water. This explanation is no longer permissible, for De Vries has found that in a very large group of substances this pressure for the solution of two different substances is approximately the same when both solutions contain in equal volumes an equal number of molecules of the dissolved bodies. De Vries did not measure the 'osmotic pressure' directly, but determined the concentration of those solutions of different substances which give up as much water to certain plant cells as they receive from the membranes of these cells. These solutions are spoken of as isotonic (from loos, equal, and Tóvos, pressure). De Vries found that in order that the solutions of those organic substances investigated by him should be isotonic, they must contain in equal volumes an equal number of molecular weights, whilst solutions of inorganic salts were found to be isotonic with the former when less concentrated. Consequently very different substances exert equal osmotic pressures; the phenomenon, therefore, cannot be dependent upon the material composition of the bodies nor upon an attraction exerted by them upon water, which certainly could not be the same for substances so very different from each other.

We cannot, therefore, accept such an attraction to explain this phenomenon. If on one side of the wall there were water particles only, and on the other, particles of another substance, for instance, sugar, for which the wall is not permeable, then upon this side the number of water particles coming in contact with the wall would be smaller the smaller their number, and consequently the larger the number of particles of sugar contained in a unit volume. The smaller the number striking the wall so much the smaller will be the number passing into and through the wall, consequently a smaller number of particles of water pass from this sugar solution towards the pure water than from the water to the sugar solution. The amount of water on the side of the sugar solution must therefore increase. If the water so passing through the wall can flow away in any other manner, then the passage will continue so long as the concentration on both sides of the wall remains unequal. If, however, the solutions are contained in closed vessels, then in consequence of the advent of the water the pressure will be increased. In proportion as this increase proceeds the amount of water

passing through the wall in a given time diminishes, and will finally cease when the pressure has reached a certain maximum ; then the interchange ceases entirely. This arises from the fact that the pressure produced by the water particles is more strongly exerted upon the wall, and consequently they press through it. In this way the equilibrium of the materials passing from both sides is established.

If the pressure be increased artificially above this maximum then more water passes out than is returned, till the equilibrium is again established.

This osmotic pressure is dependent upon the condition of the wall, and not alone upon its composition, but also upon its thickness; for naturally it is easier to force the water through one kind of wall than it is for it to pass through another of a different material. If, however, one brings consecutively in contact with the same wall, solutions of different materials, then the osmotic pressure will gradually become equal, the equality being established when the solution on each side of the wall contains an equal number of molecules of the substances to which the wall is impermeable. If these two solutions are divided by a partition only permeable to the solvent, then no alteration in pressure is produced; if, however, one solution contains in a given space more molecules than the other, then the pressure rises in this solution. The osmotic pressure as well as the depression of the freezing point may be used for the purpose of comparing and determining molecular weights. This method is, however, less convenient than the former and suffers from the fact that these septa are, as a rule, not absolutely impermeable to dissolved substances. In this method also it is found that acids and salts exhibit an exceptional behaviour similar to that described in § 79.

§ 82. Evaporation and Ebullition. If a liquid be brought into a vessel which it does not completely fill, then a portion of the liquid passes as vapour into the space above. When this formation of vapour takes place only at the surface of the liquid it is styled 'evaporation,' but when it also proceeds in the interior of the liquid itself it is described as ebullition, or boiling. Which of these two forms of vaporisation obtains, is determined by external conditions, especially by the pressure on the liquid and

by the temperature. Evaporation may also take place from the surfaces of solid bodies.

When the space above the liquid is completely void, then, as a rule, evaporation takes place very quickly; but if it be filled with air or other gas the vaporisation proceeds more slowly. The mass of the vapour increases, but only until a maximum density is reached, that is, until every unit of space contains a certain definite weight of vapour: this maximun density is dependent upon the nature of the substance and also upon the temperature. This is true whether the space be filled with air or not. The vapour tends to expand and consequently exerts a pressure on the walls of the vessel, which pressure with constant temperature is approximately, but not absolutely, proportional to the density. To this maximum density there is a corresponding maximum of pressure styled the pressure or tension of the saturated vapour. The maximum density is always reached when a sufficient amount of liquid is present. If another gas exist in the space with the vapour, then both exert a pressure, giving a total pressure equal to the sum of the two. The component pressures are spoken of as the 'partial' or individual' pressures.

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When the space filled with a saturated vapour is reduced, and therefore the vapour compressed, neither the pressure nor the density is altered, but a portion of the vapour is converted into liquid and separates out as such. If the reverse happen, then an amount of vapour is formed until the conditions of the maximum of density and of pressure are again restored. It must not, however, be concluded that by reason of the impossibility of exceeding this maximum, the production of vapour ceases when this condition has been reached; for the vaporisation continues, but as much vapour condenses and liquefies as there is fresh vapour formed. The condition of a saturated vapour therefore is no condition of rest, is not a statical but a dynamical equilibrium, a state of motion which has become stationary.

The maximum pressure of the vapour of a substance is determined by the material composition of the body and also by the temperature. At low temperatures it is frequently immeasurably small, whilst at higher temperatures it is consider

able; still there are many bodies which cannot withstand the necessary rise of temperature without suffering decomposition, and therefore in the case of many liquids it is not known whether they can in any way be converted into vapour.

When the pressure of the vapour is as great or a little greater than the pressure surrounding the liquid, then the production of vapour proceeds, not at the surface alone, but also in the interior of the liquid itself, and the liquid boils. The formation of bubbles of vapour in the mass of the liquid itself does not necessarily take place as soon as the required temperature and pressure have been reached, just as the crystallisation of a solid from its solution does not begin immediately the condition of saturation has been reached. A liquid heated to a temperature above its boiling point is described as 'superheated.' This condition is analogous to that of supersaturation in the case of solutions. When the formation of vapour takes place in a 'superheated' liquid, it proceeds rapidly and suddenly, just as crystallisation in a supersaturated solution, and may consequently occasion violent explosions. Various agencies are found to be active in giving an impetus to the production of vapour-for example, shaking-but perhaps the most effectual is the contact of solid bodies, the surfaces of which are covered with a very thin layer of air or gas, or a solid which forms a gas when brought into the liquid will also promote the production of vapour. In this thin layer of air the first vapour production takes place, which rapidly extending forms a larger bubble, into the interior of which evaporation takes place from all sides. Bodies which condense air easily upon their surface, like platinum, or porous substances containing air in the pores, like burnt clay, charcoal, &c. are specially active in promoting this production of vapour. The walls of the containing vessels, more especially those constructed of glass or porcelain, act in the same way, by reason of the thin layer of air which is retained adhering to their surfaces. If this layer of air has been removed either by strongly heating the vessel or by long continued boiling of the liquid in it, then sudden and violent ebullition may set in, which can be avoided by bringing into the liquid, platinum wire, sand, or pieces of clay pipe-stems, &c.

The nature of the relationship between vapour pressure and

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temperature is so far alike for all volatile substances that with a rise in temperature the pressure increases at first slowly, then rapidly and more rapidly until at last the increase takes place with extraordinary rapidity. If these phenomena are represented graphically with the abscissæ for the temperature and the pressure as ordinates, then the curve is found to be convex to the axis of the abcissæ, and is at first almost parallel to this axis, and finally almost perpendicular to it; as yet such representations have been made in only a few isolated cases. The law underlying this relationship has not yet been completely elucidated. As a rule, it has been deemed sufficient to fix and determine the boiling points of different substances, i.e. the temperatures at which the liquids boil under the ordinary atmospheric pressure. But since this pressure varies from time to time, and is different in different places, such determinations are of little value unless the height of the barometer be also measured. For instance, in consequence of the higher position of Tübingen or Munich, the majority of substances boil 1° or 2° lower at these places than they do at Berlin or Königsberg.

X § 83. Boiling Points.-The comparison of the boiling points of substances of analogous composition has shown the existence of a very intimate relationship between the boiling point and the composition. These relationships were first brought to light by the investigations of H. Kopp and of H. Schroeder, and have since been amplified and extended by numerous investigators. It is chiefly amongst the organic compounds that such investigations have been made, and among these it has been shown that regular changes in composition correspond to similarly regular alterations in the boiling points.

Among the numerous series of organic compounds of like atom-linkage, the members of which differ from one another by CH2, or a difference of 13.97, or approximately 14 units, in their molecular weights, the boiling points and the molecular weights form arithmetical series with approximately equal differences; still the differences in the boiling points are not exactly equal, as is the case with those of the molecular weights.

The following examples are taken from the chlorides, bromides, iodides, alcohols, and acids derived from the series of so