tion of the Lord Jesus; and, from the whole, to point out the inferences most necessary for, and useful to, mankind." The amount of the fund to be so applied cannot be less, at any period, than £,1,600, and, as nearly as can be ascertained, it will on occasion of the next competition, be about £2,400. Three-fourths of the fund divisible at each period are appointed, by the terms of the bequest, to be paid to the Author of the Treatise which shall be found by the judges, to be named as after-mentioned, to possess the most merit; and the remaining fourth to the author of the Treatise which, in the opinion of said judges, shall be next in merit to the former, "after deducting therefrom the expense of printing and binding three hundred copies of each of the said Treatises, or of purchasing three hundred Printed Copies thereof, as the said Trustees shall direct to be distributed by them among such persons to whom they shall think the same will prove most useful, or in any other manner that they shall judge proper." These Prizes form, it is believed, the most liberal encouragement ever held out in this way for the promotion of Natural Theology, and will, it is hoped, elicit performances of corresponding value, which may contribute to the farther advancement of that science. The Trustees, deeply sensible of the importance of the Founder's design, and anxious, as far as lies in them, to do full justice to his wishes, venture to give an assurance that, in appointing the judges at the proper time, nothing will be regarded but that eminence of character and qualification which shall secure an impartial and satisfactory decision. The Ministers of the Established Church of Aberdeen, the Principals and Professors of King's and Marischal Colleges of Aberdeen, and the Trustees of the Testator, are appointed to nominate and make choice of three judges, who are to decide, agreeably to certain rules prescribed in the deed of settlement, upon the comparative merits of such Treatises as shall be laid before them; and it may be proper to mention that, to discourage mean performances, the judges are empowered (if unanimous only,) to find none of the Treatises produced of sufficient merit to entitle the writers to the premiums. The Trustees, however, believe that in the present state of the literary world, this is a contingency which can scarcely occur. The time allowed by the Testator for the composition of the Treatises for the next periodical competition, extends to the first of January, 1854, and his Trustees do now intimate, in compliance with his appointment, that those who shall become Competitors for the said Prizes must transmit their Treatises to ALEXANDER and JOHN WEBSTER, Advocates in Aberdeen, agents of the Trustees, in time to be with them on or before the said first day of January, 1854, as none can be received after that day; and they must be sent free of all expences to the Trustees. The judges will then, without delay, proceed to examine and decide upon the comparative merits of such Treatises as shall be laid before them, and the Trustees will, at the first term of Whitsunday, after the determination of the judges, pay the Premiums to the successful Candidates, agreeably to the will of the Testator. As it tends much to an impartial decision that the names of the Authors should be concealed from the judges, the Trustees request that the Treatises may not be in the handwriting of their respective Authors, nor have their names annexed to them. Each Treatise must be distinguished by a peculiar motto; this motto must be written on the outside of a sealed letter, containing the Author's name and his address, and sent along with his performance. The names of the successful Candidates only shall be known by opening their letters. The other letters shall be destroyed unopened. The writers of the successful Treatises may afterwards have them returned, by applying to Messrs. WEBSTER or the Trustees, and by mentioning only the motto which they may have assumed. Letters addressed as above (post-paid) will meet with due attention. The new Missionary Quarterly. THE work of Missions to the heathen has now become one of the great facts of the age. Having survived the era of ridicule and scorn it now bids fair to enter ere long on an epoch of triumph. The grand object contemplated is in itself heavenly and sublime; and even the secondary benefits that attend the progress of this cause, are of a description to arrest the attention of all philanthropists, whose views rise no higher than the material interests of humanity. Many of the men who embarked on the Missionary enterprize, have proved themselves to be of a high order of intellect as well as piety. In every important walk of Literature, Science and Philosophy, there have been those amongst them who have pre-eminently distinguished themselves. And the published works of not a few of their number have enjoyed no ordinary popularity, while those of others have taken a foremost rank in the domain of scholastic erudition. It has, however, often been remarked that, while the separatelypublished writings of individual men have thus attained a well earned celebrity, the periodical organs of Missionary Societies and Churches, have continued to occupy a somewhat low position in the realm of Literature. And this, with regard to the greater portion of them, must in candour be freely admitted. They usually consist of threadbare items of intelligence and journals of itineracies abounding with tame and monotonous repetitions-with little or no attempt to classify facts, elicit principles, or establish any available generalization. This probably has been not the effect of choice, but the spontaneous result of circumstances. The monthly records and registers of missions have hitherto been mainly designed for their immediate friends and supporters; and of these, if not the great majority, at least an immense proportion, consist of the humbler members of the Christian Church, whose zeal and piety shine forth more conspicuously than their learning. But be the cause what it may, the fact is undoubted, that up to the present time, Missionary periodic Literature, considered merely in a Literary point of view, has been at a low ebb. It has not, on the grounds of literary merit, been enabled to find for itself a way into the great and wide spreading circles of reflective and meditative men. This we have often felt to be a great calamity; more especially when we thought of the amount of cultured ability and literary power already devoted to the Missionary cause. We therefore rejoice to have it in our power to announce to the friends of Missions in India, that this grand and long felt desideratum is now at length about to be supplied. The following statement will explain itself. And, when we add that the Editor of this new quarterly is no less celebrated a man than Isaac Taylor, author of the Natural History of Enthusi asm, we have said enough to recommend it to the attention of every member of an enlightened and intelligent public. TO COMMENCE 1ST JANUARY, 1849, THE QUARTERLY REPOSITORY OF PROTESTANT MISSIONS. At the instance of individual members of the several Evangelic Missionary Societies that are in accordance as to the broad principles on the ground of which the Gospel should be carried forth among the Heathen, the Periodical Work now announced has been undertaken. As none but the highest objects are to be kept in view in this instance, and as no ends are to be subserved which do not commend themselves as substantially good to every Christian heart, it will be a rule to admit upon the pages of the work that only which, in the genuine sense of the term, is Catholic. It is intended, in the first place, to bring together, to combine, and to condense, whatever is the most characteristic and important relating to the progress and the prospects of Christianity at and around the several Missionary Stations throughout the world. This mass of selected information, derived from the Correspondence of Missionaries immediately with the Editor, would sometimes be presented in the language of the writers; and sometimes it would be digested, so as to embody, within the compass of a few pages, a consistent account of whatever bears upon the progress of the Gospel within specified geographical limits. It will be a rule, in making available for the purposes of the QUARTERLY REPOSITORY any communications from abroad, to exclude what may be of ordinary quality, and, in its general character, of frequent occurrence; as well as whatever may, on any just grounds, be thought liable to doubt, either as to its absolute authenticity, or its exactness. In the next place. it is intended to devote a portion of the Repository to Papersmeditative or practical, of a sort adapted especially to the perusal of Missionaries themselves, actually labouring abroad; regard being had also to the benefit of those at home who may be intending and preparing so to do. Much importance is attached by the projectors of the work to this department of it; and, therefore the attention of those whose contributions may be invited, is, in this pointed manner, directed towards it. In the third place, as there is always an interchangeable Correspondence running on between the Evangelization of Heathen Lands, the Settlement of new Countries, and the Progress of Science, it is wished that, for the sake of higher objects ever kept in view, this connexion of things sacred with things secular should not be lost sight of. An intelligent Missionary, while employing his best energies in his proper field of labour, may be able incidentally to note and to record many facts relating to the physical peculiarities of the country wherein he sojourns, to its geological features, to its productions, to its Flora and its Fauna, which may have escaped the eye even of the most observant and best instructed travellers. Notices and Reports of this sort, Missionaries are therefore invited to supply; and it is hoped, by this means, and in the course of time, to render this compartment of the work a highly valuable repository of materials, flowing in from the numerous Stations of six or seven Societies, scattered over the world, and many of them occupying spots that are the least known or frequented. From the reports and incidental remarks of educated Missionaries, information may especially be looked for, bearing upon the history and physical characteristics of the different races of the human family, and upon the derivation and mixture of languages. A Treatise on Arithmetic, exemplifying the principles of its fundamental Rules. Part I. Abstract Numbers. By J. A. Wilson;-Madras, 1848. THIS treatise is so similar in design to that of Mr. Newmarch, which we recently-(No. xvi. p. xxxiv.) had the pleasure of introducing to the favorable notice of our readers, that a very few remarks, and those chiefly of a comparative kind, will suffice for our present notice. All that we said in regard to the design of Mr. Newmarch's work is equally applicable to that of Mr. Wilson's. They are almost identical, and both have our hearty commendation. We presume that Mr. W. composed his work in ignorance of the existence of Mr. N.'s: and probably, had he known of its existence, he would not have deemed it necessary to lay the present performance before the public. As it is, those who require such a work may take their choice. To our thinking, Mr. N.'s is, upon the whole, preferable to Mr. W.'s; and this for the one grand reason, which with us is all in all, it seems simpler. This merit, in our estimation, more than compensates for a considerable number of errors, some of which we took occasion to point out in our former notice. The treatise now before us seems free from such errors, but then it is not so simple throughout as the other. The work of composing such a work seems to us to bear a considerable resemblance to that of translating from one language to another, which every one knows is not an easy task. In point of fact it is neither more nor less than translating from the language of Algebra, the most concise and accurate of all languages, into the diffusa oratio of ordinary speech. Now the former of these languages being one that addresses only the eye, and being capable of being read in an indefinite number of ways, the translator has to make a choice of the best of these ways, or rather the one that is most suitable to his purpose. To illustrate what we mean, let us take a very simple algebraic expression; for example the following: We might read off this expression, or express the truth contained in it, in any of these ways, and in many others m times a, divided by n times bare equal to m divided by n, multiplied by a divided by b; or thus-If of two quantities multiples by any numbers be taken, the ratio of these multiples is equal to the ratio which is compounded of the ratio of the original quantities, and the ratio of the numbers expressing the multiples ;-or thus, If the numerator of a fraction be multiplied by one number, and the denominator by another, the result is the same as if the fraction were multiplied by C another fraction, whose numerator is the former, and whose denominator is the latter number; or thus, If the product of two numbers be divided by the product of two others, the result is the same as if the product were taken of the quotients resulting from the division of one factor of the divisor by one factor of the dividend, and of the other factor of the divisor by the other factor of the dividend; or thus, The product of two fractions is equal to a fraction whose numerator is the product of their numerators, and whose denominator is the product of their denominators. We might multiply indefinitely the modes of expressing the same truth; but these modes are sufficient to illustrate our meaning. Every one can see that the neatest of all these expressions is the first; but yet for the purpose of explaining to a learner any of the arithmetical truths taught in the formula, it is the worst of all; in fact for this purpose it is utterly useless. Now the tact of the writer of a work intended to explain the principles of arithmetical operation will consist in his ability to seize upon the very best reading of the algebraical for mula in which these principles are wrapped up. We need scarcely say that in order to do this, he must have long accustomed himself to take a large view of the bearings of these formulæ, and hence we see the absurdity of supposing that a very small stock of mathematics is sufficient to make a man a good arithmetical teacher. We should not advocate the introduction of metaphysics into a work like that before us: yet we think its author might have rendered the nature of number somewhat more intelligible than he has left it; or at least he might have shewn what constitutes the difficulty in understanding it; and this would have been a great point gained, for it is often nearly as important to know that we do not know any particular thing, and why we do not know it, as it would be actually to know it. We believe we are very apt not to give boys credit for all the capacity of accuracy of conception that they possess. We believe for example that all boys can be made to comprehend that the product of two numbers, regarded merely as number has no definite meaning, and we believe also that if they were distinctly made to apprehend that when we speak of the product of two numbers we always mean a certain number of things taken a certain number of times, they would have a more accurate. and if we may use the expression, a more hearty understanding of the process of multiplication. Let not our readers suppose that we desire to lay profane hands upon the multiplication table, or to tell our sons that 2 times 2 are not 4. All that we would tell them is that when we say that 2 times 2 are 4, we mean neither that the number two taken twice makes the number four, nor yet that two cheese-cakes or pop-guns multiplied by two cheese-cakes or pop guns make four cheese-cakes or pop-guns, but always that two cheese-cakes, or pop-guns, or horses, or men, or nations, or planets, taken two times, are four cheese-cakes or pop-guns or horses or |