Quoting a passage relative to the law that “all central forces vary inversely as the squares of the distances,” he derides the assertion that “this law is not simply an empirical one, but one deducible mathematically from the relations of space—one of which the negation is inconceivable.” Now whether this statement can or cannot be fully justified, it has at any rate none of that absurdity alleged by the reviewer. When he puts the question—“Whence does he [do I] get this?” he invites the suspicion that his mind is not characterized by much excursiveness. It seems never to have occurred to him that, if rays like those of light radiate in straight lines from a centre, the number of them falling on any given area of a sphere described from that centre, will diminish as the square of the distance increases, because the surfaces of spheres vary as the squares of their radii. For, if this has occurred to him, why does he ask whence I get the inference? The inference is so simple a one as naturally to be recognized by those whose thoughts go a little beyond their lessons in geometry.[38] If the reviewer means to ask, whence I get the implied assumption that central forces act only in straight lines, I reply that this assumption has a warrant akin to that of Newton’s first axiom, that a moving body will continue moving in a straight line unless interfered with. For that the force exerted by one centre on another should act in a curved line, implies the conception of some second force, complicating the direct effect of the first. And, even could a central force be truly conceived as acting in lines not straight, the _average_ {291} distribution of its effects upon the inner surface of the surrounding sphere, would still follow the same law. Thus, whether or not the law be accepted on _a priori_ grounds, the assumed absurdity of representing it to have _a priori_ grounds, is not very obvious. Respecting this statement of mine the reviewer goes on to say― “This is a wisdom far higher than that possessed by the discoverer of the great law of attraction, who was led to consider it from no cogitations on the relations of space, but from observations of the movements of the planets; and who was so far from rising to that clearness of view of the truth of his great discovery, which is expressed by the phrase, ‘its negation is inconceivable,’ that he actually abandoned it for a time, because (through an error in his estimate of the earth’s diameter) it did not seem fully to account for the motion of the moon.”