moved by a spirit like his own, might evolve abundant absurdities; supplying ample occasion for blazoning the tops of pages with insulting words. * * * * * [_A letter, drawn from_ Prof. Tait _by the foregoing criticisms, and published by him in_ Nature, _initiated a controversy carried on in that periodical between March 26th and June 18th, 1874. Partly in justification of my position, and partly as tending to make clearer the nature and origin of physical axioms, I append certain portions of the correspondence, with some additional explanations and comments. For the purpose of elucidation I prefix the theses I have maintained._] {297} THESES. 1. _If A produces B, then 2 A will produce 2 B._ This is the blank form of causal relation quantitatively considered, when the causes and effects are simple—that is, are unimpeded by other causes and uncomplicated by other effects; and whenever two or more causes co-operate, there is no possibility of determining the relation between the compound cause and the compound effect except by assuming that between each co-operating cause and its separate effect there exists this same quantitative relation. 2. _This truth holds whatever the natures of the simple causes and simple effects; and is an_ a priori _assumption made in conducting every experiment and in reasoning from it._ Every process of weighing, every chemical analysis, every physical investigation, proceeds on this truth without assigning warrant for it; and in allowing for the effect of any minor cause that interferes with the major cause, this same truth is assumed. 3. _When A is an impressed force and B the produced motion, then the general truth that if A produces B, 2 A will produce 2 B, becomes the more special truth called the Second Law of Motion._ Newton’s amplified statement of this Law is:—“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 his further clause, asserting that this law holds whether the directions of the forces are or are not the same, asserts a proportionality between each force and its produced motion, such as we have seen to be invariably assumed between each cause and its separate effect, when there are co-operating causes. 4. _This Law may be affirmed, without specification of the modes in which the impressed force and the resulting motion are to be estimated._ Newton’s statement is abstract. Taking for granted right modes of measurement, it asserts that the alteration of motion (rightly measured) is proportional to the impressed force (rightly measured). 5. _No_ a posteriori _proof of the general ultimate physical truth (or of this more special truth it includes) is possible; because every supposed process of verification assumes it._