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had been grouped into "a separate division of mathematics." Why he was not aware of this is easily explained. The title, "Descriptive Geometry," has never been adopted in England for the subject to which it was originally applied by the French: its modern restricted use is known only to professed mathematicians, and, as it now turns out, not even to all of these. This candor of Mr. Spencer, however, the reviewer takes advantage of, - with what fairness we have seen. And then, showing the disingenuousness of his criticism, he seeks to ward off the charge of misrepresentation by saying "it is possible that Mr. Spencer has in mind certain propositions in the Higher Geometry' concerning relations of position and direction in points and lines." Indeed! it is possible that Mr. Spencer means that which, by his definition, he obviously does mean! Having first founded a charge of ignorance on a misrepresentation, the reviewer admits the possibility of another interpretation, which is, in truth, the only one Mr. Spencer's words will bear! There remains but to note the second clause of his last sentence: "But these [propositions in the Higher Geometry] cannot be made to stand alone, or independently of dimensional properties." To this the rejoinder is nothing else but a direct contradiction. If the reviewer asks for proof, we refer him to the recently published German work of Reye, entitled, "Geometrie der Lage." This will supply him with a whole volume full of propositions that wholly ignore "dimensional properties," are absolutely non-quantitative.

The readers of the "Christian Examiner" will remember an article which appeared in March of last year, entitled "Positivism in Theology." It is to this that most of the remarks we have to make will more especially apply. But first we offer a few words relating to the general plan of Mr. Spencer's system.

An early and thorough student of science in its various departments, and with a strongly philosophical turn of mind, it was but natural that Mr. Spencer's attention should have been drawn to the necessity and possibility of a more perfect organization than had hitherto been made of the general principles of knowledge, so as to form a connected and comprehensive philosophy of nature. This inclination was entirely coincident with the great tendency of modern inquiry, which is towards the disclosure of universal interdependence, harmony, and unity in nature. The problem of philosophy, as conceived by Mr. Spencer, was to represent this order and unity in thought. As the system was thus to be a mental reflex of the truth of nature, it was inevitable that he should take for its central and controlling idea the largest principle of connection and action which science has revealed in the universe; and this he discovered to be the Law of Evolution. The principle thus shadowed forth in so many directions, Mr. Spencer has worked out with more precision and completeness than any other thinker; and, holding it to be a universal law of nature, he has made it the organizing principle of his philosophical system. With it, that system, as such, must stand or fall. But to this scheme, which is to comprise some ten volumes in its development, he has prefixed an Introductory Essay of a hundred and twenty-two pages, discussing the question how far philosophy can go, and where she must stop, the bounds of legitimate inquiry, the limits of the knowable and the sphere of the unknowable; and he has here made an earnest and able attempt to fix the basis of a reconciliation between religion and science.

in the arc of a circle, which circle has its centre at the bisection of the arc of the complementary segment. This theorem he afterward published, with a demonstration, in The Civil Engineer and Architect's Journal for July, 1840, p. 224.

This introductory part, however, is by no means an essential portion of the philosophical system. Had Mr. Spencer not entered at all upon the question of the connection of the knowable and unknowable, his system of philosophy would still have been substantially what it is. For it is a perfectly possible thing, without expressing any opinion concerning the origin of things, to propound generalizations respecting the universal course of things, the order of phenomena, the connection and succession of events, as known to us in time and space. The general doctrine of evolution may be enun

VOL. LXXXII. -NEW SERIES, VOL. III. NO. II.

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ciated and worked out in full detail, quite apart from all theological or ontological or metaphysical questions; and its truth or error is not in the least affected by the truth or error of Mr. Spencer's views respecting religion and science. Yet his critics have constantly committed the mistake of supposing, that, if they could throw doubt upon Mr. Spencer's doctrine regarding the relation of the Universe and its Cause, they thereby effectually disposed of his philosophy.

Now, so far as the philosophy proper is concerned, our reviewer has very little to say about it. He denies the adequacy of Mr. Spencer's method of inquiry to attain the result proposed, and carps at the law of Evolution. Mr. Spencer adopts the method by which modern knowledge has been created, - first, the establishment of data; second, generalizing from these data; third, verification of the generalizations. His idea is, that, when we have thus reached the most general truth attainable, we have also arrived at the highest unity of knowledge; or, that the process by which knowledge is created is competent also to "unify" it. Not at all, says the reviewer. "Mere generalization is powerless to unify knowledge" (p.240). Now, what is unifying knowledge but reducing many facts to one fact? and what is this but generalizing? What is the highest unification of knowledge but the reduction of all facts to different forms of one fact? and what is this but generalization carried to its highest degree? To say that mere generalization is powerless to unify knowledge is to say that mere generalization is powerless to achieve generalization. Having thus, as he supposes, by a dash of his pen, discredited the grand tendency of modern intellect, what does the reader imagine he offers instead? He offers us the old file at which metaphysicians have been gnawing these thousands of years; and which will probably continue as sharp as at first, so long as this species of mental enterprise continues. "Its unity must be found in the equipoise and dynamic correlation of being and thought, which are welded into one in the act of knowledge itself." And, pray, what unification of fragmentary knowledges has ever been accomplished by that recipe?

Again, as to the fundamental conception of Mr. Spencer's philosophy. "Further, in assuming universal nebula as the homogeneous of progressive heterogeneity, Mr. Spencer really makes an enormous assumption opposed to facts. What sort of homogeneity is that which would exist among sixty-two chemical elements, probably differing in atomic shape, and certainly differing in chemical affinities and properties?" (p.243.) It might be thought that, before a reviewer ventured so confidently to expose this "enormous assumption opposed to facts," he would have taken some care to acquaint himself with the current views of chemists on the matter in question. What is his authority for supposing, that the sixtytwo chemical elements are considered as elements, in any other sense than as substances which we are at present unable to decompose? No chemist of any prudence, who bears in mind what Davy did with the alkalies, would commit himself to the assertion, that what we regard for convenience' sake as simple bodies are really simple bodies. On the contrary, chemists in general tacitly assume the great probability that all these bodies, which as yet resist our powers of decomposition, are really compound. The whole chemical notation is based upon an implied supposition of this kind. The endeavor to reduce the various atomic weights to multiples of hydrogen, involves the suspicion that the so-called elements are all built up out of some common unit. And various attempts have been made to represent the modes in which this original unit may be so grouped and re-grouped as to form atoms answering to the atomic weights of the different elements. Even the strictures that are passed, and legitimately passed, upon the belief that the atoms of other elements are multiples of the atoms of hydrogen, - strictures based upon the fact that the atomic weights do not exactly correspond with this assumption, - even these strictures are not supposed to tell against the belief that the various kinds of matter are built up of homogeneous units, but only against the idea that the atom of hydrogen is that unit. If hydrogen is compound, which we have now good reason for believing, the anomalies in the chemical scale no longer stand in the

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way of the belief in the fundamental homogeneity of matter. But the belief that the so-called elementary bodies are not really elementary is no longer merely suspected: it is proved as clearly as is possible without actual separation of the components. The phenomena of spectrum analysis render the assumption, that the so-called elementary bodies are really elementary, quite inconceivable. Were their atoms simple, each of them could produce only a single line in the spectrum. But each of them produces more than one, and some of them a great number. Even those of small atomic weight, such as nitrogen, have three or more lines; and those of higher atomic weights have some of them very many; as instance iron, which has eighty-three lines. Being produced by the absorption of certain ethereal undulations by atoms oscillating synchronously with them, it is impossible that the atom of a so-called element should produce very many lines, unless it were composed of very many atoms oscillating in different periods.

But, even supposing it were true that there are sixty-two elements, properly so called, and that, instead of beginning with absolute homogeneity, evolution begins with a form of matter that is to this extent heterogeneous, it by no means follows that the law of Evolution is untrue. Mr. Spencer has nowhere made the "enormous assumption" ascribed to him. He has himself pointed out, that the formula has to be taken with a qualification; that there is no such thing in nature as absolute homogeneity; that, save under unimaginable conditions, absolute homogeneity is impossible. And, to meet the fact rigorously, he describes the process of evolution as a transformation of the relatively homogeneous into the relatively heterogeneous, through a progressive increase of heterogeneity. All that is alleged is, that, with whatever stage of the process we begin, every further stage increases the degree of multiformity. Whether the first stage, as known to us, was or was not absolute uniformity matters not; and, as Mr. Spencer himself asserts that the first stage was not and could not be absolute uniformity, he will probably not feel much discomfited by the reviewer's statement, that

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