TO THE REV. SAMUEL MARSDEN, PRINCIPAL CHAPLAIN TO HIS MAJESTY'S TERRITORY OF Nɛw SOUTH WALES, On his Return to that Colony. Sic fortis Etruria crevit, Scilicet et rerum facta est pulcherrima Roma. HEA EAVEN speed thee, MARSDEN! o'er the wat'ry plain; For, since the deep with canvas has been crown'd, Was never man a nobler voyage bound; Nor ever tide, from BRITAIN's crowded shore, Kind to each various shape Misfortune wears, To Guilt, that needs most cure, a heart of stone. The man to punish, not the mind amend. Heedless of Heaven's more generous code, that wills Then, as though wrong with wrong resolv'd to pay, Such Britain's blot;-or rather such till now, Go, then, sublimely good! sublimely great! Inspired us. Among the works that have a direct claim to our attention, we have first to notice "Elements of Geometry, Geometrical Analysis, and Plane Trigonometry." By John Leslie, Professor of Mathematics in the Uni versity of Edinburgh, 8vo. There has of late years been a strange unhinging of the men of talents of the Edinburgh school from the posts for which their own natural genius appears to have designed them, and an appropriation of them to purposes for which they by no means appear to be duly gifted. Mr. Leslie was first introduced before the world in the character of an adept in natural philosophy, through the medium of his "Experimental Inquiry into the Nature and Propagation of Heat." Mr. Playfair was at that time well known, and we may add only known, in the character of a mathematician, and as filling the mathematical chair at Edinburgh with great credit to himself, and, in many respects, with advantage to the world. The death of Dr. Robison made a vacancy in a chair for which the previous studies and apparent inclinations of Mr. Leslie had amply fitted him; but as this was a superior professorship to that of the mathematics, Mr. Playfair proposed himself as a successor to Dr. Robison, and at the same time offered all his interest to Mr. Leslie to seat him in the chair, from which he would consequently remove. The whole city, and, indeed, the whole of North Britain, was thrown into a violent commotion upon this subject; not so much, however, from a comparison of the respective abilities of the two candidates for the respective offices to which they aspired, as from certain broad hints which Mr. Leslie had thrown out in Inquiry" we have just adthe " verted to, that he was in his heart attached to the deistical, perhaps the atheistical principles of Mr. Hume, and his open recommendation of one of his most dangerous publications. The philosophers, however, at length succeeded in obtaining a triumph over the Scotch church and its adherents, Professor Playfair was elected to succeed Dr. Robison, and Mr. Leslie installed in the mathematical chair. The consequence of which has hitherto been, that the former instead of beginning to teach, had to begin to learn, and has unfortunately, even from the first, attached himself to an erro- . neous theory; and the latter has given sufficient proof in the work now before us, that he is just as little qualified to succeed Professor Playfair, as Professor Playfair is to succeed Professor Robison. The author's language in the work before us, (in which correctness and simplicity of style is peculiarly requisite) is, at least, as loose as his religious principles. In regard to plan, Professor Leslie does not "consider the Elements of Euclid, with all its merits, as a finished production." And he has hence endeavoured to deviate from Euclid as widely as possible, omitting the axioms as unnecessary, and giving us what he calls ideas of a right line and angle, instead of definitions of them. "A Treatise on Plane and Spherical Trigonometry." By Robert Woodhouse, A. M. F. R S. 8vo. This is a work simpler in its pretensions, and smaller in its size; but we hesitate not to assert, superior in its merit to the preceding of Professor Leslie. Mr W. commences with proving, though not very elegantly, that arcs are the measures of angles. He then exlinearhibits definitions of the principal For since the deep with canvas has been crown'd, Nor ever tide from BRITAIN's crowded shore, Once more I view thy valleys fair, Ye vales, with downy verdure spread, Ye lakes, that catch the golden beam Scenes on this bursting heart imprest gentleman who reads the history of the present times for improvement or amusement, or views with any anxiety the operations of the armies of Europe, may, by a perusal of it, be enabled to calculate, or form some correct notions of the marches and evolutions of the armies, and the time in which they can move the columns from one situation to another." The work before us will have its advantage we have no doubt, and will be found serviceable in a variety of points; but, without many allowances, will rather confuse and mislead in the object to which the author here directs his attention. For all the calculations are made in reference to the drilling ground alone, and when occupied by a single battalion. In this situation there can be no doubt, that "stepping out in quick time" may be estimated as equal to three miles and three furlongs per hour: but such an estimation can never be applied to any spot out of the drilling ground; such a rapidity never could be practised on the field, and never has been attempted: for in the first place, it would be impossible to maintain the distinct lines in any degree of regularity; and next, if the most perfect order could be maintained, under such unexampled speed, the troops would be too much exhausted by it, for the ultimate and more important object they must ever have in view. The work, however, upon the whole, is well entitled to our commendation. It is dedicated, by permission, to Sir David Dundas, and is illustrated by thirty-five well-engraved copper-plates. "The Doctrine of Life Annuities and Assurances analytically investigated and explained. Together with several useful Tables connected with the subject; and a variety of practical rules for the illustration of the same." By Fracis Baily, of the Stock Exchange, 8vo. 11. 4s. 6d. "An Account of the several Life Assurance Companies established in London, containing a view of their respective merits and advantages." By Francis Baily. The subject to which these publications allude, is of very high consequence to mankind in general, in a political, financial, and commercial view, but especially so to so populous and speculative a metropolis as our own. The latter of the two, however, is only a small part of the former, published as a separate tract, for the greater facility of purchase and reference by those who have no leisure or inclination to pursue the inquiry into its more recondite ramifications. We are glad this subject has fallen into such able hands. Mr. Baily gives ample proof of having studied it with close attention, both theoretically and practically, and we do not think it possible to peruse this result of his studies without gaining some portion of very valuable information. In a well-arranged preface, the author enters into the history of Life Annuities and Reversions, both in our own country and abroad: with the first, he seems far best acquainted, and has traced it with sufficient accuracy. There is a meagerness in the last which we shall hope to see filled up in another edition. His principal domestic range is from Sir William Petty's observations to those published at different times, and in different forms, by Dr. Price, Baron Masseres, and Mr. Morgan. The body of the work is divided into fourteen chapters. The first contains a few elementary principles of the Laws of Chance: some Remarks on the Probabilities of Life, and an account of the several Tables of of Observations made at different parts of the world This chapter is altogether preliminary. The second shews the method of determining the value of annuities on any single or joint lives; on the longest of any number of lives, &c. Chapter III. the four necessary problems for the solution of all cases of absolute reversionary annuities; and at the termination are introduced formula of two or three lives, extending to almost every possible case. Chapter IV. contains various cases of annuities depending on survivorships between two and three lives. These cases might have been augmented; and, in our opinion, with advantage to the subject. Chap. V. relates to such cases of Contingent Reversionary Annuities, as could not, for want of some previous information, be inserted in the two preceding chapters. The sixth treats of Assurances; a subject of great importance and extensive utility in the present day. A full explanation of the doctrine is given in the problems introduced into this section of the work. Chap. VII. contains the method of determining the value of annuities on successive lives; the value of fines in Copyhold estates held on lives; the value of presentations, advowsons, and things of a like kind. The eighth chapter is devoted to an investigation of the value of Contingent Assurances. This appears to be one of the best written parts of the work, and replete with most original matter. It is, indeed, almost a new field, Mr. Morgan being the only writer who has preceded the present in the same precise line. The three ensuing chapters complete the analysis of the science, and relate to such subjects as could not conveniently be introduced into either of the preceding ones. Chap. XII. comprehends a variety of very use. ful questions connected with the subject, to which are added rules for their solution, and a numerous collection of examples. Chap. XIII. applies several of the more important questions contained in the preceding chapter to some of the most useful and momentous concerns of life; especially to the method of forming the best schemes for providing annuities for the benefit of old age, and for widows. The last chapter takes a view of the various Companies or Societies that have been formed in our own metropolis, for the purpose of granting Annuities, Assurances, and Endowments. In prosecuting which the writer observes, that "uninterested in, and unconnected with, any of these Societies, I have been anxious only to give a clear and unpreju diced account, deduced from their own plans and proposals, as submitted by them to the public." At the end of this chapter we find alse a brief account of the recent plan adopted by government, for converting the three per cent. Stocks into life annuities. The Tables of Observations, and of Life Annuities, deduced from the main inquiry, form a collection of all that has been hitherto published on the subject in our own country; and they appear carefully drawn up. We also meet with tables of the value of assurances for single and joint lives, according to the observations made officially in Sweden, as well as by M. de Parcieux; and these tables, Mr. Baily informs us, have been caculated expressly for the present work. We admit the general merit of this work: the notation equally avoids circumlocution and ambiguity: some of the author's affirmations, however, are advanced too much upon hazard; he is somewhat too |