1806. In reply to these allegations, let me inquire, Cannot a matter exist of which the sensible properties do not admit of being measured by human means? Because some kinds of matter can be measured by “those sensible qualities which undergo quantitative addition, subtraction, and division,” does it follow that there may not be matter which is incapable of being thus measured? And wherefore would the method of obtaining philosophical truth be “futile” in the one case, because inapplicable in the other? Because the inertias of A and B have been discovered, by means of their gravitation, does it follow that the inertias of X and Y cannot be discovered by their self-repellent power? Why should the inapplicability of gravitation in the one case render its employment futile in the other?
1807. It is self-evident, that matter without weight cannot be estimated by weighing, but I deny that on that account such weightless matter may not be otherwise estimated. The inertias of A and B cannot be better measured by gravitation than those of X and Y by repulsion, as already shown.
1808. You seem to infer, in paragraph second, page sixth, (p. 268,) that we should be equally destitute of the means of measuring matter accurately, “were any kind of matter heavy indeed, but not so heavy, in proportion to its quantity of matter, as other kinds.”
1809. If, in the case of all matter, weight be admitted to be the only measure of quantity, it were inconsistent to suppose any given quantity of matter, of any one kind, to have less weight than an equal quantity of another kind; but upon what other than a conventional basis is it to be assumed that there is more matter in a cubic inch of platinum than in a cubic inch of tin? in a cubic inch of mercury than in a cubic inch of iron? Judging by the chemical efficacy of the masses, although the weight of mercury is to that of iron as 13.6 is to 8, there are more equivalents of the latter than the former in any given bulk, since by weight twenty-eight parts of iron are equivalent to two hundred and two parts of mercury.
1810. Weight is one of the properties of certain kinds of matter, and has been advantageously resorted to, in preference to any other property, in estimating the quantity of the matter to which it appertains. Nevertheless, measurement by bulk is found expedient or necessary in many cases. But may we not appeal to any general property which admits of being measured or estimated? Farraday has inferred that the quantity of electricity is as the quantity of gas which it evolves. Light has been considered as proportional in quantity to the surface which it illuminates with a given intensity at a certain distance. The quantity of caloric has been held to be directly as the weight of water which it will render aeriform; and has also been estimated by the degree of its expansive or thermometric influence. What scale-beam is more delicate than the thermoscope of Melloni?
1811. In the last paragraph but one, seventh page, (p. 270,) you suggest, that “perhaps some persons might conceive that the identity of weight and inertia is obvious at once, for both are merely resistance to motion; inertia, resistance to all motion, or change of motion; weight, resistance to motion upward.”
1812. I am surprised that you should think the opinion of any person worthy of attention, who should entertain so narrow a view of weight, as antagonist of momentum, as that above quoted, “that it is a resistance to motion upward.” Agreeably to the definition given at the commencement of the letter, weight, in its usual practical sense, is only one case of the general force which causes all ponderable masses of matter to gravitate toward each other, and which is of course liable to resist any conflicting motion, whatever may be the direction. When, in the form of solar attraction, it overcomes that inertia of the planets which would otherwise cause them to leave their orbits, does gravitation “resist motion upward?”
1813. In the next paragraph you allege, that “there is a difference in these two kinds of resistance to motion. Inertia is instantaneous, weight is continuous, resistance.”
1814. It is to this allegation I object, that as you have defined inertia to be “resistance to motion, or to change of motion,” it follows that it can be instantaneous only where the impulse which it resists is instantaneous. It cannot be less continuous than the force by which it is overcome.
1815. Gravity has been considered as acting upon falling bodies by an infinity of impulses, each producing an adequate acceleration; but to every such accelerating impulse, producing of course a “change of motion,” will there not be a commensurate resistance from inertia? and the impulses and resistances being both infinite, will not one be as continuous as the other?