that the axioms called "the laws of motion" are true, resolves itself into a fulfilled prevision that some celestial body or bodies will be seen in a specified place, or in specified places, in the heavens, at some assigned time. Now, the day, hour, and minute, of this verifying observation can be fixed only on the assumption that the Earth's motion in its orbit and its motion round its axis continue undiminished. Mark, then, the parallelism. One who chose to deny that things which are equal to the same thing are equal to one another, could never have it proved to him by showing the truth of deduced propositions; since the testing process would in every case assume that which he denied. Similarly, one who refused to admit that motion, uninterfered with, continues in the same straight line at the same velocity, could not have it proved to him by the fulfillment of an astronomical prediction; because he would say that both the spectator's position in space and the position of the event in time were those alleged only if the Earth's motions of translation and rotation were undiminished, which was the very thing he called in question. Evidently such a skeptic might object that the seeming fulfillment of the prediction, say a transit of Venus, may be effected by various combinations of the changing positions of Venus, of the Earth, and of the spectator on the Earth. The appearances may occur as anticipated, though Venus is at some other place than the calculated one; provided the Earth also is at some other place, and the spectator's position on the Earth is different. And, if the first law of motion is not assumed, it must be admitted that the Earth and the spectator may occupy these other places at the predicted time: supposing that, in the absence of the first law, this predicted time can be ascertained, which it cannot. Thus the testing process inevitably begs the question.
That the perfect congruity of all astronomical observations with all deductions from "the laws of motion" gives coherence to this group of intuitions and perceptions, and so furnishes a warrant for the entire aggregate of them which it would not have were any of them at variance, is unquestionable. But it does not therefore follow that astronomical observations can furnish a test for each individual assumption, out of the many which are simultaneously made. I will not dwell on the fact that the process of verification assumes the validity of the assumptions on which acts of reasoning proceed; for the reply may be that these are shown to be valid apart from astronomy. Nor will I insist that the assumptions underlying mathematical inferences, geometrical and numerical, are involved; since it may be said that these are justifiable separately by our terrestrial experiences. But, passing over all else that is taken for granted, it suffices to point out that, in making every astronomical prediction, the three laws of motion and the law of gravitation are all assumed; that, if the first law of motion is to be held proved by the fulfillment of the prediction, it can be so only by taking for granted that the two other laws of
