150 THE POPULAR SCIENCE MONTHLY, 



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 ob- 

 servation 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 ; be- 

 cause he would say that both the spectator's position in space and.tbe 

 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 ob- 

 ject that the seeming fulfillment of the prediction, say a transit of 

 Venus, may be efiected by various combinations of the changing posi- 

 tions 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 difi*erent. 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 pre- 

 dicted time: supposing that, in the absence of the first law, this pre- 

 dicted 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 w^hich it would not have were any of them 

 at variance, is unquestionable. But it does not therefore follow that as- 

 tronomical observations can furnish a test for each individual as sum2> 

 tion, 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. Kor 

 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 



