-- question the consistency of establishing laws to exact penalties for those crimes against the commission of which we have offered no degree of prevention in that philanthropic spirit which is demanded of every educated individual in this favoured land? I look, then, upon education as the great lever, opposed to physical force, by which the mind of the country is to be elevated, and by which wholesome reforms in every department of our public institutions, and what is of most consequence, in all our private sentiments and actions, are to be rationally and safely propelled: for unless public reform conduces very extensively to private reformation it is worse than useless; but at the same time that I state this, I do sincerely believe, that the private reformation that has of late years so apparently taken place, is the foundation of all desire for reform in our public institutions. I believe the moral force combined against church-abuses, or the incongruities of any other temporal establishments, to be irresistible: and as proof of this assertion, I draw notice to the fact of real anti-reformers the decided sticklers for no manner or measure of reform-being now-a-days so exceedingly rare. Ask ancient men if the swearing and drinking so prevalent in their youthful days among the better classes of society, have a comparative existence at all now? Where is the infidel work that dare openly make its appearance? Indeed, the Times Newspaper, a little time back, refused to insert an advertisement of a curtailed edition of Thomas Paine's works; and should any churchman assert that people are no better now, let us ask, what then becomes of the efficiency of the established church of the land? And although Parliament has been called on to pass a bill for the better observance of the Sabbath, it is not because the Sabbath is neglected, but because the public mind is partially aroused to observe that holy day in a more devotional manner than formerly; and thus the call on Parliament to enact further laws, is a proof of the improvement of the national mind in religious obedience; and moral fruit, as the consequence of intellectual culture, must be confidently looked for; or, the Creator has given us contradictory commands. The analogy to my mind is perfectly clear. For God has placed his creatures in such a situation, and granted them such faculties as necessarily lead to their advancement in wealth, learning, and all the arts and sciences of life. Now, if the consequence of this advancement be a regular progress from bad to worse, if the development of the intellectual faculties tend to a proportionate depravity of the moral character-we cannot but say, that such a state of things is at direct variance not only with our general notions of a beneficent Deity, but with the facts on which those notions are established, namely, every other arrangement that we see throughout creation: and it is at decided variance with the revealed word of God. No assertion can be more absurd than that which lays down as truth, that a rude, uncultivated state of life, is to be preferred for its purity to a state of civilization. All savages are children in understanding, but in malice men. Education is the separating barrier between selfishness, rapacity, cruelty, deceit, sensuality all virtues of barbarian life, and prudence, morality, soVOL. II.-July, 1835. C ciality, and religion, those component parts of civilized character. In all successful and permanent efforts of missionaries among savages, civilization and conversion have gone hand in hand. And those who think that more virtue is to be found in a half-civilized condition of society, are under that common delusion of the imagination which connects what is morally, with what is physically, beautiful. A pretty cottage by the side of a wood, or in a lonely valley near a purling brook-where seemingly nought but the melody of the nightingale, the cooing of the dove, the lowing of cows, the bleating of lambs, and the hum of bees is heard, associates ideas of rural innocence as connected with its inmates. But, alas! a knowledge of human nature confirms the scriptural account, that there is something inherent in the breast of man as disposed to evil, that no external connection can eradicate: and if we find not a country and a crown bartered, we find the mess of pottage in the same predicament. This pretty cottage, in its pretty situation, will bear no comparison with the new brick house in the populous street, as regards the common origin and law of association; but we may rest assured, that no nook or corner of the most retired valley is pure, unless made so by the cleansing gift of Almighty grace, very mainly acting through the converted understanding. Indeed, if our religion be of any importance in the amelioration of mankind, and if enlightened views of it must be gained ere a right practice of its moral code can be begun, do we not at once see the paramount importance of education, and the necessarily ordained connection between intellectual and moral improvement. And Scripture is written in such a tone, as seems to presuppose in us a natural power, or a capacity for acquiring the power, to distinguish her inculcation of virtue and reprobation of vice, justly and rationally. And that it is necessary to cultivate this power, we must learn, from the fact of the religion of the ignorant being often worse than no religion at all; as the records of the world have shewn us even Christianity herself as a gross and debasing superstition. Men may advance, it is true, to a degree of great intellectual cultivation and refinement of manner, and yet continue in a state of utter irreligion; but all experience shews, that a savage, though prostrating himself before a crucifix, cannot be a Christian. Moral, intellectual, and religious virtues alike are brought out, as we may say, by education. The philosopher, the saint, or the hero-the wise, the good, or the great man, very often lie concealed in the plebeian, which a proper education might have disinterred and brought to light. Gray says, with great truth, in his Elegy on a Country Churchyard "Perhaps in this neglected spot is laid Some heart once pregnant with celestial fire; Some village Hampden, that with dauntless breast And Bonnet has asked the question, "Would Newton, had he been born in the most remote part of Calefornia, of barbarous parents, have discovered the system of the world?" That Newton would have been an illustrious savage, in art, if not physical force, there can be no doubt. Happy indeed should we be, who live in a country which gives a living example to the world of the intimate union that exists between a moral and intellectual culture; and whose individual goodness, as I have said above, is the evident foundation of all desire for general improvement in the institutions of her ancient, and originally less adulterated, constitution. But yet there is much to surmount, before "every valley shall be exalted, every mountain and hill made low: the crooked be made straight; and the rough places be made plain:" but let no one despair-and to draw back in such a critical season is absolute cowardice and dereliction of an imperative duty. Let us have an educating as well as an educated ministry, of church or conventicle; and let the people resort in companies to those who are apt to teach,' willing to communicate." The people must, in natural connection with their own individual exertions, come strongly to the aid of" the powers that be; as Lord Brougham aptly said at the anniversary of the British and Foreign School Society:-"the efforts of Parliament to do their duty,—of the Government to do theirs,would be in vain, unless that meeting encouraged Parliament, and stimulated Government." The main point is, that the votes at every general election be given freely to the friends of education, tolerance, and civil and religious liberty. 66 99.66 Since I have observed on the increase of individual moral excellence, so coeval with the increase of education in this country, and have given exhortations that tend to its continuance-and, under God's help, may it go on and prosper-I cannot help concluding with a passage from Dr. Arnold's last volume of Practical Sermons, which incites us to a continual advancement, a holy shining more and more, in our spiritual as well as temporarily educational course: "In your education for this life," he preaches to the youth of Rugby School," the fulness of the knowledge of manhood is not expected of you in youth or in childhood; he is satisfying his parents, and answering their wishes for him, who, never going backwards, nor ceasing to go forwards, strengthens his mind week by week, and month by month, and year by year; and removes one piece of ignorance after another; and opens and enlarges, gradually, the range of his knowledge, till his faculties have come to their full ripeness. And even so is it in our education for eternity. Our Father would have us always going forwards, always overcoming some temptation, some bad habit, some bad temper; always growing in confidence and love towards Him, and becoming more and more like his first-born, Jesus."* KLARA. * Vol. III. p. 24.-See also Sermon XVI. THE RELATIONS OF NUMBER. THE powers of numbers, and their relation to each other, have been in a variety of ways demonstrated; but rarely indeed with any important practical application: we have ingenious theories of the wondrous powers of the number 9, and a variety of arithmetical lergerdemain is abroad, which appears to the curious very singular and astonishing. Napier's bones or rods afford some good illustrations of the multiplying powers; but there appears to have been no instance of the successful application of the "occult powers of numbers" till the invention of the " Arithmetical Frames," by Mr. Martin, which are, without question, applied to a use the most important and extensive. But when we come to make an examination of these, we are unable to ascertain, except in one or two cases, the principles upon which they are constructed. In these frames we have what is most extraordinary, a system of arrangement which carries out, ad infinitum, practical exhibitions of all the elementary rules, not singly only, but also in every variety of combination which the ten digits will make, affording demonstrable proofs of the correctness or incorrectness of every figure; at the same time that none but the teacher who has been previously informed of the mode of detecting error, can by any possibility be informed of it. A dozen exercises of fifteen or sixteen figures each, may be worked in one rule only, or through the whole four rules, and be checked by the master at a mere glance, while those exercises may be varied to the extent of many thousands of millions times, and be proved by the same mode and with the same facility. It has often occurred to mathematicians, that a series of numbers might by some possibility be arranged, so as to produce uniform and known results in an almost infinite series; but this suspected power of the arrangement of numbers has never been shown, excepting in a few cases of particular numbers; and even these have not been applied to any practical purpose, excepting by Patrick Whytock, to whom we shall hereafter refer. But this arrangement which is founded on the peculiar properties of certain decimal fractions is defective, as it only refers to the simple rules, whereas the arithmetical frames or tablets constructed by Mr. Martin, comprize also the compound rules; and this appears most extraordinary; for there cannot well be worse decimal relations, supposing they are constructed on this principle, than those of the numbers 4, 12, and 20, which form the integral parts of our common currency; but Mr. Martin has arranged and can apply, if necessary, his principle through all the weights and measures, affording an infinite variety of examples, whose solutions bear such a relation to their propositions, that their correctness or incorrectness is immediately discoverable by him who has learnt the mode of discovery; and which may be acquired, by any one conversant with addition and multiplication, in a few minutes. Nor is this all, for the frames are so arranged that the smallest as well as the largest examples may be given; that the working of the examples of one rule gives examples in another, and the working again of these examples in a third, and so on-proving the correctness of each, even to the pupils themselves, and pointing out error; at the same time that the master has a counter check, which he can apply in a moment to a whole morning's set of exercises. Such a plan, where a large number of boys are to be taught, as in National and Lancasterian schools, must be of incalculable advantage; and even in private schools must afford great assistance to teachers, from the variety of examples presented, and the ease with which their answers may be ascertained. DESCRIPTION OF THE FRAMES. The "Arithmetical Frames" consist of six frames, about 18 inches high and 1 foot broad. The first of which is fitted up with little balls transversely arranged on four brass rods, as the ball frame of the infant schools; but to this, which only forms the top part of the frame, nine cubical rods vertically placed, and revolving on pivots, are attached: on one side of these rods are small pictures about an inch square, of ships, horses, cats, cows, and such like figures differently coloured; their object is, as is also that of the balls, to teach the infant to count, and to connect abstract signs with tangible objects. The other three sides of the rollers are filled up with three numeration tables, so ingeniously disposed, that by the turning of the rods, every variety of change of figure may be produced so strikingly, that a few hours are generally sufficient to teach a child the principles of numeration and notation with the rudiments of addition. : The succeeding frames comprise a frame for each of the following rules the addition frame consists of 12 cubical rods or rollers, horizontally placed, and by the simple turning of these, an infinite number of examples may be produced, and their answers discovered in a moment. To the subtraction frames, which are constructed to hold only two rollers at a time, containing the subtractors and the subtrahend, large slates are also attached, on which the remainders are worked, one below the other, forming an example in addition, which is added up. The multiplication and the division frames are made to contain only one roller, the former has a slide upon which the multipliers are printed, which shows one figure at a time through a square hole immediately under the unit of the multiplicand, and the latter has a slide for the divisors moving up and down upon the dividends to change the examples; by which simple contrivance, as many changes may be produced as upon a peal of 12 bells, stated to be several thousands of millions. In these two latter frames there is still a recapitulation of preceding rules, with different examples applied throughout the compound as well as through the simple rules;-the whole forming a system of teaching the theory of arithmetic so complete, as to make improvements extremely difficult, and presenting a combination of figures whose results, are, as we have stated, "most extraordinary in the history of the relations of number; "—and their effects on the children who are taught by them, as is exemplified at the Borough-Road Cen-tral Schools; to use the words of Lord Brougham, in his speech on Education" present the most extraordinary spectacle of the progress of obtaining information which might be made by children, and which he had never seen or heard of at any place, in any country, |