These, cleared from entanglements, are the theses held by me, and defended in the following pages. {298} APPENDIX A. (_From_ Nature, _April 16, 1874._) Absence from town has delayed what further remarks I have to make respecting the disputed origin of physical axioms. The particular physical axiom in connection with which the general question was raised, was the Second Law of Motion. It stands in the _Principia_ as follows:― “_The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed._ “If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.” As this, like each of the other Laws of Motion, is called an axiom;[41] as the paragraph appended to it is simply an amplification, or re-statement in a more concrete form; as there are no facts named as bases of induction, nor any justifying experiment; and as Newton proceeds forthwith to draw deductions; it was a legitimate inference that he regarded this truth as _a priori_. My statement to this effect was based on the contents of the _Principia_ itself; and I think I was warranted in assuming that the nature of the Laws of Motion, as conceived by Newton, was to be thence inferred. The passages quoted by the _British Quarterly_ Reviewer from Newton’s correspondence, which were unknown to me, show that this was not Newton’s conception of them. Thus far, then, my opponent has the best of the {299} argument. Several qualifying considerations have to be set down, however. (1) Clearly, the statements contained in the _Principia_ do not convey Newton’s conception; otherwise there would have been no need for his explanations. The passages quoted prove that he wished to exclude these cardinal truths from the class of hypotheses, which he said he did not make; and to do this he had to define them. (2) By calling them “axioms,” and by yet describing them as principles “_deduced_ from phenomena,” he makes it manifest that he gives the word “axiom” a sense widely unlike the sense in which it is usually accepted. (3) Further, the quotations fail to warrant the statement that the Laws of Motion are proved true by the truth of the _Principia_. For if the fulfilment of astronomical predictions made in pursuance of the _Principia_, is held to be the evidence “on which they chiefly rest to this day,” then, until thus justified, they are unquestionably hypotheses. Yet Newton says they are not hypotheses.