the solution, just as the tension of the vapours of molecular quantities of the given substances will be equal, and determined by the laws of Gay-Lussac, Mariotte, and Avogadro-Gerhardt. Those formulæ (Chapter VII., Notes 23 and 24) by which the gaseous state of matter is determined, may also be applied in the present case. So, for example, the osmotic pressure _p_, in centimetres of mercury, of a one per cent. solution of sugar, may be calculated according to the formula for gases: M_p_ = 6200_s_(273 + _t_), where M is the molecular weight, _s_ the weight in grams of a cubic centimetre of vapour, and _t_ its temperature. For sugar M = 342 (because its molecular composition is C_{12}H_{22}O_{11}). The specific gravity of the solution of sugar is 1·003, hence the weight of sugar _s_ contained in a 1 per cent. solution = 0·01003 gram. The observation was made at _t_ = 14°. Hence, according to the formula, we find _p_ = 52·2 centimetres. And experiments carried on at 14° gave 53·5 centimetres, which is very near to the above. (5) For the solutions of salts, acids, and similar substances, which conduct an electric current, the calculated pressure is usually (but not always in a definite or multiple number of times) less than the observed by _i_ times, and this _i_ for dilute solutions of MgSO_{4} is nearly 1, for CO_{2} = 1, for KCl, NaCl, KI, KNO_{3} greater than 1, and approximates to 2, for BaCl_{2}, MgCl_{2}, K_{2}CO_{3}, and others between 2 and 3, for HCl, H_{2}SO_{4}, NaNO_{3}, CaN_{2}O_{6}, and others nearly 2 and so on. It should be remarked that the above deductions are only applicable (and with a certain degree of accuracy) to dilute solutions, and in this respect resemble the generalisations of Michel and Kraft (see Note 44). Nevertheless, the arithmetical relation found by Van't Hoff between the formation of vapours and the transition into dilute solutions forms an important scientific discovery, which should facilitate the explanation of the nature of solutions, while the osmotic pressure of solutions already forms a very important aspect of the study of solutions. In this respect it is necessary to mention that Prof. Konovaloff (1891, and subsequently others also) discovered the dependence (and it may be a sufficient explanation) of the osmotic pressure upon the differences of the tensions of aqueous vapours and aqueous solutions; this, however, already enters into a special province of physical chemistry (certain data are given in Note 49 and following), and to this physical side of the question also belongs one of the extreme consequences of the resemblance of osmotic pressure to gaseous pressure, which is that the