do we esteem the efforts of the School-Book Society, the Christian School-Book Society, and the Government Council of Education, to provide school-books at much lower prices than could be afforded by the booksellers on the demand-and-supply principle. Of course we must be understood now as speaking of the mere fact that some books are provided; various articles and notices that have occurred in our pages render it all but superfluous to state that as to the books provided, we greatly prefer the principle adopted by the Christian School-Book Society to that acted on by the other bodies that we have mentioned. At present we have before us the works published or adopted by the Council of Education. They have hitherto published three works, and adopted one. Of Adam Smith's Theory of Moral Sentiments, Stewart's History of Bengal, and Addison's Essays, it is altogether unnecessary for us to speak. They have long been classical works in our language; and it is only necessary to say that the present reprints are very well got up; and that the value of Addison's Essays is greatly enhanced by Mr. Macaulay's Critique, extracted from the Edinburgh Review, and prefixed to the volume. Mr. Newmarch's In work is an original one, not published under the auspices of the Council of Education, but now adopted by them. It therefore claims our notice as an original issue of the Calcutta Press. The treatise is one very much to our liking. We still remember, and shall remember if we live till our school-boy days be much less recent than they are now, the utter loathing and disgust which attended our own initiation into the practice of arithmetic. those days the idea had never apparently been entertained, that boys had any thing to do in the learning of arithmetic, but to follow the rule prescribed in the text-book. We well remember having ventured to ask why, in order to find the interest of a sum of money for a given number of days, we were told to "multiply by the number of days, and by twice the rate per cent. and divide by 73,000." The question was regarded as a species of lese majesté against the autho'rity of the dictatorial text-book! We esteem it as a matter of thankfulness that this system of things has not been introduced into India. By a strange anomaly the teaching of arithmetic was, and we suspect frequently is, even in the large and good schools at home, handed over to the writing-master; as if there were any connection between the merely mechanical art of penmanship, and the highly scientific study of the properties and powers of numbers. How this should have been, and still more how it should still be permitted to be, it were hard to determine; but we think we perceive a guide-post leading us to the solution of the mystery in the name that was, and we suppose is, given to the study. The writing-master's duty was to teach cyphering, or the merely mechanical formation of the digits by which numbers are represented; and by degrees his province was extended until he took the whole field of arithmetic out of the hand of the mathematician, on whom it ought to have been inalienably entailed. The greatest merit that such a work as this can possess is unquestionably clearness. This Mr. Newmarch has in general attained in a very considerable degree. We think it was Euler who, in preparing an elementary work on Algebra, took a boy of ordinary capacity and made him read over the draft of the manuscript in his presence, and then incorporated with the original text the whole of the explanations that were found necessary to enable him thoroughly to comprehend the several parts. The principle, if not the actual detail of this plan, should be adopted by every one who composes an educational work. Having carefully read over the treatise before us, we have no hesitation in saying that it will prove a great acquisition to those who are now learning arithmetic, and not less to those who have learned it, as too many have, merely by rote and rule. We know that we should cordially have hailed it, had it been put into our hands when we first began to suspect the deficiency of our own arithmetical education. In the course of our perusal, in addition to the usnal number or typographical errata that attach to all works that are printed in India, especially those containing figures and signs, we detected a few slips which are fairly chargeable on the author; and to one or two of which we shall frankly call his attention, assuring ourselves that he will as frankly receive our suggestions. At p. 42 we have the following "DEFINITION. The greatest common measure of two or more proposed numbers is the greatest number which is contained in each of the proposed numbers an exact number of times without a remainder. "Cor.-If of two or more proposed numbers one contain each of the others an exact number of times; that number which contains each of the others, is of course the greatest common measure of all the proposed numbers." It is scarcely necessary to state that this corollary is quite erroneous; the number in question being, not the greatest common measure, but the least common multiple, of the proposed numbers. At p. 84 we have following statement: "On the multiplication of vulgar fraction by a whole number. The fractional multiplicand must be a concrete quantity, and the integral multiplier an abstract number." Now in all multiplication the one factor must be an abstract number and the other a concrete quantity; but we do not know why the fractional multiplicand may not as well be the abstract number, and the integral multiplier the concrete quantity. We would therefore submit that the above quoted sentence would be rendered more accurate by the addition of the words, "or vice versa," or others of the like import. Altogether we may be allowed to say that we think the matter would have been considerably simplified had the author taken a slightly modified view of the nature of a fraction, and had represented it as in every case a mere indication of the operation of divi sion. This we think is the simplest notion we can have of a fraction, and has the advantage of being applicable equally to those fractions which represent concrete quantities, and those which represent mere ratios. Upon the whole we have no hesitation in pronouncing the work before us to be a really good book, and one fitted in no small degree to be useful to scholars and teachers, and to all, as we have said, who wish to remedy the defects of their early education. The East India Calculator's Manual; or a series of Arithmetical Calculations on a Novel System; illustrated by examples; with less than one-fourth the usual labour. Adapted to general use, especially to the ordinary purposes of business.—By H. A. Knott: (late Secretary to the West of England Bank, Bristol, and formerly Head Accountant to the Herefordshire Banking Company, Hereford.) Calcutta, 1847, price 16 Rs. THIS is a book of no small pretension. The Author in his preface quotes Plato and "A Pythagorean," and speaks of his labor as a philosophical speculation. We should have been very glad had we been able to bear him out in his opinion of its merits, but with all desire to discover that philosophy has not, Astræa-like, taken her flight from our Palatial city, we must acknowledge that we have not been able to trace her lurking in the Calculator's Manual. It is but fair to the author to test his system by the example that himself selects as the perfection of it. In his preface he says"The author particularly would here notice his process for dividing by 15 (see Sec. 4, page 15) as being extremely simple Example 482-12 "He will not pretend to state, in this age of science that processes-with less ex pense of figures and trouble-will not be invented, but he cannot conceive any readier methods than those recommended in this treatise." Now on turning to Sec. 4, p. 13 (not 15) we find the method in question thus set forth "To divide by 15-Cut off the unit in the dividend, which will be the unit in the remainder; then deduct one-third, and if there be a remainder, it will stand for the tens in the remainder. Note to be carefully observed respecting remainders. From and including 0 to 9, no alteration required. 10 to 14, the unit of the lesser line must be encreased by 1 before subtraction. For 15 there will be no remainder. From and including 16 to 19 take the difference between it and 15 for the remainder. 20 to 29 ditto and increase the unit of the lesser line by 1 as before." * NOTE. Add 1 to the unit according to rule. Now to our humble thinking this method, so far from being the simplest that can be invented, is about as complicated as can well be imagined In the first place, there are few practised calculators who cannot divide by 15, or indeed any number under 20, by inspection, or as it is called in the ordinary arithmetical books, by short division; and surely this is vastly simpler and shorter than our author's method. Then again there is no calculator who does not know that a thirtieth part of a number subtracted from its tenth part gives its fifteenth part; and this is all that our author's rule tells us. But the rule regarding remainders is so involved, even when it is understood, (and as stated in the Manual it is not very easily understood), that the trouble of recalling it to mind would be ill compensated by the advantage of it. Our remarks on this method, selected by the author himself as the most favorable specimen of his work, are equally applicable to the remainder of its contents. An intelligent culculator does not want it, and an unintelligent one will be far safer and less liable to error in following the ordinary methods. One word by the way on Arithmetical treatises generally. The time has surely come, when Rules, as distinguished from Reasons, should be utterly banished from such treatises. Surely it would have been far better, recurring to the method alluded to, if the author had stated it thus, "subtract a thirtieth part of the dividend from its tenth part." This every one could have understood; and it would have involved in it the substance, not only of the rule, but of the clumsy note also. Altogether we must say that Mr. Knott's work contrasts very unfavorably with that of Mr. Newmarch, which formed the subject of the notion immediately preceding the present. The utility of the Aristotelian Logic; or the Remarks of Bacon, Locke, Reid and Stewart on that subject considered; being the substance of three Lectures delivered to the Senior Students of the Hindu College, Calcutta ; by William Knighton, M.R.A.S., officiating Professor of Literature in that Institution, &c. &c. Calcutta, 1847. It is not with the view of minutely criticizing this work-though there are some passages in it fairly open to friendly criticism-that we introduce it among our Miscellaneous Notices. It is rather to hail its appearance as the indication of progress in a right direction. For many a year, neither Logic nor Moral Philosophy, nor Mental Philosophy, nor Political Economy formed any part of the systematic course of study in the Hindu College. English Literature,-meaning by that little else than History and Poetry-appeared to constitute the main staple of instruction. The science of Mathematics, under so competent a scholar as the late Dr. John Tytler, had some justice done to it; but to Natural Philosophy, in its various departments, seldom was adequate attention paid. Of late years, things have been very much mending. Marked deficiencies have been gradually, to a larger or smaller extent, supplied. Fresh vigour has been thrown into some of the older studies, while new topics of instruction have been wisely and judiciously added. Amongst the latter we reckon the study of Logic. On Mr. Knighton, it devolved as a part of his regular duty to lecture upon it. Now it is well known that against the science of Logic various heavy charges have been brought by modern writers of the highest reputation in the domain of Philosophy, such as Brown, Locke, Reid and Stewart. And Mr. Knighton, having found that the writings of these celebrated authors were "continually in the hands of the students of the Government Colleges," without their "having any thing before them in the way of refutation of the reiterated charges" preferred against the science which it was his duty to expound, he very properly resolved to supply this want by writing out and publishing his vindicatory Lectures," at the request of some of the Students to whom they were originally delivered." Hence the origin of the present publication. In prosecuting his task-which, on the whole, he does with considerable tact and judgment-he has largely availed himself, as he plainly tells us in his preface, of the remarks of distinguished Logicians, especially of Whately and Mill. "Whenever," says he, "I could discover any thing bearing upon the point at issue, in the writings of these authors, I have invariably adopted it, sensible that by putting their thoughts into words of my own, I might weaken their force, but could add nothing to their weight or lucidness. This then must be my excuse for the large quantity of quotations, which will be found in the following pages." That The great aim of the author is to shew that all the charges against the science of Logic are, or ought to be, levelled at the abuse and not the right or legitimate use of it. In this attempt he is quite successful. Indeed we have little doubt that a great deal of the disparaging language employed towards it by many eminent writers ought, in fairness and candour, to be uuderstood as solely orchiefly applicable to its abuse or greatly exaggerated pretensions and claims. And in the first exposure of gigantic but long venerated errors, there is the same tendency, as in the discovery of flagrant imposture or daring fraud, to rush into the opposite extreme of indiscriminate censure. there is such a thing as a rational and useful logic it were preposterous, in unqualified terms, to deny. But that any logic is competent for all purposes it were equally preposterous, in unqualified terms, to assert. On this subject the father of modern Philosophy appears, with his wonted penetrating sagacity and sense of equity, to have hit the precise point with reference alike to its utility and inutility, when in his great work "De Augmentis Scientiarum," he thus writes:— "Those who recommend logic as the best and surest instrument for improving the sciences, very justly observe that the understanding left |