells. Since the osmotic tension of this protoplasm is known, we can easily calculate the osmotic tension of the solution from the degree of dilution required.

Red Blood Corpuscles as Indicators of Isotony.—In 1886, Hamburger showed that the weakest solutions of various substances which would allow the deposition of the red blood cells, without being dilute enough to dissolve the hæmoglobin, were isotonic to one another, and also to the blood serum, and to the contents of the blood corpuscles. This is Hamburger's method of determining the osmotic tension of a liquid. The diluted solution is gradually increased in strength until, when a drop of blood is added to it, the corpuscles are just precipitated, and no hæmoglobin is dissolved.

The Hæmatocrite.—In 1891, Hedin devised an instrument for determining the influence of different solutions on the red blood corpuscles. This instrument, the hæmatocrite, is a graduated pipette, designed to measure the volume of the globules separated by centrifugation from a given volume of blood under the influence of the liquid whose osmotic pressure is to be measured. The method depends on the principle that solutions isotonic to the blood corpuscles and to the blood serum will not alter the volume of the blood corpuscles, whereas hypertonic solutions decrease that volume.

Action of Solutions of Different Degrees of Concentration on Living Cells.—We have just seen that a living cell, whether vegetable or animal, is not altered in volume when immersed in an isotonic solution that does not act upon it chemically. When immersed in a hypertonic solution, it retracts; in a slightly hypotonic solution it absorbs water and becomes turgescent, while in a very hypotonic solution it swells up and bursts. In a hypertonic solution the red blood cells retract and fall to the bottom of the glass, the rapidity with which they are deposited depending on the amount of retraction. In a hypotonic solution they swell up and burst, the hæmoglobin dissolving in the liquid and colouring it red. This is the phenomenon of hæmatolysis. According to Hamburger, the serum of blood may be considerably diluted with water before producing hæmatolysis. Experimenting with the blood of the frog, he found that the globules remained intact in size and shape when irrigated with a salt solution containing .64 per cent. of salt, this solution being isotonic with the frog's blood serum. On the other hand, they did not begin to lose their hæmoglobin till the proportion of salt was reduced to below .22 per cent. Thus frog's serum may be diluted with 200 per cent. of water before producing hæmatolysis. In mammals the blood corpuscles remain invariable in a salt solution of about .9 per cent., and begin to lose their hæmoglobin approximately in a .6 per cent. solution. A solution of .9 per cent. of NaCl is therefore isotonic to the contents of the red blood corpuscles, to the serum of the blood, and to the cells of the tissues. It by no means follows that the cells of the blood and tissues undergo no change when irrigated with a .9 per cent. solution of chloride of sodium. They do not lose or gain water, it is true, and they retain their volume and their specific gravity. But they do undergo a chemical alteration, by the exchange of their electrolytes with those of the solution. Hamburger has pointed out that in mammals the shape of the red corpuscles is altered in every liquid other than the blood serum; even in the lymph of the same animal there is a diminution of the long diameter, and an increase of the shorter diameter, while the concave discs become more spherical.

All the cells of a living organism are extremely sensitive to slight differences of osmotic pressure—the cells of epithelial tissue and of the nervous system as well as the blood cells. For instance, the introduction of too concentrated a saline solution into the nasal cavity will set up rhinitis and destroy the terminations of the olfactory nerves. Pure water, on the other hand, is itself a caustic. There is a spring at Gastein, in the Tyrol, which is called the poison spring, the "Gift-Brunnen." The water of this spring is almost absolutely pure, hence it has a tendency to distend and burst the epithelium cells of the digestive tract, and thus gives rise to the deleterious effects which have given it its name. Ordinary drinking water is never pure, it contains in solution salts from the soil and gases from the atmosphere. These give it an osmotic pressure which prevents the deleterious effects of a strongly hypotonic liquid. During a surgical operation it is of the first importance not to injure the living surfaces by flooding them with strongly hypertonic or hypotonic solutions. This precaution becomes still more important when foreign liquids are brought into contact with the delicate cells of the large surfaces of the serous membranes. Gardeners are well aware of the noxious influence of a low osmotic pressure. They water the soil around the roots of a plant, so that the water may take up some of the salts from the soil before being absorbed by the plant. Pure water poured over the heart of a delicate plant may burst its cells owing to its low osmotic pressure. In many medical and surgical applications, on the other hand, a low osmotic pressure is of advantage. Thus, in order to remove the dry crusts of eczema and impetigo, the most efficacious application is a compress of cotton wool soaked in warm distilled water. Under the influence of such a hypotonic solution the dry cells rapidly swell up, burst, and are dissolved.

Cooking is also very much a question of osmotic pressure. If salt is put into the water in which potatoes and other vegetables are boiled, osmosis is set up and a current of water passes from the vegetable cells to the salt water. The cellular tissue of the vegetable becomes contracted and dried, and the membranes become adherent, the vegetable loses weight and becomes difficult of digestion, in consequence of its hard and waxy consistency, which prevents the action of the digestive juices. Vegetables should be cooked in soft water, and should be salted after cooking. When so treated, a potato absorbs water, the cells swell up, the skin bursts, the grains of starch also swell up and burst, and the pulp becomes more friable. The digestive juice is thus able to penetrate the different parts of the vegetable rapidly, and digestion is facilitated. Any one can easily prove for himself that a potato boiled in salt water diminishes in weight, whilst its weight increases when it is cooked in soft water.

The method of cryoscopy is also of considerable service in forensic medicine. As shown by Carrara, the cryoscopy of the blood is an important aid in determining the question whether a body found in the water was thrown in before or after death. In the former case the concentration of the blood will be much diminished. In certain experiments on dogs the cryoscopic examination of the blood showed a freezing point of -.6° C. The dog was then drowned, when the freezing point of the blood in the left ventricle was increased to -.29° C., and that in the right ventricle to -.42° C. On the other hand, when a dog was killed before being thrown into the water, the osmotic pressure of the blood was hardly decreased even after an immersion of 72 hours. In the case of persons or animals drowned in sea water, a similar alteration of the point of congelation is observed, but in the reverse direction. In this case the osmotic pressure is raised considerably in those who are drowned, whereas no such rise is observed in those who are thrown into the sea after death.

The circulation of the sap in plants and trees is also in great part due to osmotic pressure. The aspiration of the water from the soil is due to the intracellular osmotic pressure in the roots, which causes the sap to rise in the stem of a plant as it would in the tube of a manometer. From a knowledge of the osmotic pressure of the intracellular liquid of the roots, we may calculate the height to which the sap can be raised in the trunk of a tree, i.e. the maximum height to which the tree can possibly grow. Suppose, for instance, the plasma of the rootlets has an osmotic pressure of six atmospheres, corresponding to that of a 9 per cent. solution of sugar. A pressure of six atmospheres is equal to the weight of a column of water 6 × .76 × 13.596 = 61.95 metres high. This, then, is the maximum height to which this osmotic pressure is able to lift the sap. That is to say, a tree whose rootlets contain a solution of sugar of 9 per cent. concentration, or its equivalent, can grow to a height of 62 metres.

Cryoscopy is also of great use in practical medicine, more especially for the examination of the urine. The freezing point of urine varies from -1.26° C. to -2.35°. Koryani has studied the ratio of the point of congelation of urine to that of a solution containing an equal quantity of chloride of sodium. He finds that the ratio (freezing point of urine) / (freezing point of NaCl) increases when the circulation through the tubules of the kidney is diminished.

Hans Koeppe has shown that the hydrochloric acid of the gastric juice is produced by the osmotic exchanges between the blood and the gastric contents. The ion Na⁺ of the salt in the stomach contents exchanges with an ion H⁺ of the monobasic salts of the blood, NaHCO₃ + NaCl = HCl + Na₂CO₃.

Influence of Muscular Contraction on the Intramuscular Osmotic Pressure.—When a muscle is immersed in an isotonic salt solution it does not change in weight. In a hypertonic solution it loses weight in consequence of a loss of water, which passes from the muscle into the solution to equalize the osmotic pressure. It gains weight in a hypotonic solution, the water current setting towards the point of higher concentration. It is easy, therefore, to tell whether the osmotic pressure in a muscle is above or below that of a given solution, by observing whether the muscle gains or loses weight when immersed in it. Thus we may measure the osmotic pressure in a muscle by finding a salt solution in which the muscle neither gains nor loses weight. In this way we have been able to prove that the osmotic pressure of a tired muscle is higher than that of the normal muscle. Our experiments were carried out on the muscles of frogs. After having pithed the frog, one of the hind legs is removed by a single stroke of the scissors. The leg is skinned, dried with blotting paper, and weighed. It is then placed in a salt solution whose freezing point is -.53° C. At 15° C. such a solution has an osmotic pressure of 6.6 atmospheres. We next proceed to determine the osmotic pressure of the corresponding leg after it has been tired by muscular work. For this it is stimulated by an intermittent faradic current passing once a second for five minutes. The leg is then skinned, dried, weighed, and placed in the same salt solution. After eight hours' immersion the legs are weighed again. The following are the results of six experiments, the numbers representing fractions of the original weight:—

Change of weight of untired leg—

Change of weight of stimulated leg—

This result shows that muscular work provoked by electric stimulation noticeably increases the osmotic pressure of the muscle.

In order to discover the exact osmotic pressure in the stimulated muscles we repeated the series of experiments, using more and more concentrated solutions. In a solution whose freezing point was -.57°, we obtained the following values:—

Change of weight of untired leg—

Change of weight of stimulated leg—