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Learning Mathematics.

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A president Examiner of articled clerks at the Law Institution has observed upon this forcing system:

I for one, and I am glad of the opportunity of expressing it, abhor all Cramming; and I hold very cheaply the system of Competitive Examination, which is nowadays begun almost in the nursery, and thought so highly of in some quarters as a test. It is not to be expected, without inverting the natural order of things, that a youth of twenty or twenty-one should have exhausted those stores of learning which Coke speaks of as requiring not less than the lucubrationes viginti annorum; and remember that those twenty years would begin at that period of life on which most of you are now but entering. In this view the papers before you have been prepared, and our aim as examiners has been to set such questions as will prove you to possess the elements of a liberal education; and that you have so far acquired the principles of common law, equity, conveyancing, criminal law, and bankruptcy, that you are entitled to enter upon the practice of your profession, leaving its complete mastery to that experience which time alone can supply. I need not remind you of the men who, beginning as attorneys, have attained to high positions in the State. The portrait of Lord Chancellor Truro hangs before you on these walls. I had the privilege of knowing him personally; his example may well stimulate your ambition, and animate your exertions, for never man won high place with more unremitting labour than he did; not, however, at the expense of his childhood or of his youth, not by the sacrifice of all else for mere mental culture, but by the full-grown energies, by the well-directed vigour and power of the man, for he was between thirty and forty years of age before he was called to the bar.

MATHEMATICS.

Mathematics drew from Edmund Gurney the odd definition, that “a mathematician is like one that goes to market to buy an axe to break an egg."

Bacon complains that men do not sufficiently understand the excellent use of the Pure Mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh quick eye, and a body ready to put itself into any postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended. And as for the Mixed Mathematics, I only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed;" thus foretelling the advance of Natural Philosophy.

However, the understanding of Applied Mathematics is not unattainable under ordinary circumstances. Lord Rosse has observed that, without any special mathematical knowledge, a well-informed man may often, in the results announced, and from the observations elicited, obtain very interesting glimpses of the nature of mathematical processes, and some general idea as to the progress making in that direction. In applied mathematics there is much more of general interest, and the results are often perfectly intelligible without special education. In proof of this Lord Rosse adduces, that "at the meeting of the British Association at Oxford, the general results of a very abstruse investigation in applied mathematics in physical astronomy were made very interesting. The subject was so brought forward as to rivet the attention of the whole section, and there were many ladies present. The paper was given in by M. Leverrier, and the subject was the identification of a comet. How wonderful from its origin has been the progress of mathematical science! Beginning perhaps three thousand years ago almost from nothing—one simple relation of magnitude suggesting another, and those relations gradually becoming more complicated, more interesting, I may add more important, till at length in our day it has expanded into a science which enables us to weigh the planets, and, more wonderful still, to calculate the course they will take when acted continually upon by forces varying in magnitude and direction."

We trace in Porson's habits of thought the influence which the study of mathematics had upon him.* He was to his dying day fond of these studies. There are still preserved many papers of his scribbled over with mathematical calculations; and when the fit seized him in the street which caused his death, an equation was found in his pocket.

ARISTOTLE.

Aristotle's Philosophy, from its being upheld by the Roman Catholic theology, was lowered in a corresponding degree by the Reformation. Hence it fell into undeserved

In enabling him to give to English scholarship its accuracy and certainty, -as a substratum on which to rest other branches of knowledge often more useful in themselves. See Mr. Luard's able Cambridge Essay.

Geology in Education.

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neglect during the latter part of the seventeenth and the whole of the eighteenth century. Of late years, however, the true worth of his writings has been more fully appreciated, and the study of his best treatises has been much revived. Dr. Holland remarks: "The whole of Aristotle's writings on Sleep, and other collateral topics, deserve much more frequent perusal than is given to them in the present day." The geological theory of Lyell, viz. that the causes which produce geological phenomena are in constant and gradual operation, is the theory of Aristotle and John Ray brought down to our present state of knowledge.

It has been well said that Solomon, Aristotle, and Bacon are the only three men, since our race appeared on earth, who would have been justified in saying that " they took all knowledge for their province."

GEOLOGY IN EDUCATION.

The genius of Werner, of De Saussure, and of Cuvier, laid the foundations on which Geology now rests. They gave us the first glimpse of the fauna and flora of the earlier ages of our planet. Professor Jameson soon saw that these investigations would also lead to much curious information in regard to the former physical and geographical distribution of plants and animals; and to the changes which the animated world in general, and particular genera and species, have undergone, and probably are still undergoing; and he would naturally be led to speculate on the changes that must have taken place in the climate of the globe during these various changes and revolutions. The writings of Blumenbach, Von Hoff, Cuvier, Brongniart, Steffens, and other naturalists, are proofs of what has been done by following up the views of Werner. Ami Boué, speaking of the services Professor Jameson has rendered to science, says: "He has spread valuable working pupils all over the world, and he was the electric spark which originated the beginning of true geology in Great Britain."

It is not much more than seventy years since Bishop Watson, a man of no mean abilities and of no slight distinction, turned the science of geology into open ridicule. He said that the geologists who attempted to speculate on the internal formation of the globe reminded him only

of a gnat which might be perched upon the shoulders of an elephant, and might, by the reach of its tiny puncture, affect to tell him what was the whole internal structure of the majestic animal below.* Listen now to the language of an eminent man of the present day Sir David Brewster, on the same great subject: "How interesting must it be to study such phenomena-to escape for a while from the works of manto go back to primeval times, and learn how its Maker moulded the earth-how He wore down the primitive mass into the strata of its present surface-how He deposited the precious metals in its bowelshow He filled it with races of living animals, and again buried them in its depths, to chronicle the steps of creative power-how He covered its surface with its fruit-bearing soil, and spread out the waters of the deep as the great highway of nations, to unite into one brotherhood the different races of his creatures, and to bless them by the interchange of their produce and their affections!" And again, referring to the discoveries of the great Cuvier in connexion with geology, he says: "In thus deciphering the handwriting of nature on her tablets of stone, the same distinguished naturalist discovered that all organised beings were not created at the same period. In the commissariat of Providence the stores were provided before the arrival of the host that was to devour them. Plants were created before animals, the molluscous fishes next appeared, then the reptiles, and last of all the mammiferous quadrupeds completed the scale of animal life." Such are the terms in which able men now refer to geological science.+

Fortunately, the science of Geology is an eminently popular one. The arguments which go to establish its leading doctrines require no long course of previous study to make them intelligible, and its professors, in this country at least, have been no way disposed to confine their teaching to the sanctuaries of learning. Wherever an audience can be gathered together, some eminent geologist is always ready to discourse for the benefit of the gentiles of science, who have rewarded their instructors by a larger share of popularity than is generally bestowed on the professors of other branches of physical knowledge. The consequence is, that a smattering of Geology is now very generally diffused amongst the upper and middle classes in this country -an excellent thing in itself, since even a smattering of natural science helps to enlarge and elevate the mind, but sometimes inconvenient, because few learn enough to get a

* Mr. Watson, among other qualities, which certainly contributed to his advancement in life, possessed a happy confidence in himself, and an opinion of his own fitness for any situation to which he should think proper to aspire, though totally destitute at the time of every qualification requisite to the discharge of its functions. On the 19th of November 1764, he informs us, "I was unanimously elected by the Senate, assembled in full congregation, Professor of Chemistry. At the time this honour was conferred upon me I knew nothing at all of chemistry; had never read a syllable on the subject, nor seen a single experiment in it."-Quarterly Review, vol. xviii. p. 233.

† Sir John Pakington, M.P.

The best Education.

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correct idea of the extent of their own ignorance as compared with the smallness of their knowledge. In the interest of science, the main point to be gained is that, out of the large number who approach the threshold, a sufficient number should be induced to enter into her service, and that each of these should find work fit for his strength and his special faculties. Measured in this way, the progress of Geology seems to be sufficiently satisfactory.*

THE BEST EDUCATION.

Philip de Mornay enjoins: "The best thing to be instilled into the minds of children, is to fear God. This is the beginning, the middle, and the end, of wisdom. Next, they ought to be induced to be kind one to another. Great care ought to be taken to guard against speaking on improper subjects in their presence, since lasting impressions are made at a very early age; on the contrary, our conversation ought to be on good and instructive topics. Imperceptibly to themselves or others, they derive great benefit from such discourse; for it is quite certain that children take the tinge either of good or evil, without the process being discovered."

True excellence is only to be arrived at by the true Education; for in Education, as in all the rest of life, there are two ways of acting. "The one way, when the learner looks upon his powers as his own, and works them in a self-confident, hard spirit; which is by far the quickest way to temporary success. The other, when the learner, looking upon all his powers as given to him, works humbly in a tentative spirit, distrusting self, keeping the heart open to improvement, thinking that every body and every thing can teach him something; putting himself, in fact, in God's hand, as a learner, not as a judge. To such a spirit belongs the promise that he shall be led into all truth. Directly we imagine we know a thing, we close our stores, and shut the gates against fresh treasures; but whilst laying up truth, still think that all is incomplete, still humbly think, however broad and firm and deep the foundation we have laid may be, that eternity shall not suffice for the su Saturday Review.

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