concentration, i.e. to the number of gramme-molecules of the solute contained in a litre of the solution. Many physical properties are quite independent of the nature of the solute, depending only on its degree of molecular concentration.

Normal Solution.—A normal solution is one which contains one gramme-molecule of the solute per litre. A decinormal solution contains one-tenth of a gramme-molecule of the solute per litre, and a centinormal solution one-hundredth of a gramme-molecule. A normal solution of urea, for example,

contains 60 grammes of urea per litre, while a normal solution of sugar contains 342 grammes of sugar per litre.

The Dissolved Substance is a Gas.—Van t' Hoff, using the data obtained by the botanist Pfeffer, showed that the dissolved matter in a solution behaved exactly as if it were a gas. The analogy is complete in every respect. Like the gaseous molecules, the molecules of a solute are mobile with respect to one another. Like those of a gas, the molecules of a solute tend to spread themselves equally, and to fill the whole space at their disposal, i.e. the whole volume of the solution. The surface of the solution represents the vessel containing the gas, which confines it within definite limits and prevents further expansion.

Osmotic Pressure.—Like the molecules of a gas, the molecules of a solute exercise pressure on the boundaries of the space containing it. This osmotic pressure follows exactly the same laws as gaseous pressure. It has the same constants, and all the notions acquired by the study of gaseous pressure are applicable to osmotic pressure. Osmotic pressure is in fact the gaseous pressure of the molecules of the solute.

When a gas dilates and increases in volume, its temperature falls, and cold is produced. Similarly, when a soluble substance is dissolved, it increases in volume, and the temperature of the liquid falls. This phenomenon is well known as a means of producing cold by a refrigerating mixture.

The phenomena of life are governed by the laws of gaseous pressure, since all these phenomena take place in solutions. The fundamental laws of biology are those of the distribution of substances in solution, which is regulated by the laws of gaseous pressure, since all these laws are applicable also to osmotic pressure.

Boyle's Law.—When a gas is compressed its volume is diminished. If the pressure is doubled, the volume is reduced to one-half. The quantity V × P, that is the volume multiplied by the pressure, is constant.

Gay-Lussac's Law.—For a difference of temperature of a degree Centigrade all gases dilate or contract by 1 / 273 of their volume at 0° Centigrade.

Dalton's Law.—In a gaseous mixture, the total pressure is equal to the sum of the pressures which each gas would exert if it alone filled the whole of the receptacle.

Pressure proportional to Molecular Concentration.—The above laws are completely independent of the chemical nature of the gas, they depend only on the number of gaseous molecules in a given space, i.e. on the molecular concentration. If we double the mass of the gas in a given space, we double the number of molecules, and we also double the pressure, whatever the nature of the molecules. We may also double the pressure by compressing the molecules of a gas, or of several gases, into a space half the original size. The molecular concentration of a gas, or of a mixture of gases, is the ratio of the number of molecules to the volume they occupy. The pressure of a gas or of a mixture of gases is proportional to its molecular concentration. This is a better and a shorter way of expressing both Boyle's law and Dalton's law.

One gramme-molecule of a gas, whatever its nature, condensed into the volume of 1 litre, has a pressure of 22.35 atmospheres. Similarly one gramme-molecule of a solute, whatever its nature, when dissolved in a litre of water, has the same pressure, viz. 22.35 atmospheres.

Absolute Zero.—According to Gay-Lussac's law, the volume of a gas diminishes by 1 / 273 of its volume at 0° C. for each degree fall of temperature. Thus if the contraction is the same for all temperatures, the volume would be reduced to zero at -273° C. This is the absolute zero of temperature. Temperatures measured from this point are called absolute temperatures, and are designated by the symbol T. If t° indicates the Centigrade temperature above the freezing point of water, then the absolute temperature is equal to t° + 273°.

The Gaseous Constant.—Consider a mass of gas at 0° C. under a pressure P_o, with volume V_o. At the absolute temperature T, if the pressure be unaltered, the volume of this gas will be V_oT / 273. Therefore the constant PV, the product of the pressure by the volume, will be represented by P_oV_oT / 273.

At the same temperature, but under another pressure P′ the gas will have a different volume V′. Since, according to Boyle's law, PV is constant (P′V′ = P_oV_o), it will still equal P_oV_oT / 273. Therefore P_oV_o / 273 is also constant. This quantity is called "the gaseous constant," and if we represent it by the symbol R, we obtain the general formula PV = RT for all gases, or PV / T = R.

Suppose, for instance, we have a gramme-molecule of a gas at 0° C. in a space of 1 litre. It has a pressure of 22.35 atmospheres at 0° C., or 273° absolute temperature. Since PV = RT, R = PV / T = 1 × 22.35 / 273 = .0819. This number .0819 is the numerical value of the constant R for all gases, volume being measured in litres and pressure in atmospheres.

Substances in solution behave exactly like gases, they follow the same laws and have the same constants. All the conceptions which have been acquired by the study of gases are applicable to solutions, and therefore to the phenomena of life. The osmotic pressure of a solution is the force with which the molecules of the solute, like gaseous molecules, strive to diffuse into space, and press on the limits which confine them, the containing vessel being represented by the surfaces of the solution. Osmotic pressure is measured in exactly the same way as gaseous pressure. To measure steam pressure we insert a manometer in the walls of the boiler. In the same way we may use a manometer to measure osmotic pressure. We attach the tube to the walls of the porous vessel, allow the solvent to increase in volume under the pressure of the solute, and measure the rise of the liquid in the manometer tube.

Pfeffer's Apparatus.—Pfeffer has designed an apparatus for the measurement of osmotic pressure. It consists of a vessel of porous porcelain, the pores of which are filled with a colloidal solution of ferrocyanide of copper. This forms a semi-permeable membrane which permits the passage of water into the vessel, but prevents the passage of sugar or of any

colloid. The stopper which hermetically closes the vessel is pierced for the reception of a mercury manometer. The vessel is filled with a solution of sugar and plunged in a bath of water. The volume of the solution in the interior of the vessel can vary, since water passes easily in either direction through the pores of the vessel. The boundary of the solvent has become extensible, and its volume can increase or diminish in accordance with the osmotic pressure of the solute. Under the pressure of the sugar water is sucked into the vessel like air into a bellows, the solution passes into the tube of the manometer, and raises the column of mercury until its pressure balances the osmotic pressure of the sugar molecules.

Osmotic Pressure