not rest upon sufficient proof, and contained a good deal of arbitrary assumption. Professor Norton, of course, is not of my opinion, and argues that my objections "are destitute of any real force." This was his undoubted right; and, had he confined himself to the defensive, I should have deemed a reply unnecessary; but, as he goes on to attack my own theory with arguments which have a plausible appearance, I think it worth while submitting his article to examination.

The contents of his ably written paper may be summarized, as it appears to me, in the three following propositions:1st. That in molecular science all our general principles are but probable hypotheses.

2nd. That his own principles are not arbitrary assumptions. 3rd. That I in my Elements of Molecular Mechanics' assume principles destitute of sufficient proof.

To these three propositions I beg leave to offer a short reply, which, I hope, will be of interest to all who are engaged, either directly or indirectly, in promoting molecular science.

I.

And to begin with the first proposition, Professor Norton says:

"No theory of molecular physics can, in the nature of things, have any other foundation than general principles to be regarded as hypotheses that have been rendered more or less probable, either by induction from observation, or by à priori reasonings. Molecular physics cannot be erected, like mathematics, upon a foundation known to be eternally sure, that of self-evident truth."

These words express an opinion, which is by no means uncommon among physicists, for the obvious reason that they cannot, by the help of physics alone, undertake to establish fundamental principles; a work, which requires a higher knowledge of speculative science, than it is the fashion for them to acquire. Hence I do not wonder that mere physicists, even with their hands full of good scientific materials, can build only hypothetical theories. The cement, which alone can keep together the stones of a scientific building, is an article which cannot be prepared by the skill of the chemist, but only by the application of general philosophy to experimental truth; and only in proportion as physicists are conversant with general philosophy can they hope to build theories of a character truly scientific, viz. independent of hypotheses; for hypothesis begins there only, where real science ends. I do not wish to develope this point at greater length. I am satisfied that this mere hint will suffice for those whose judgment is of any weight in matters of this sort. They will see at once that I had good reasons for

saying (Molecular Mechanics,' p. 2) that a work which was intended to lay down the very first foundation of a molecular theory, could not possibly rest on hypothetical ground, and that I had embodied in the work, as principles of molecular mechanics, those propositions only which were evident, or which I thought I had the power of rigorously demonstrating from known laws of nature; a proposition which seems to have amazed Professor Norton. But even he will allow, I hope, that, in my capacity of Professor of Philosophy, I can aspire to something better than those hypotheses which are the lot of mere experimentalists.

any

And now to come to his assertion. I would observe in the first place that, if "no theory of molecular physics can have other foundation than general principles to be regarded as hypotheses," then no physical theory can lead to any other than hypothetical conclusions; and as hypothetical conclusions cannot be called "established truths" in any true sense of the words, it follows that neither Professor Norton's theory nor its principles are "established truths." And this would suffice to justify my stricture that his theory rests upon a great deal of

arbitrary assumption."

66

But I must add secondly, in justice to molecular science, that Professor Norton's opinion of it is far from being accurate. Molecular science is not without established principles: it is not a pure heap of hypotheses. That material substance is endowed with active power, passivity, and inertia, for causing, receiving, and conserving local motion: that no natural cause can communicate a finite velocity to a body in an infinitesimal unit of time that in the impact of bodies no communication of motion can be made by means of a true and immediate contact of matter with matter: that an increase or decrease of intensity in motion is always due to a real production or extinction of velocity: that material substance acts, cæteris paribus, with different intensity on bodies placed at different distances: that material substance is not prevented by intervening bodies from acting on other bodies placed at a greater distance that the primitive components of molecules are unextended elements: that these primitive elements obey the Newtonian law of action: and other points of the like nature, with all their corollaries, are not mere hypotheses, but "established truths," about which I think that the readers of the Elements of Molecular Mechanics' can entertain no doubt. And whilst we must admit that we cannot by means of these truths alone attain to a knowledge of all the secrets of molecular science, we do nevertheless affirm that we have in them a solid foundation to build upon. So false is it that molecular science has no established principles, that even Professor Norton's theory, of which some fundamental prin

ciples are, in my opinion, not sufficiently probable, contains undoubtedly a great deal of "established truth."

But "molecular physics," says he, "cannot be erected, like mathematics, upon a foundation known from the first to be eternally sure, that of self-evident truth." This remark of my learned critic does not show that molecular physics cannot be erected on certain truth, but only that physical science, whether molecular or not, does not deal, like mathematics, with truths which consist of necessary relations, but with truths dependent upon contingent facts. The first are known mainly by reason, the secondly mainly by observation and no one demurs to physical certainty on the ground that it is not mathematical. Professor Norton adds:

"Mechanical axioms may exist as mere figments of the mind, and have often risen like bubbles in the minds of speculative philosophers, shone with an evanescent splendour, and suddenly burst at the touch of a hard fact."

I do not deny that axioms may exist as mere figments in the minds of "speculative" philosophers; but the learned Professor has surely forgotten that all philosophers, who build theories, are "speculative" philosophers. Otherwise how is it possible that he should write a theory of molecular physics, and yet be so hard on speculative philosophers amongst whom his work places him?

But Professor Norton apparently wishes to designate as "speculative philosophers" a particular school of philosophers, whose speculations have their origin in à priori reasonings instead of natural facts. If so, I may safely reply that such a school (to which he imagines me to belong) has never existed. There has indeed been a school of philosophers, whose physical speculations are now known to have been in most instances illustrious failures; nevertheless, that school notoriously abided by facts; and their failure was caused by misinterpretation of facts, not by any desire of substituting à priori grounds for à posteriori arguments. In what does modern speculation differ from that of the ancients? We possess, to be sure, a greater number of experimental data; but this advantage (which does not change the nature of scientific speculation) is frequently counterbalanced in a great measure by the vagueness and shallowness of our philosophical acquirements. Facts and laws are only materials for speculation: something more is needed for building sound physical theories: and this something is not so much the power of imagining new hypotheses, as the art of reasoning and an intimate acquaintance with those speculative principles which apply to the interpretation of facts. Such principles are the

supreme test of scientific hypotheses: and if our men of science were less afraid of speculative knowledge than they appear to be, we should be less familiar with the sight of "bubbles shining with an evanescent splendour, and suddenly bursting at the touch of a hard fact," or, let me add, of a still harder principle. Professor Norton thus continues:

"Our author is another instance of a learned philosopher, who has faith in such unsubstantialities, and thinks to substitute them, as a proper basis for a theory of molecular mechanics, in place of the general conceptions, to which the progress of science leads, and by which alone its highest inductions find any explanation-regards the latter as arbitrary assumptions, and his own mental convictions of what matter must be and how it must act as the only reliable foundation upon which to build."

This passage is made up of assertions which may easily be retorted against my critic. But to answer directly. The progress of science leads without doubt to general conceptions, which are sometimes very good, and at other times very questionable, according as those who deal with the matter are more or less conversant with the principles of speculation and the highly important art of reasoning. But the question lies not in this it lies in the truth or falsehood of the assertion that I "substituted” unsubstantialities for those general conceptions. Now, I think that everyone who has read my 'Elements of Molecular Mechanics' can bear witness to the gratuitousness of the assertion. What Professor Norton calls "unsubstantialities" (probably because he cannot touch them with his finger) are considerations which have not been substituted in the place of the general conceptions to which the progress of science leads, but have been added, for the greater satisfaction of a class of readers, under the form of scholia, to the theorems by which those general conceptions are shown to be legitimate results of the progress of science: and have been appended not to prove those theorems (which had no need of a second demonstration) but to meet the "unsubstantialities" of some metaphysicians, who are yet to be reconciled with modern science in certain matters: and, lastly, they have been printed in a smaller type, lest the reader should mistake them for the substance of the work, and engage unawares in the awful mysteries of philosophical speculation (Introd. p. 6). Let Professor Norton read again the first pages of my work: I do not doubt but that he will discover his mistake.

He states likewise that I regard those general conceptions (to which the progress of science leads) as arbitrary assumptions, and my own mental convictions as the only reliable foundation upon which to build. Surely, Professor Norton himself relies

upon his own mental convictions, and considers as arbitrary assumptions those conceptions which clash with them and he may easily understand that I cannot but do the same. But such mental convictions as he attributes to me are quite impossible; for if a man, in matters dependent on facts and laws of nature, should disregard "the general conceptions to which the progress of science leads," how could he ever find a ground on which to rest his mental convictions?

The truth is that Professor Norton has failed to realize to himself the spirit in which my Elements of Molecular Mechanics' were written. He is mistaken in his assumption that I virtually claimed for my method a superiority which he is not ready to recognize. The geometrical method, which I adopted, has its own advantages, independently of the writer who employs it, as everyone must allow but I was so far from claiming any superiority for the method as employed in my work, that I explicitly declared the contrary. As the employment of the geometrical method may have given to the work an air of dogmatism in questions regarding which there are great differences of opinion among philosophers, I beg to say once for all that I have merely stated my own views, without pretending to make further discussion unnecessary (p. 10). Professor Norton has apparently failed to notice these words.

But the whole passage in which I am thus attacked deserves to be here inserted:

"It is true that he takes exceptions to Principles 3rd and 4th from the inductive point of view. Upon this ground (the only legitimate one to be occupied) I am quite ready to meet him: but I wish to enter here, at the outset, a demurrer against the virtual claim of the superiority of his own à priori method of establishing his fundamental principles. Such a claim is implied in the intimation that 'no one has up to this day established the truth of such propositions' as will be best appreciated by those who have read Professor Bayma's book."

My American critic acknowledges that I argued against two of his principles "from the inductive point of view." Hence my intimation that no one had yet established the truth of such propositions, was obviously drawn "from the inductive point of view." How could then my learned critic construe it into a virtual claim of the superiority of any à priori method?

The learned Professor shows a great hostility to what he rather invidiously styles "my à priori method." But a method in which arguments are presented under a syllogistic form, is not necessarily an à priori method. Professor Norton seems to remember only two methods, the à priori and the inductive. He seems to have forgotten that there is a third, the à posteriori