In a short preamble, M. Melanderjelm, who anxiously urged the necessity of a second measurement, informs the reader of several circumstances which rendered probable the supposed inexactitude of the measurement in 1736. The instruments, carried with difficulty over mountains, might have sustained some slight injury; the observers were unaccompanied (and this seems to have been a great omission) by an adroit workman: the zenith sector, therefore, when used, was probably not so exact as it ought to have been, and a slight difference in the determination of the latitude materially vitiates the result of the calculation. For these reasons, M. Melander. jelm urged M. Svanberg to undertake a voyage to Lapland, and proposed to the Academy of Sciences at Stockholm to appoint that gentleman to the expedition, the chief object of which was to examine the effect of the attraction of the mountains. His solicitations were successful. In 1799, M. Suunberg undertook the voyage ; and the result of his investigation was, that the effect of the mountains near the measured base did not materially influence the accuracy of the former measurement. · A new measurement therefore seemed re. quisite, to ascert sin what other cause had existed for the error; a memoir urging its necessity was presented to the king ; and, at the expence of the State, it was accordingly ordered. The promoter of this object, too old himself for the practical execution of it, delegated MM. Ofverbom and SVANBERG for that purpose ; who departed from Stockholm for LapJand in 1801, and in their first expedition examined the localities and prepared signals. In their second expedition, they were accompanied by two assistants, and provided with their sole astronomical instrument, a repeating circle of Borda, made by Lenoir, under the inspection of Delambre; and Delambre sent with the instrument standards of the French metre and toise. I his second expedition was begun in January 1802, and completed in March 1803. In a second preface, M. SVANBERG speaks for himself ; arguing, somewhat unnecessarily, concerning the utility of these kinds of operations, and the opinion of the ancients on this point. He inclines, perhaps with some inexactitude of judgment, towards the suggestion of Freret, that the antients constructed their measures by a modulus which was the earth's circumference, or a part of it; and that the Nilometer and pyramids were the vast and stable registers of such mea. surements. Except in these particular3, however, we find nothing which does not become a mathematician, and from which a mathematician may not gain instruction. The first expedition was devoted to the erection of proper signals, and the second second commenced with observations on the pole-star, made at Malhorn, the most southern extremity of the arc, in order to determine the latitude of that place : but, from the inaccuracy of the first pendulum employed, the observations first taken were not introduced into the computations; and those on which the gentlemen relied were made with a second pendulum more accurate than the first, and which was by some accident left behind. With regard to the azimuth observations, they were indeed taken at both extremities, but M. SVANBERG has calculated those only which were made at Mala horn. — The result of the operations performed by these mathematicians differs from that which was afforded by the operations of 1736; and the writer, with some hesitation, ata tributes this difference to the observations made by the French astronomers. He is also corroborated in his opinion by certain discrepancies which he recognized in the observations made in South America by Bouguer and Condamine ; greater than those which he supposes to exist between the Lapland measurements of 1736 and 1803. . M. SVANBERG's work is divided into four sections. In the first he describes the rods or rules used for measuring the base line, and the precautions and contrivances designed to ascertain and to ensure their rectilinear direction. Indeed, the Swedish Mathematician is so scrupulous that, from the properties of the Catenarian curve, he investigates what degree of curvature would be produced in the rods from a weight pro. ducing fexure, and what would be the error committed if they assumed a curvilinear form : the error was found to be insensible. In this same section, he also relates the peculiar circumstances of difficulty arising from the season in which their observations were made. From the dullness of the vaporous atmosphere, the signals placed at the extremity of the base could not be perceived, and the observers were obliged to remedy this inconvenience by stakes or piquets placed in certain positions. Having remarked some anomalous circumstances attending this operation, and ascertained their cause, the author, with his usual scrupulousness, computes the effect of that cause. Section II. describes the trigonometrical operations, and in- , vestigates the theorems necessary to them ; but M. SVANBERG first slightly discusses the proper form for signals, and then describes that which they used. It was a quadrangular pyramid, the prolonged axis of which carried a parallelogram with an opening in it: this opening was, when it could become so, the signal; and under other circumstances, the pyramid was the signal-The instrument which served as a thcodolite, and which was used in determining latitudes, was (as we have already mentioned) Borda's repeating circle. In the common use of this instrument, the resulting angle is divided by the number of observations: but M. SVANBERG doubts whether, by this method, we can find a value of the angle which is most probably the true value ; and after certain calculations, which are not by many degrees made sufficiently intelligible to the reader, he proposes a new method of deriving the true angle from the angle which the instrument at the end of the operation exhibits. We do not here perceive much that is deserving of notice from its importance ; and, besides, the first mathematician in Europe has, after examination, given his opinion decidedly in favour of the superior accuracy of the ordinary method. The errors are so small, that it is perhaps indifferent which method is adopted. · When Borda's circle is used as a theodolite, the angles observed must, by a proper formula, be reduced to the horizon: such a formula is contained in this section; and M. Delambre (no mean name in astronomical science,) says respecting it, “ il (Svanberg) la deduit d'une maniere tres géometrique, plus rigoureuse et plus élégante que celle dont je m'étais servi dons mon memoire sur la détermination d'un arc du meridien; mais," &c. The latter part of the passage speaks of a new formula given by Delambre, and inserted in the first volume of the Measurement of an Arc of the Meridian, M. SVANBERG also gives a demonstration of that elegant theorem, of which (we believe) Legendre is the author*. If, · in a spherical triangle, the sides of which are very small com pared with the radius of the sphere, from each of the angles be deducted one third of the excess of their sum above two right angles, the reduced angles of such triangle may be taken as the angles of a rectilinear triangle, the sides of which are equal to the sides of the spherical triangle. In this case, then, the triangle is solved as a rectilinear triangle. Next follows the series of angles of position, from which M. SVANBERG formed his triangles. The third section relates to astronomical observations; and as Polaris was the star observed in the determination of the latitudes, the author investigates expressions for the variations in latitudes dependent on the diminution of the obliquity of the ecliptic, and the precession of the equinoxes. * A demonstration of this theorem has been given in one of the numbers of Leyburn's Mathematical Repository, a work to which we have before aliuded, and which well deserves the attention and patronage of mathematicians. Secting ricityo 3307* tant ion Section IV. is intitled the theory of the Spheroid ; for the author, intending the greatest exactness, calculates formula, from which parts of the arc of the meridian may be computed, supposing the earth to be an ellipsoid of revolution. If he be on the side of exactness, he is on the safe side: but is suck exactness at all requisite ? By the comparison of Bouguer's measurement with that of Méchain and Delambre, (executed during the Revolution,) the earth's excentricity is :-by the comparison of 334, 29 Svanberg with Bouguer, coor, calculating the refrac 323,529 tions according to Prony's experiments, 220,780 :—and by the comparison of SVANBERG with Méchain and Delambre, ? 307,405 In order to reconcile these quantities, he proposes some corrections of Delambre's and Bouguer's measurements, and thence puts down the excentricity, This, no doubt, is a very important work, being an accurate and scientific account of a mensuration made in Lapland with as great attention to exactness, and on principles equally just, with those that have been performed in France and in England. We have heard but little of Swedish mathematicians and astronomers : but their late operations, and the present publication, must assign to them in the rank of science a very distinguished place. M. SVANBERG seems to have been thoroughly competent to the undertaking; and he made several of his computations on grounds more exact and precise than those which either the French or the English observers assumed. We wish that he had calculated the difference between the results from his more exact theory, the spheroidal form of the earth, for instance, and those which are derived from the common and more simple theory. Three terrestrial measurements are now before the public, on the accuracy of which we may rely :-the Lapland mea. surement by SVANBERG ; the French, by Delambre and Méchain; and the English, by Mudge ;—and will not the superior excellence of our instruments, with the skill of the observers, render the last the most perfect ? For this production, of which Delambre speaks with the highest commendation, the French National Institute decreed to M. SVANDERG the prize of the medal founded by Lalande. restrial which we may rench, by I will not ART. Another with whicho anticipated th ART. IV. Bélisaire, &c. ; i.c. Belisarius, by Madame De GINL'16. 2 Vols. 12mo. Imported by Dulau. M adame De Genlis has anticipated the involuntary ex clamation, with which we received her present perform. ance — " Another historical romance !”—and we do not appear to have been singular in making it, since she says that the journalists have repeated for the last five or six years, whenever a new romance has appeared, (that is, almost every week,) that it is a bad species of composition; that an historical romance cannot be a good book,' &c. To this lady's declaration that such a sweeping censure would have prompted her to burn all her plans of romances, if she had not been constantly encouraged and applauded by the public, a satisfactory answer might perhaps be given ; and if we could flatter ourselves that our voice could penetrate into the chambers of the Thuilleries, where the fair author is now said to hold her residence, we should presume to whisper in her ear that splendid and agreeable talents may be employed in a bad species of composition: that the public must make the best of whatever is offered to their perusal, while it is incumbent on the guardians of literature to direct the efforts of those who write, to such objects as are best calculated to reward the general curiosity; and that the eagerness, with which readers of taste in both countries have pur. chased and admired the later works of Madame De GENLIS, while it does homage to her uncommon powers of interesting and amusing, gives no more sanction to the historical romance, than our adoration of the immortal genius of Shakspeare exa presses our conviction that the heterogeneous absurdities of tragi-comedy afford the fairest scope for the display of dramatic excellence. We regret that the Parisian reviewers should have incurred the just displeasure of this entertaining writer, not only by condemning in the gross the style which she has adopted, but also by an unfair and false representation of one of her former productions. We trust that we are entirely free from this cen. sure, however we may have participated in the sentiments from which she disagrecs; and though the story of the siege of La Rochelle did not appear to us free from objection, we were far from incurring the guilt so accurately described by Dogberry “ Marry, Sir, they have committed folse report, thirdly, they have belied a lady, secondarily, they are slanderers, sixthly and lastly, they have verified unjust things, "-and possibly the injured fémale might be excused, if she summed up all their offence in the words of the same indictment, -". And, to conclude, they are lying knaves.”! We wish, however, that she had been saa tisfied |