similar passages in the works of Burns make Warton's observation appear, which occurs in the first volume of his admirable essay on Pope:-"If the imagination be lively, the passions will be strong. True genius seldom resides in a cold phlegmatic constitution. The same temperament and the same sensibility that makes a man a poet or a painter, will be apt to make a man a lover and a debauchee."-Bear witness to the truth of this, ye departed children of genius and indiscretion! Reflect and act upon it, ye who may yet survive! We must not dismiss these Reliques' without repeating to Mr. Cromek our thanks for the obligation which he has conferred on literature by this publication. His ardent zeal and indefatigable industry in recovering all the fragments of his author, that were scattered about his native country or elsewhere, are highly commendable, and are recorded in modest and feeling language in his preface. It is to this sentiment of veneration for the remains of Genius, that we are indebted for many valuable additions to our stock of innocent and rational entertainment.-We shall say no more on the few pieces or letters in this volume which perhaps had better not have been published. Mr. Cromek tells us that he has kept back much of his collection; and we are bound to conclude, from the manner in which this selection has on the whole been conducted, that, while we have nothing to regret in what is withholden, the utmost caution and judgment, (and, after all, what caution and judgment will be sufficient to please every body?) that were consistent with a due respect for the memory of the author and a due value for his exalted talents, were exercised on what is admitted *. Let, then, Mr. Cromek fairly indulge the hope which concludes his preface: In the manner of laying these papers before the public, I honestly declare that I have done my best; and I trust I may fairly presume to hope that the man who has contributed to extend the bounds of literature by adding another genuine volume to the writings of Robert Burns, has some claim on the gratitude of his countrymen. On this occasion I certainly feel something of the sublime and heart-swelling gratification, which he experiences, who casts another stone on the Cairn of a great and lamented chief." We must except the carelessness by which the song of "Evan Banks," the property of H. M. Williams, is here again given to Burns. ART. ART. X. The Doctrine of Interest and Annuities analytically inves gated and explained; together with several useful Tables connected with the Subject. By Francis Baily, of the Stock Exchange. 4to. 15e. Boards. Richardson. 188. Nthe subject set forth in the title-page, the present is perhaps as complete a treatise as any that we possess. It contains not, indeed, much novel matter: but this could not be expected, when we consider that the investigation is of no great intricacy, and has frequently engaged the attention of respectable mathematicians. Dr. Price's work, as edited by Mr. Morgan, affords, with much other matter, the substance probably of all that Mr. Baily's treatise includes: but then the related matter is neither arranged nor collected, but is dispersed through various parts of the volumes. While this circum stance forms no objection against that most valuable publication, it furnishes a reason for the appearance of the one which is now before us. Mr. Baily, however, finds in that work some ground of dissent and controversy. The Doctor objected to De Moivre's method of ascertaining the present values of annuities payable half yearly, quarterly, &c., and gave theorems of his own for that purpose; which theorems, or rather the principle on which their demonstration is founded, Mr. Baily reprobates in strong terms.. We wish that he had demonstrated its fallacy by cogent reasons; or (which he certainly ought to have done) had luminously exposed the two different modes of computa tion. If r denote the interest of 11. for a year, then, according to Dr. Price, the value of an annuity for n years, payable half yearly, See Phil. Trans. Vol. 66. Part I. and Observations on Rever sionary Payments, p. 382. fifth edition. This formula, however, Mr. B. says, is true only when the interest is paid yearly:-if the interest were paid half yearly, then the formula would agree with that of Dr. Price. Mr. B. gives several formula for the present values of annuities payable quarterly, &c. on the several suppositions that the interest is payable half yearly, quarterly, or momently. Thus, if the present value of an annuity, payable quarterly, (the interest being received half yearly,) be required, it equals but, if the interest be payable quarterly, then the present value equals Mr. Baily is of opinion that a want of attention to this condition of the problem, viz. the periodical payments of the interest, occasioned what he is pleased to consider as Dr. Price's errors: for he says; I presume that it was an inattention to this distinction between the periodical payments of the annuity, and of the interest, which led Dr. Price and Mr. Morgan to attack Mr. de Moivre's method of de. ducing the value of annuities payable YEARLY, HALF-YEARLY, QUARTERLY, &c. The works of that profound analyst, however, suffer little from such incautious remarks. See Phil. Trans. vol. lxvi. p. 12, or Price's Obs. on Rev. Pay. vol. i p. 241. 263.; and Mr. Morgan's note in p. 251 of the same volume; ed. 1803. Also P. 99 of my Tables for the purchasing and renewing of Leases, 2d edition. The other passage in which, on the same grounds, Mr. B. censures Dr. Price, is this: About five years after Mr. Robertson had given (in 1779) to the Royal Society The Investigations of twenty Cases of Compound Interest, Dr. Price (whose labours on this subject are entitled to the highest respect and commendation) sent to the Royal Society a paper con taining Short and easy Theorems for finding, in all cases, the differences between the values of annuities payable Yearly, and of the same annuities payable Half-yearly, Quarterly, or Momently. In this paper, the learned author gives a new method of determining the value of an nuities payable at less intervals than a whole year; and the results are different from those obtained by the method then in use. For, it should be observed that, hitherto, the method of finding the value of half yearly or quarterly annuities was always on the supposition of a given annual rate of interest; and this is the only correct mode where the periods of the payments of the annuity only are supposed to vary. It is on this principle that all the preceding writers, from Mr. Ward down down to the period here alluded to, have founded their rules for deter mining the values of such annuities: but Dr. Price has assumed as an hypothesis, that the periods for the payment of the interest alia vary with the annuity in every such case; a circumstance by no means connected with the preceding one, since the two hypotheses are totally independent of each other, 'M. D'Alembert in his memoir Sur les Annuités, inserted in the eighth volume of his Opuscules Mathematiques (1780), has entered into an investigation of this very subject and in which he supporte the principles laid down by all former authors, in opposition to this new hypothesis. He has also given a very ingenious explana tion of his theory, by means of the Logarithmic Curve: a method, however, which had been adopted above sixty years before, by Dr. Keill, in his elegant little tract On Logarithms, inserted at the end of his edition of Euclid.' We cannot say that we are convinced of Dr. Price's errone ous mode of computation by either of these passages, since the author does not distinctly shew why it is necessarily wrong. On the other hand, a note in the second volume of the Reversionary Payments gives some sort of a proof that De Moivre's mode of computation, which Mr. B. adopts, is erroneous: for it is there stated that, according to that mode, the present value of an annuity payable quarterly, to continue 70 years, at 6 per cent. rate of interest, would exceed the value of the perpetuity paid annually. This seems to be a real objection against De Moivre's principle of computation; and we wish that Mr. B., since he is conscious of its existence, had endeavoured to answer it. Perhaps, however, it is of no great practical importance whether Dr. Price's or De Moivre's mode of computation be adopted; because it is, with reference to transactions in life, of no consequence to know the value of annuities payable every month, or week, or momently. As a mere speculative question, however, if it had been more particularly and precisely stated, with the arguments pro and con, we would with pleasure have directed our attention to it, and have distinctly given our judgment. Several useful tables are inserted in this work but we notice that, in the one for Renewals, the seven per cent. column is omitted; and yet, according to the practice of corporate bodies who receive fines for renewals, this is the column which is most frequently wanted.-In arranging and stating his matter, the author has laboured with very considerable success. He endeavours to make himself understood: but he indulges in hopes too sanguine, when he thinks that he has made the passage through his book perfectly easy to a person who is acquainted with the solution of simple equations, with loga rithms, and with the method of series. This last term, how ever, is somewhat vague, and may be made to imply, by a great extension of meaning, almost all pure mathematics. In a second part, the author proposes to deliver the doctrine of Life Annuities and Assurances. ART. XI. The First Book of Titus Lucretius Carus; of the Nature of IN PP. 79. 48. 6d. N our review of Mr. Goods translation of Lucretius, (Vol. 54. N. S. p. 387) we fully examined the character, the different degrees of praise attributed in different ages to that character, and, in short, the whole history of the Epicurean Poet. We also gave a detailed account of the merits of his translators; and, after having observed that Creech, the first Englishman who versified the whole of this author, had left a vacuum in our literature that was not yet filled, even by the translator then immediately under our review, we invited some future attempt to render Lucretius into good English rhyme. We are happy to announce that this attempt has been successfully made by Mr. Drummond; we say successfully, though he has yet presented us with only the first book of his original: but, after such a specimen, we strenu ously encourage him to proceed; and, if he does not, he will play the part of genius concealing its strength ; -"parientis viribus, atque Extenuantis eas consultò." Creech wrote in rhyme, and scarcely in rhyme; since he was by nature a versifier, and only by courtesy a poet. However, he adopted the proper sort of verse for a classical translation; for had Mr. Good written blank verse like Milton him- ̈ self, or any other great hero of this measure, still it would have been blank verse, and, as such, unfit for a classical translation. We want every check that can be imposed-onus when translating a Greek, and much more a Latin writer into English, in order that we may not bury the original thought under a pyramid of modern words, as barbarous in structure as it is enormous in size. Such a check is afforded by rhyme, while blank verse creates and indulges every license. The objection to the former that it is difficult, and consequently leads to the paltry labour of looking for the jingle of the couplet, inducing a neglect of the sense and of just expression, is an objection made by those who never prac tically |