I do not see what advantage is gained to philosophy by such an enumeration of qualities as this, which, after all, does not pretend to completeness; nor do I see anything either precise or fundamental in such distinctions as that of elasticity, a mode of cohesion, and elasticity, a mode of repulsion. But a question in which our philosophy is really concerned is how far any of these qualities are universal qualities of matter. Sir W. Hamilton holds that they are none of them necessary qualities of matter, and therefore of course not universal, and argues this point at some length. With regard to one of his Secundo-primary qualities, I will make some remarks.
4. Inertia.—In discussing the Ideas which enter into the Mechanical Sciences[305], I have stated that the Idea of Force and Resistance to Force, that is, of Force and Matter, are the necessary foundations of those sciences. Force cannot act without matter to act on; Matter cannot exist without Force to keep its parts together and to keep it in its place. But Force acting upon matter may either be Force producing rest, or Force producing motion. If we consider Force producing motion, the motion produced, that is, the velocity produced, must depend upon the quantity of matter moved. It cannot be that the same power, acting in the same way, shall produce the same velocity by pushing a small pebble and a large rock. If this were so, we could have no science on such matters. It must needs be that the same force produces a smaller velocity in the larger body; and this according to some measure of its largeness. The measure of the degree in which the body thus resists this communication of motion is inertia. And the inertia is necessarily supposed to be proportional to the quantity of matter, because it is by this inertia that this existence and quantity of the matter is measured. If therefore any Science concerning Force and Matter is to exist, matter must have inertia, and the inertia must be proportional to the quantity of matter.
5. Sir W. Hamilton, in opposition to this, says, that we can conceive a body occupying space, and yet without attraction or repulsion for another body, and wholly indifferent to this or that position, in space, to motion and to rest. He infers thence that inertia is not a necessary quality of bodies.
To this I reply, that even if we can conceive such bodies, (which in fact man, living in a world of matter cannot conceive,) at any rate we cannot conceive any science about such bodies. If bodies were indifferent to motion and rest, Forces could not be measured by their effects; nor could be measured or known in any way. Such bodies might float about like clouds, visible to the eye, but intangible, and governed by no laws of motion. But if we have any science about bodies, they must be tangible, and governed by laws of motion. Not, then, from any observed properties of bodies, but from the possibility of any science about bodies, does it follow that all bodies have inertia.
6. Gravity.—Reasoning of the same kind may be employed about weight. We can conceive, it is urged, matter without weight. But I reply, we cannot conceive a science which deals with matter that has no weight:—a science, I mean, which deals with the quantity of matter of bodies, as arising from the sum of their elements. For the quantity of matter of bodies is and must be measured by those sensible properties of matter which undergo quantitative addition, subtraction and division, as the matter is added, subtracted, and divided. The quantity of matter cannot be known in any other way. But this mode of measuring the quantity of matter, in order to be true at all, must be universally true. If it were only partially true—if some kinds of matter had weight and others had not—the limits of the mode of measuring matter by weight would be arbitrary: and therefore the whole procedure would be arbitrary, and as a mode of obtaining philosophical truth, altogether futile. But we suppose truth respecting the composition of bodies to be attainable; therefore we must suppose the rule, which is the necessary basis of such truth, to be itself true.
Sir W. Hamilton has replied to these arguments, but, as I conceive, without affecting the force of them. I will repeat here the answer which I have already given[306], and will reprint in the Appendix the Memoir by which his objections were occasioned.
He says, (1), that our reasoning assumes that we must necessarily have it in our power to ascertain the Quantity of Matter; whereas this may be a problem out of the reach of human determination.
To this I reply, that my reasoning does assume that there is a science, or sciences, which make assertions concerning the Quantity of Matter: Mechanics and Chemistry are such sciences. My assertion is, that to make such sciences possible, Quantity of Matter must be proportional to Weight. If my opponent deny that Mechanics and Chemistry can exist as science, he may invalidate my proof; but not otherwise.
(2) He says that there are two conceivable ways of estimating the Quantity of Matter: by the Space occupied, and by the Weight or Inertia; and that I assume the second measure gratuitously.
To which I reply, that the most elementary steps in Mechanics and in Chemistry contradict the notion that the Quantity of Matter is proportionate to the Space. They proceed necessarily on a distinction between Space and Matter:—between mere Extension and material Substance.