148 THE POPULAR SCIENCE MONTHLY. 



maticiaD, standing among the very first, such qualified agreement as 

 is implied in saying that the first law of motion cannot be proved by 

 terrestrial observations (which is in large measure what I undertook 

 to show in the paragraphs which the reviewer passes over so con- 

 temptuously). But his last sentence, telling us what he thought " every 

 tolerably educated man was aware " of, is the one which chiefly de- 

 mands attention. In it he uses the word law — a word which, con- 

 veniently wide in meaning, suits his purpose remarkably well. But 

 we are here speaking of physical axioms. The question is, whether 

 the justification of a physical axiom consists in showing that, by as- 

 suming its truth, we can explain the observed phenomena. If it does, 

 then ail distinction between hypothesis and axiom disappears. Mathe- 

 matical axioms, for which there is no other definition than that which 

 Prof. Taiu gives of physical axioms, must stand on the same footing. 

 Henceforth we must hold that our warrant for asserting that " things 

 which are equal to the same thing are equal to one another " consists 

 in the observed truth of the geometrical and other propositions dedu- 

 cible from it and the associated axioms — the observed truth, mind ; for 

 the fabric of deductions yields none of the required warrant until these 

 deductions have been tested by measurement. When we have de- 

 scribed squares on the three sides of a right-angled triangle, cut them 

 out in paper, and, by weighing them, have found that the one on the 

 hypothenuse balances the other two, then we have got a fact which, 

 joined with other facts similarly ascertained, justifies us in asserting 

 that things which are equal to the same thing are equal to one an- 

 other ! Even as it stands, this implication will not, I think, be readily 

 accepted ; but we shall find that its unacceptability becomes still more 

 conspicuous when the analysis is pursued to the end. 



Continuinpj his arojument to show that the laws of motion have no 

 a 2yriori warrant, the reviewer says : 



" Mr. Spencer asserts that Newton gave no proof of the Laws of Motion. 

 The whole of the ' Principia ' was the proof, and the fact that, taken as a system, 

 these laws account for the lunar and planetary motions, is the warrant on which 

 they chiefly rest to this day." 



I have first to point out that here, as before, the reviewer escapes 

 by raising a new issue. I did not ask what he thinks about the " Prin- 

 cipia " and the proof of the laws of motion by it ; nor did I ask Avhether 

 others at this day hold the assertion of these laws to be justified 

 mainly by the evidence the Solar System aflTords. I asked what New- 

 ton thought. The reviewer had represented the belief that the second 

 law of motion is knowable a priori, as too absurd even for me openly 

 to enunciate. I pointed out that since Newton enunciates it openly 

 under the title of an axiom, and ofiers no proof whatever of it, he did 

 explicitly what I am blamed for doing implicitly. And thereupon I 

 invited the reviewer to say what he thought of Newton. Instead of 



