The first physical compound which possesses a permanent specific constitution is called “a molecule.” Those physicists who assume matter to be intrinsically extended and continuous, by the name of molecule understand a little mass filling the space occupied by its volume, hard, indivisible, and unchangeable, to which they also give the name of “atom.” But this opinion, which is a relic of the ancient physical theories, is fast losing ground among the men of science, owing to the fact that molecules are subject to internal movements, and therefore composed of discrete parts. Such discrete parts must be simple and unextended elements, as we have demonstrated. Hence a molecule is nothing but a number of simple elements (some attractive and some repulsive) permanently connected by mutual action in one dynamical system. We say permanently connected; because no system of elements which lacks stability can constitute permanent substances, such as we meet everywhere in nature. Yet the stability of the molecular system is not an absolute, but only a relative, unchangeableness; for, although the bond which unites the parts of the molecular system must (at least in the case of primitive molecules) remain always the same in kind, it can (even in the case of primitive molecules) become different in degree within the limits of its own kind. And thus any molecule can be altered by heat, by cold, by pressure, etc., without its specific constitution being impaired. A molecule of hydrogen is specifically the same at two different temperatures, because the change of temperature merely modifies the bond of the constituent elements, without destroying it or making it specifically different; and the same is true of all other natural substances.
The material constituent of a molecular system is, as we have said, a number of primitive elements. These elements may be more or less numerous, and possess greater or less power, either attractive or repulsive; on condition, however, that attraction shall prevail in the system; for without the prevalence of attraction no permanent composition is possible.
The formal constituent of a molecular system, or that which causes the said primitive elements to be a molecule, is the determination by which the elements are bound with one another in a definite manner, and subjected to a definite law of motion with respect to one another. Such a determination is in each of the component elements the resultant of the actions of all the others.
The matter of the molecular system is disposed to receive such a determination, or natural form, by the relative disposition of the elements involved in the system. Such a disposition is local; for the resultant of the actions by which the elements are bound with one another depends on their relative distances as a condition.
The efficient cause of the molecular system are the elements themselves; for it is by the exertion of their respective powers that they unite in one permanent system when placed under suitable mechanical conditions. The original conditions under which the molecules of the primitive compound substances were formed must be traced to the sole will of the Creator, who from the beginning disposed all things in accordance with the ends to be obtained through them in the course of all centuries.
Molecules may differ from one another, both as to their matter and as to their form. They differ in matter when they consist of a different number of primitive elements, or of elements possessing different degrees of active power or of a different proportion of attractive and repulsive elements. They differ as to their form, when their constitution subjects them to different mechanical laws; for as the law of movement and of mutual action which prevails within a molecule is a formal result of its molecular constitution, we can always ascertain the difference of the constitution by the difference of the law.
It is well known that the law according to which a system of material points acts and moves can be expressed or represented by a certain number of mathematical formulas. The equations by which the mutual dynamical relations of the elements in a molecular system should be represented are of three classes. Some should represent the mutual actions to which such elements are subjected at any given moment of time; and these equations would contain differentials of the second order. Other equations should represent the velocities with which such elements move at any instant of time; and these equations would contain differentials of the first order. Other equations, in fine, should determine the place occupied by each of such elements at any given moment, and consequently the figure of the molecular system; and these last equations would be free from differential terms. The equations exhibiting the mutual actions must be obtained from the consideration of positive data, like all other equations expressing the conditions of a given problem. The equations exhibiting the velocities of the vibrating elements can be obtained by the integration of the preceding ones. The equations determining the relative position of the elements at any moment of time will arise from the integration of those which express the velocities of the vibrating points. Had we sufficient data concerning the internal actions of a molecule, and sufficient mathematical skill to carry out all the operations required, we would be able to determine with mathematical accuracy the whole constitution of such a molecule, and all the properties flowing from such a constitution. This, unfortunately, we cannot do as yet with regard to the molecule of any natural substance in particular; and, therefore, we must content ourselves with the general principle that those molecular systems are of the same kind whose constitution can be exhibited by mathematical formulas of the same form, and those molecules are of a different kind whose constitution is represented by mathematical formulas of a different form. This principle is self-evident; for the formulas by which the mechanical relations of the elements are determined cannot be of the same form, unless the conditions which they express are of the same nature; whereas it is no less evident that two molecular systems cannot be of the same kind when their mechanical constitution implies conditions of a different nature.
Two molecules of the same kind may differ accidentally—that is, as to their mode of being—without any essential change in their specific constitution. Thus, two molecules of hydrogen may be under different pressure, or at a different temperature, without any specific change. In this case, the mechanical relations between the elements of the molecule undergo an accidental change, and the equations by which such relations are expressed are also accidentally modified, inasmuch as some of the quantities involved in them acquire a different value; but the form of the equations, which is the exponent of the specific nature of the substance, remains unchanged.
From these remarks four conclusions can be drawn. The first is that molecules consisting of a different number of constituent elements always differ in kind. For it is impossible for such molecules to be represented by equations of the same form.