For our purpose, the study of two of the fundamental quantitative laws governing action in solution and of their application to analytical phenomena, will be sufficient: these are, ‹the law of chemical or homogeneous equilibrium›, in which the ‹law of mass action› is included, and the law of ‹physical› or ‹heterogeneous equilibrium›. «The Law of Chemical Equilibrium.»—The law of chemical equilibrium may be expressed, for a simple case, by saying that if two substances ‹A› and ‹B› interact at a constant temperature to give two compounds ‹C› and ‹D› and, vice versa, ‹C› and ‹D› interact with each other to produce ‹A› and ‹B›, then equilibrium will be reached ‹when the ratio of the product of the concentrations of› ‹A› ‹and of› ‹B› ‹to the product of the concentrations of› ‹C› ‹and of› ‹D› ‹has a definite, constant value›, which is a value characteristic of the equilibrium between the compounds involved, at the given temperature. The action may be expressed in the chemical equation ‹A› + ‹B› ⇄ ‹C› + ‹D›, in which ‹A›, ‹B›, ‹C› and ‹D› represent four different substances reacting in the molecular proportions indicated by their symbols, which as usual represent molecular weights. And the condition for equilibrium may be expressed in the mathematical equation [‹A›] × [‹B›] / ([‹C›] × [‹D›]) = ‹k›. [‹A›], [‹B›], [‹C›] and [‹D›] are used to represent the concentrations[166] of [p092] the four reacting substances and ‹k› is some definite number, called the equilibrium constant. The law was discovered by Guldberg and Waage in 1867, and, with certain limiting conditions (see below) it has been fully established by extensive experimental work.[167] The significance of the law may be interpreted on the basis of the following considerations. If we start with the two substances ‹A› and ‹B› alone and have one mole of each in one liter (as gas or in solution) at a given temperature, then, all the conditions being given,—the temperature, the concentrations, and the nature of the substances,—the reaction ‹A› + ‹B› → ‹C› + ‹D›, leading to the formation of ‹C› and ‹D›, ‹will proceed with a perfectly definite velocity›. The molecules of ‹A› and of ‹B› move in all directions (kinetic theory of gases and solutions), and molecules of ‹A› will collide with molecules of ‹B› a definite number of times in unit time and will form a definite number[168] of molecules of ‹C› and ‹D› per minute. The velocity of chemical change of a given substance (‹chemical velocity›) is also measured in terms of moles, and is represented by the number of moles or the fraction of a mole changed per minute. If ‹v′›_{1} stands for the velocity of the action between ‹A› and ‹B›, under the given conditions, then ‹v′›_{1} = ‹k›_{1},