“Returning to the general issue, perhaps the ‘Senior Wrangler’ will pay some respect to the judgment of one {306} who was a Senior Wrangler too, and a great deal more—who was distinguished not only as a mathematician but as an astronomer, a physicist, and also as an inquirer into the methods of science: I mean Sir John Herschel. In his _Discourse on the Study of Natural Philosophy_, he says:― “‘When we would lay down general rules for guiding and facilitating our search, among a great mass of assembled facts, for their common cause, we must have regard to the characters of that relation which we intend by cause and effect.’ “Of these ‘characters’ he sets down the third and fourth in the following terms:― “‘Increase or diminution of the effect, with the increased or diminished intensity of the cause, in cases which admit of increase and diminution.’ “‘Proportionality of the effect to its cause in all cases of _direct unimpeded_ action.’ “Observe that, in Sir J. Herschel’s view, these are ‘characters’ of the relation of cause and effect to be accepted as ‘general rules for _guiding_ and facilitating our search’ among physical phenomena—truths that must be taken for granted _before_ the search, not truths derived _from_ the search. Clearly, the ‘proportionality of the effect to its cause in all cases of direct and unimpeded action’ is here taken as _a priori_. Sir J. Herschel would, therefore, have asserted, with Mr. Spencer, that the Second Law of Motion is _a priori_; since this is one of the cases of the ‘proportionality of the effect to its cause.’ “And now let the ‘Senior Wrangler’ do what Sir J. Herschel has not done or thought of doing—_prove_ the proportionality of cause and effect. Neither he, nor any other of Mr. Spencer’s opponents, has made the smallest attempt to deal with this main issue. Mr. Spencer alleges that this cognition of proportionality is _a priori_: not in the old sense, but in the sense that it grows out of experiences that precede reasoning. His opponents, following Prof. Tait in the assertion that Physics is a purely experimental science, containing, therefore, no _a priori_ truths, affirm that this {307} cognition is _a posteriori_—a product of conscious induction. Let us hear what are the experiments. It is required to establish the truth that there is proportionality between causes and effects, _by a process which nowhere assumes_ that if one unit of force produces a certain unit of effect, two units of such force will produce two units of such effect. Until the ‘Senior Wrangler’ has done this he has left Mr. Spencer’s position untouched.” APPENDIX B.