3. Power of resistance to swelling increases from the exterior to the interior, according to a parabolic law; i.e. the external layers of the body attain the maximum swelling sooner than the internal portions. (L. Mathiessen and A. Schwarz.) 4. The volume of the swollen body is smaller than its original volume, plus that of the liquid absorbed. (Quincke.) 5. Swelling is accompanied by development of heat.[53] [53] Duvernoy, E. Wiedemann, and Lüdeking, Wied. Ann. xxv. 1885, p. 145. The production of heat is simply due to the contraction, and not to any chemical phenomenon, such as hydration.[54] This explains a fact well known to tanners, viz. that skins swell in cold water and “fall” in warm water. Riecke[55] concludes that the degree of swelling, _m__{2}/M (where _m__{2} = mass of water absorbed, M = mass of the body swollen), in a space filled with aqueous vapour, unsaturated, is a function of the pressure and temperature. [54] Rodewald. Thermodynamik der Quellung, Zeit. f. Phys. Chem. xxiv. 1897, p. 193. [55] Zur Lehre von d. Quellung, Wied. Ann. liii. 1894, p. 564. The velocity of swelling (Pascheles) may be expressed by the formula-- _d_Q/_dt_ = (M - Q)K where M = maximum of swelling, Q = amount of swelling in the time _t_, and K = a constant. The differential quotient _d_Q/_dt_ gives the velocity for each moment, and it will be seen that the swelling becomes slower and slower as the maximum is approached. Thus, the law of the velocity of swelling is identical with that of the velocity of inversion of cane sugar, itself an application of the law of masses.[56] [56] Nernst and Schönfliess. Einleitung in die mathematische Behandlung der Naturwissenschaft, München 2 Aufl. 67. For every process of swelling, the constant K must be determined experimentally from observation of M, and it may be shown that-- K = 1/_t_ log(M/(M - Q)) whence the value of K may be calculated for each series of determinations. On the manner in which water is held in swollen colloid bodies, three hypotheses have been put forward.[57] [57] See also Colloidal Chemistry, H. R. Procter, M.Sc., Brit. Assoc. Reports, Dublin, 1908. 1. The hypothesis that colloids have a structure in the form of a honeycomb. (Bütschli.) 2. The water is absorbed at the surface of colloids in a specially condensed form.[58] [58] Wilhemy. Pogg. Ann. cxix. pp. 121, 122. The water forms, with the swollen body, a “solid solution.” (Nägeli.) Swelling, and its opposite, contraction, are connected with the surface tension between the swelling or contracting bodies and the surrounding solution. With diminished surface tension, the surfaces of contact between the two become greater, i.e. swelling takes place, with simultaneous diminution of the volume of the whole system, and vice versa.