follows the Laws of Gaseous Pressure.—This osmotic pressure is in fact gaseous pressure, and may be measured in millimetres of mercury in just the same way. We may thus show that osmotic pressure follows the laws of gaseous pressure as defined by Boyle, Dalton, and Gay-Lussac. The coefficient of pressure variation for change of temperature is the same for a solute as for a gas. The formula PV = RT is applicable to both. The numerical value of the constant R is also the same for a solute as for a gas. being .0819 for one gramme-molecule of either, when the volume is expressed in litres and the pressure in atmospheres. The formula PV = RT shows that for a given mass, with the same volume, the pressure increases in proportion to the absolute temperature.

Osmotic Pressure of Sugar.—A normal solution of sugar, containing 342 grammes of sugar per litre, has a pressure of 22.35 atmospheres, and it may well be asked why such an enormous pressure is not more evident. The reason will be found in the immense frictional resistance to diffusion. Frictional resistance is proportional to the area of the surfaces in contact, and this area increases rapidly with each division of the substance. When a solute is resolved into its component molecules, its surface is enormously increased, and therefore the friction between the molecules of the solute and those of the solvent.

Isotonic Solutions.—Two solutions which have the same

osmotic pressure are said to be iso-osmotic or isotonic. When comparing two solutions of different concentration, the solution with the higher osmotic pressure is said to be hypertonic, and that with the lower osmotic pressure hypotonic.

Lowering of the Freezing Point.—Pure water freezes at 0° C. Raoult showed that the introduction of a non-ionizable substance, such as sugar or alcohol, lowers the freezing point of a solution in proportion to the molecular concentration of the solute. One gramme-molecule of the solute introduced into one litre of the solution lowers its temperature of congelation by 1.85° C. Thus a normal solution of any non-ionizable substance in water freezes at -1.85° C. The measurement of this lowering of the freezing point is called Cryoscopy, a method which is becoming of great utility in medicine.

Cryoscopy of Blood.—In order to determine the osmotic pressure of the blood at 37° C., i.e. 98.6° F., the normal temperature, we proceed as follows. On freezing the blood, we find that it congeals at -.56°. Its molecular concentration is therefore .56 / 1.85 = .30, or about one-third of a gramme-molecule per litre. Its osmotic pressure at 0° C. is therefore .3 × 22.35 = 6.7 atmospheres. The increase of pressure with temperature is the same as for a gas, viz. 1/273, or .00367 of its pressure at 0° for every degree rise of temperature. The increase of pressure at 37° is therefore .00367 × 37 × 6.7 = .9 atmospheres. The total osmotic pressure at 37° is therefore 6.7 + .9 = 7.6 atmospheres.

Rise of Boiling Point.—Water under atmospheric pressure boils at a temperature of 100° C. The addition of a solute whose solution does not conduct electricity, such as sugar, causes a rise in the boiling point proportional to the molecular concentration of that solute.

Lowering of the Vapour Tension.—The vapour tension of a liquid is lowered by the addition of a solute. A liquid boils at the temperature at which its vapour tension equals that of the atmosphere. Since an aqueous solution of sugar at atmospheric pressure does not begin to boil at 100° C., it is manifest that its vapour tension is then less than that of the

atmosphere. The addition of a solute such as sugar, whose solution is not ionizable, and therefore does not conduct electricity, lowers the vapour tension of the solution in proportion to the molecular concentration of the solute.

Corresponding Values.—We have thus found five properties of a solution which vary proportionally, so that from the measurement of any one of them we can determine the corresponding values of all the others. These are—