[169] Since in any chemical action, which has not reached a condition of equilibrium, the concentrations of the reacting substances change continuously, the relation between the velocity of the action and the concentrations, for any moment, is found by the application of the calculus to the experimental data. (‹Cf. Elements of Calculus›, by Young and Linebarger (1900), 168, 181, 240; Mellor, ‹Higher Mathematics for Students of Chemistry and Physics› (1902), 197.) [170] Nernst, ‹loc. cit.›, 541, etc.; Ostwald, ‹loc. cit.›, 107, etc.; Walker, ‹loc. cit.›, 257; Smith, ‹loc. cit.›, 250, and 180 (‹Stud.›). [171] If a component takes part more than once in the action, its concentration is raised to the power corresponding to the coefficient expressing the number of its molecules taking part in the action. For instance, for ‹A› + 2 ‹B› → ‹C› + ‹D›, ‹v›_{1} = ‹k›_{1} × [‹A›] × [‹B›]^2; (see below). [172] ‹Cf.› Van 't Hoff, ‹loc. cit.›, I, 206. [173] The concentrations are calculated from the data given by Bodenstein, ‹Z. phys. Chem.›, «22», 16 (1897). (‹Cf.› Van 't Hoff ‹loc. cit.›, «I», 110.) [174] The fundamental meaning of the law is most accurately defined in thermodynamic terms, that is, in terms of the work or energy relations connected with changes of gaseous or osmotic pressures. [175] Van 't Hoff, ‹loc. cit.›, «I», 104, 159, etc. [176] In regard to the variations of the equilibrium constant with changes of temperature and the relations which govern these changes see Smith's ‹Inorganic Chemistry› (1909), p. 260. [177] The limitations are indicated in the preceding section. [178] Stieglitz, ‹Am. Chem. J.›, «23», 406 (1900). [179] ‹Vide› Stieglitz, ‹loc. cit.› [180] The table is based on the results of Noyes and Cooper, given in "The Electrical Conductivity of Aqueous Solutions," ‹Carnegie Institution Publications›, No. «63», pp. 138, 141 (1907). [181] Ostwald [‹Z. phys. Chem.›, «2», 278 (1888)], was the first to develop this relation from the conductivity data for so-called "weak acids," and the law of chemical equilibrium, holding in such and similar cases, is often called ‹Ostwald's Law of Dilution›. [182] The equilibrium ratio, used as an illustration in the text, is the equilibrium ratio for monobasic acids. For polybasic acids, the ratio would have the form demanded by the rule given p. 94. For instance, for H_{2}X ⇄ 2 H^{+} + X^{2−}, the expression [H^{+}]^2 × [X^{2−}] / [H_{2}X] should be constant, provided the ionization occurs according to the law of chemical equilibrium in its simplest terms. In point of fact, for ‹strong› acids, this ratio holds as little as does the equilibrium ratio for the monobasic acids.