Page:Popular Science Monthly Volume 4.djvu/567

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answering to the axiom that action and reaction are equal and opposite. In the last case, as in the first, ideas of the terms and their relations require to be made, by practice in thinking, so vivid that the involved truths may be mentally seen. But when the individual experiences have been multiplied enough to produce distinctness in the representations of the elements dealt with, then, in the one case, as in the other, those mental forms, generated by ancestral experiences, cannot be occupied by the elements of one of these ultimate truths without perception of its necessity. If Prof. Tait does not admit this, what does he mean by speaking of "physical axioms" and by saying that the cultured are enabled "to see at once their necessary truth?"

Again, if there are no physical truths which must be classed as a priori, I ask why Prof. Tait joins Sir W. Thomson in accepting, as bases for Physics, Newton's Laws of Motion? Though Newton gives illustrations of prolonged motion in bodies that are little resisted, he gives no proof that a body in motion will continue moving, if uninterfered with, in the same direction at the same velocity; nor, on turning to the enunciation of this law, quoted in the above-named work, do I find that Prof. Tait does more than exemplify it by facts which can themselves be asserted only by taking the law for granted. Does Prof. Tait deny that the first law of motion is a physical truth? If so, what does he call it? Does he admit it to be a physical truth, and, denying that it is a priori, assert that it is established a posteriori—that is, by conscious induction from observation and experiment? If so, what is the inductive reasoning which can establish it? Let us glance at the several conceivable arguments which we must suppose him to rely on.

A body set in motion soon ceases to move if it encounters much friction, or much resistance from other bodies struck. If less of its energy is expended in moving, or otherwise affecting, other bodies, or in overcoming friction, its motion continues longer. And it continues longest when, as over smooth ice, it meets with the smallest amount of obstruction from other matter. May we then, proceeding by the method of concomitant variations, infer that were it wholly unobstructed its motion would continue undiminished? If so, we assume that the diminution of its motion observed in experience is proportionate to the amount of energy abstracted from it in producing other motion, either molar or molecular. We assume that no variation has taken place in its rate, save that caused by deductions in giving motion to other matter; for, if its motion be supposed to have otherwise varied, the conclusion, that the differences in the distances traveled result from differences in the obstructions met with, is vitiated. Thus the truth to be established is already taken for granted in the premises. Nor is the question begged in this way only. In every case where it is remarked that a body stops the sooner, the more it is obstructed by other bodies or media, the law of inertia is assumed to hold in the obstructing bodies or media. The very conception of greater or less