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But these volumes are as significant in their omissions as in any thing that they assert. Where the Church affects to see a great mountain of dogma, Schenkel sees nothing of the sort. The idea of a Church, of a communion, does indeed pervade his book; but it is a Church without dogmas, without a ritual. Its only creeds are righteousness and love. So simple is its structure, that there seems to be no reason to suppose that Jesus ever took the pains to form it that Dr. Schenkel indicates. Such as it is, it might have grown-it must have grown out of a heart like that which Jesus carried in his breast. But Dr. Schenkel's negative result is full of hope. It reconciles us to a great deal of passionate attachment to the person of Jesus, to consider, that, just in proportion as the Church discovers him in his real character, it must, if it is honest, cease to believe the pernicious doctrines it has cherished in his name. So much has been achieved already, that it seems not too much to hope, that, when his form shall be revealed in all its beauty, he will be seen, not sitting on a throne demanding homage, but looking up as Beatrice looked into the everlasting glory of another greater than himself. Then God grant that the great Church that he has led so long, following his gaze, as Dante followed Beatrice's in the wondrous tale, may see at length that vision of the Father ever present with his children, which flooded him with so much strength and peace!

ART. IV.-HERBERT SPENCER AND HIS REVIEWERS.

THAT the highest interest of man is to know the truth, and the highest prerogative of intellect to discover it, are propositions which, though questioned by none, are reduced to practice by few. Numerous causes-such as preconceived ideas, deference to popular belief, dread of inconsistency, party feeling, and bias of temperament-act powerfully to warp the judgment and mislead the intellect in the work of

inquiry. So potent are these disturbing influences, that it becomes the highest discipline of the highest natures to guard against them. Even the most gifted minds are liable to be perverted in their action by circumstances commonly regarded as trivial. The great Newton, whose majestic intellect we are wont to think moved in unequalled serenity above the clouds of passion, was so disturbed by the collisions incident to discussion in the meetings of the Royal Society, that he desired the interchange of opinion to take the form of private conference, declaring that "what's done before many witnesses is seldom without some further concern than that for truth." But, while the attainment of truth is hindered by many causes, and we are hence bound to extend a large charity to opponents, there are certain excesses into which writers are prone to fall that we are not for a moment at liberty to tolerate. In these times, when no interests are too vital and no opinions too sacred to escape the assaults of destructive criticism, and when all grades and classes of thinkers are drawn into the vortex of controversy, the danger from over-zeal and over-timidity, as well as from less worthy motives, is greatly heightened; and we are required to insist, with redoubled emphasis, upon a rigorous circumspection in the treatment of adverse views. With the increasing seriousness of conviction and boldness of inquiry which mark our age, a higher standard of justice and honor, and a more thorough conscientiousness in the management of discussion, are to be imperatively demanded. Carelessness of statement, gratuitous imputation of evil motives, misrepresentations of meaning, and all the petty tricks by which a writer seeks to bring an author into reproach, should be sternly reprobated.

Among other ways in which a hostile critic may easily injure an author whose views he dislikes is that of picking out some real or apparent error or incompleteness of knowledge, and so presenting it as to carry an implication damaging to his works. at large. An example of this has been furnished by the "North-American Review," in a reference to the pamphlet on the Classification of the Sciences:

"In Mr. Spencer's subdivisions of mathematics, he has given a prominence to 'Descriptive Geometry' which might be regarded as arising from the partiality of the civil engineer for a branch of his own art, were it not that he says, 'I was ignorant of the existence of this as a separate division of mathematics, until it was described to me by Mr. Hirst, whom I have also to thank for pointing out the omission of the subdivision "Kinematics." It was only when seeking to affiliate and define "Descriptive Geometry," that I reached the conclusion, that there is a negatively quantitative mathematics, as well as a positively quantitative mathematics. In explanation of the term "negatively quantitative," it will suffice to instance the proposition that certain three lines will meet in a point as a negatively quantitative proposition, since it asserts the absence of any quantity of space between their intersections. Similarly, the assertion that certain three points, will always fall in a straight line is negatively quantitative, since the conception of a straight line implies the negative of any lateral quantity or deviation.' The propositions selected by Mr. Spencer to illustrate what he calls Descriptive Geometry' are by no means peculiar to, or characteristic of, the art to which mathematicians have given this name. In the most elaborate and extensive treatises, no more is claimed for this art, than that it is an account, in a scientific order, of certain methods of geometrical construction useful in engineering and architecture, but inferior in scientific extension even to trigonometry, to which Mr. Spencer does not deign to descend. 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: but these cannot be made to stand alone or independently of dimensional properties; and, if they could, they would be as appropriately named ‘quantitative' mathematics as 'negatively quantitative.'” *

Must we then conclude that the writer who assumes to estimate a philosophical system like that of Mr. Spencer in the "North-American Review" is really unaware of the fundamental distinction between Science and Art? It would almost seem so. Ignoring the fact that Science is a statement of the relations among phenomena, and can include in its various divisions nothing more than the various classes of those relations, from which all practice based on knowledge

* North-American Review, April, 1865, p. 470.

of them is excluded, he actually supposes, that, by "Descriptive Geometry" Mr. Spencer means the art of plan-drawing! "Descriptive Geometry," in its scientific sense, no more means "certain methods of geometrical construction useful in engineering," &c., than "Geometry," in its scientific sense, means certain methods of earth-measuring. As from Geometry, which was originally a mathematical art, there has grown up a division of pure mathematics which has usurped the name of the art; so, beginning with the "Géométritric Descriptive" of Monge, in which theorems and their applications to drawing were mingled together, there has grown up a system of theorems which takes the name of "Descriptive Geometry,” while omitting all mention of the practice which gave that name. If, because certain manufacturers and retailers are called "chemists," the reviewer had supposed that by "chemistry," as a branch of science, Mr. Spencer meant certain methods of preparing medicines and making dyes, he would have drawn an equally rational inference. He gains, however, by thus confounding science and art. It enables him to insinuate, by the quotation he makes, that Mr. Spencer, though educated as a civil engineer, was unacquainted with the branch of mathematical art which is especially familiar to engineers.* This insinuation it is unnecessary to meet: it disappears along with the reviewer's mistake on which it is based. It is needful only to point out what Mr. Spencer's admission really amounts to. Here, as in various places, Mr. Spencer has been careful to acknowledge aid derived from others; and, without stating that he was unacquainted with the propositions of "Descriptive Geometry," he candidly says he was not aware that they

*It is somewhat unfortunate for the writer's inference, that Mr. Spencer's first contribution to engineering literature (written before he was nineteen) is an account of a new and easier method of performing one of the most difficult problems of plan-drawing; namely, the delineation of the spiral courses of skew arches. See The Civil Engineer and Architect's Journal" for May, 1839, p. 164.

دو

† It happens, again unfortunate for the reviewer, that one division of "Descriptive Geometry owes an original theorem to Mr. Spencer, which dates back to the time when he was seventeen; the theorem, namely, that the centres of the circles inscribed in all the triangles contained in any segment of a circle fall

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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,

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.