_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 x 22.35 = A / 1.85 x 22.35. _Determination of Molecular Weight._--The lowering of the freezing point also enables us to calculate the molecular {23} 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 Abbe 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 role in the arena of life. It is found at work in all the phenomena of life. When osmotic pressure fails, life itself ceases. * * * * * {24} CHAPTER III ELECTROLYTIC SOLUTIONS