Indestructibility of matter.—“The indestructibility of matter,” says the writer,[181] “is an unquestionable truth. But in what sense, and upon what grounds, is this indestructibility predicated of matter? The unanimous answer of the atomists is: Experience teaches that all the changes to which matter is subject are but variations of form, and that amid these variations there is an unvarying constant—the mass or quantity of matter. The constancy of the mass is attested by the balance, which shows that neither fusion nor sublimation, neither generation nor corruption, can add to, or detract from, the weight of a body subjected to experiment. When a pound of carbon is burned, the balance demonstrates the continuous existence of this pound in the carbonic acid, which is the product of combustion, and from which the original weight of carbon may be recovered. [pg 787] The quantity of matter is measured by its weight, and this weight is unchangeable.”
So far all is right; but he continues: “Such is the fact familiar to every one, and its interpretation equally familiar. To test the correctness of this interpretation we may be permitted slightly to vary the method of verifying it. Instead of burning the pound of carbon, let us simply carry it to the summit of a mountain, or remove it to a lower latitude; is its weight still the same? Relatively it is; it will still balance the original counterpoise. But the absolute weight is no longer the same.... It is thus evident that the constancy, upon the observation of which the assertion of the indestructibility of matter is based, is simply the constancy of a relation, and that the ordinary statement of the fact is crude and inadequate. Indeed, while it is true that the weight of a body is a measure of its mass, this is but a single case of the more general fact that the masses of bodies are inversely as the velocities imparted to them by the action of the same force, or, more generally still, inversely as the accelerations produced in them by the same force. In the case of gravity, the forces of attraction are directly proportional to the masses, so that the action of the forces (weight) is the simplest measure of the relation between any two masses as such; but in any inquiry relating to the validity of the atomic theory, it is necessary to bear in mind that this weight is not the equivalent, or rather the presentation, of an absolute substantive entity in one of the bodies (the body weighed), but the mere expression of a relation between two bodies mutually attracting each other. And it is further necessary to remember that this weight may be indefinitely reduced, without any diminution in the mass of the body weighed, by a mere change of its position in reference to the body between which and the body weighed the relation subsists.”
The aim of the author is, as we shall see, to prove that “there are and can be no absolute constants of mass”; hence he endeavors at the very outset to shake our opposite conviction by showing that there is no absolute measure of masses. Such is the drift of the passage we have transcribed.
But we beg to remark that absolute quantities may be known to be absolute independently of any absolute measurement. Three kinds of quantity are conceivable: intensive quantity, which is measured by degrees; dimensive quantity, which is measured by distances; and numerical quantity, which is measured by discrete units. Of course dimensive quantity is altogether relative, inasmuch as it entirely consists of relations, and cannot be measured but by relative and arbitrary measures; but intensive quantity, though measured by arbitrary degrees, is altogether absolute, because it consists of a reality whose value is independent of correlative terms. And in the same manner numerical quantity is altogether absolute, because it consists of absolute units, by which it can be measured, absolutely speaking, though we may fail to reach such units, and are then obliged to measure it by some other standard. Now, the mass, or the quantity of matter in a body, is a numerical quantity; for it consists of a number of primitive units, independent of one another for their essence and for their existence, and therefore absolute in regard to their substantial being. Consequently, every mass of matter has an absolute value corresponding to the number of absolute [pg 788] units it contains; and thus every mass of matter is “an absolute constant of mass.” It is true that we have no means of ascertaining the absolute number of primitive units contained in a given mass; hence we are constrained to measure the quantity of matter by a relative measure—that is, by comparing it with an equal volume of another substance, whose density and weight we assume as the measure of other densities and weights. But does our ignorance of the absolute number of primitive units contained in a given mass interfere with their real existence? or, can our method of measuring change the nature of the thing measured?
We are told that “the weight of a body may be indefinitely reduced without any diminution in the mass of the body weighed.” Would not this show that, contrary to the author's opinion, the body weighed possesses “an absolute constant of mass”? We are told at the same time that “the weight of a body is a measure of its mass.” This cannot be true, unless, while the mass remains unchanged, the weight also remains unchanged. Hence the author's idea of carrying the pound of carbon to the summit of a mountain in order to diminish its weight, is inconsistent with the law of measurement, which forbids the employment of two weights and measures for measuring one and the same quantity.
The atomists measure the quantity of matter by its weight, because they know that every particle of matter is subject to gravitation, and therefore that the weights, all other things being equal, are proportionate to the number of primitive particles contained in the bodies. Thus, if a body contains a number, m, of primitive particles, and each of these particles is subject to the gravitation, g, while another body contains a number, m´, of primitive particles subject to the same gravitation, the ratio of the weights of the two bodies will be the same as the ratio of the two masses; for
mg : m´g : : m : m´;
and if the two bodies were carried to the summit of a mountain, where the gravitation is reduced to g´, the weights would indeed be changed, but their ratio would remain unaltered, and we would still have
mg´ : m´g´ : : m : m´.
Hence, whether we weigh two bodies in the valley or at the summit of the mountain, so long as we keep the same unit of gravitation for both, the ratio of their masses remains the same. This shows that the quantity of matter existing in those bodies implies “a constant of mass” independent of the intensity of gravitation, and that the ratio of the two masses is the ratio of two “absolute” quantities—that is, of two numbers of primitive material units.