cated) air, is a very effectual and commodious agent in the operations of refining and affaying, and will confiderably accelerate the cupellation of gold and filver, as the imperfect metals are fpeedily diffipated by the fire it produces, while the perfect ones refift it much more powerfully. This method, however, though very expeditious, cannot furnish refults which are strictly accurate, because a small portion of the gold and filver is diffipated in the operation. Two objections may be made against experiments of the kind which we are now confidering. The firft is, that as the bodies, on which thefe experiments are made, are in contact with burning coal, the metals are revivified, and the greater part of the neutral falts or mineral fubftances, in the compofition of which there is an acid, is decompofed. The fecond is, that we are not fure, that the coal does not furnish the bodies, which undergo this operation, with alkali and earth,--a circumftance which, if it takes place, may contribute to their fufibility. For M. Lavoifier's folution of the fe objections we refer our readers to the volume. VII. Concerning Vitriolic Ammoniacal Salt, or Secret Sal Ammoniac of Glauber. By M. CORNETTE. VIII. Concerning Nitrous Sal Ammoniac. By the fame. ANATOM Y. Mem. I. Concerning fome Particularities in the Structure of the Medulla Spinalis. By M. SABATIER. II. Continuation of the Refearches of M. Vico D'AZYR, concerning the Structure of the Brain. This interefting Memoir contains a comparative view of the ftructure of the brain, in men and other animals. The ingenious Academician is too judicious and modeft to afpire to the knowledge of the mechanism of the intellectual functions in man, for the wifeft philofopher must acknowledge his ignorance in this matter. The Author, therefore, only proposes to inveftigate the arrangement, which is peculiar to the human brain, and which diftinguishes it from that of the animal fpecies, wherein fenfibility is, generally speaking, lefs vigorous and lefs extenfive. He points out thefe diverfities by an accurate infpection of the brain in quadrupeds, birds, fishes, reptiles, and infects; and his obfervations are illuftrated by a great number of plates, elegantly engraved. Though it be evidently beyond the reach of human investigation, in the prefent ftate of our intellectual faculties, to point out the nexus, or efficient principles, that render a certain ftructure favourable to a more perfect exertion of fenfibility and intelligence, yet, from our Author's anatomy of the human brain, we fee in it fomething peculiar, and analogous to man's fuperior rank in the sphere of intelligence, when compared with the brute creation. ASTRO ASTRONOMY and GEOGRAPHY. Mem. I. Concerning the Obliquity of the Ecliptic, and its Diminution. By M. LE GENTIL. This is the third time that the fubject here announced has been treated by this laborious Academician. He here gives a farther account of his obfervations, compared with thofe of the eminent men who have preceded him in the fame line.-This Memoir is followed by two obfervations of the folfticial heights of the fun in June 1782 and 1783, which he made at the Royal Obfervatory. II. On the Figure of the Earth. By M. DE LA PLACE. The figure of our globe, that of its ftrata, and the law according to which their denfity varies from the center to the furface, have not been hitherto accurately afcertained. Nature feems to have placed unfurmountable obftacles in the way of inquirers into this difficult fubject. What then is to be done? All we can do, fays this Academician, is, to deduce from the phenomena, which depend on the conftitution of the earth, and which are obfervable at its furface, the limits between which the true elements of the phyfical theory of our planet are comprehended, if we cannot arrive at the direct and accurate knowledge of these elements. Thefe inquiries are not only interefting in themselves, but ufeful in aftronomy. The Author exhibits, in this Memoir, all that is known, with refpect to the conflitution of our globe, from obfervations, and from theory; and endeavours to determine, with all poffible precifion, the figure which it must be supposed to have, by calculating the principal phenomena depending upon its conftitution, fuch as the variation of gravity from the Equator to the Poles, the parallaxes, eclipfes, the preceffion of the equinoxes, and the nutation of the earth's axis. 111. Concerning the Ufe of Marine Clocks relative to Navigation, and more efpecially to Geography. In this Memoir, the Marquis DE CHABERT determines the difference of longitude between fome points in the Leeward Inlands,-in the Coafts of North America, at Fort Royal in Martinico, and at Cape François in St. Domingo, by Obfervations made during the campaign of D'Estaing, in the years 1778 and 1779, and that of Count de Graffe, in 1781 and 1782. IV. On an Eclipfe of the Moon, March 18th, 1783, and allo on the Dimenfions of the Moon's Shadow.-V. Concerning the Change of Inclination that must take place in the Orbits of the Planets. By M. DE LA LANDE. VI. Obfervations on two total Eclipfes of the Moon in 1783.VII. On the Comet of 1783. By M. MESSIER. VIII. New analytical Methods for the Solution of different afronomical Questions: XVillth Memoir.-In which the analytical formula that were demonftrated in the preceding Memoirs are ap plied to the Determination of the Parallax of Mars. By M. DioNIS DU SEJOUR. IX. X. XI. XII. XIII. On the total Eclipfe of the Moon, the 18th of March, 1783.-Occultations of fome Stars of the Pleiades, obferved at Paris, February 9th 1783, and compared with the correfpond nt Occultations, obfer ved at Bude, Drontheim, and Bagdar On the Comet of 1783. By M. MECHAIN. MATHEMATICS and MECHANICS. - Mem. I. Spherical Trigonometry, deduced, in a compendious and complete Manner, from the algebraical Solution of the most simple of its general Problems, by means of the different Transformations, of which, the Proportions of Sines and Co-fines, of Tangents and Cotangents, Secants and Co fecants of the fame Arch, or the fame plane Angle, render that Solution fufceptible, and containing fome new and ufeful Formule and Obfervations. By the Abbé GUA. 11. Different Measures of Spherical Areas and fo'id Angles, triangular and polygonal, of which a jufficient Number of the Elements is fuppofed to be known. By the Same. III New Propofitions not lefs useful than curious, relative to the Tetraedron, or an Effay on Tetraedrometry. By the Same. IV. Concerning the Approximations of Formula, which are Functions of great Numbers. By M. DE LA PLACE. Part IV. V. Concerning the Calculation of Probabilities. containing Reflections on the Method of determining the Probability of future, by the Obfervation of paft Events. By the Marquis DE CONDORCET. VI. Theorem on Equations in finite Differences. By M. CHARLES. VII. Remarks on the Manner of integrating, by Approximation, differential Equations, and Equations of partial Differences. By M. COUSIN. VIII. Remarks on the Mathematical Theory of the Motion of Fluids. By the Same. IX. Concerning Births, Marriages, and Deaths at Paris, from the Year 1771 to 1784, and through the whole Extent of France, during the Years 178: and 1782. By M. DE LA PLACE. This Memoir contains an ingenious method of calculating the popu→ lation of a country. There are annexed to it Two Tables, furnifhed by a learned magiftrate, who has been much occupied in this fubject, with a view to public utility. From the firit, which takes in a feries of fourteen years, and regards only the city of Paris, it appears that the total lift, during that period, of births, marriages, and deaths, was as follows: APP. Rev. Vol. LXXVI. Births Γ The Second Table, which regards the population of the whole kingdom of France, the island of Corfica included, exhibits, for the years 1781 and 1782, the following refults: For 1781, 970,406 Births male and female; 236,503 Marriages; 881,138 Deaths.-For 1782, 975,703 Births; 224,890 Marriages; 948,502 Deaths. The rules which the Academician lays down, to eftimate, from fuch materials as thefe, the population of a country, are learned and ingenious. There are many contingent circumftances, that render it impoffible to come to a rigorous accuracy in calculations of this kind, and these M. de la Place points out with his ufual penetration. He fhews, however, by what method of calculation a probability of a thousand to one may be obtained, that an estimate of the population of the kingdom of France fhall not be inaccurate to the amount of half a million. Mem. X. Concerning a Method of integrating ordinary differential Equations, when they are of the higher Degrees, and in those Cafes, in which their complete Integrals are Algebraical. By M. MONGE Xi Concerning the Integration of Equations of finite Differences, which are not linear. By the Same. ART. III. The Norwegian Account of Haco's Expedition against Scotland, A. D. 1263, now first published in the original Inlandic from the Flateyan and Frifian Manufcripts, with a literal English Version and Notes. By the Rev. James Johnstone, A. M. Chaplain to his Britannic Majefty's Envoy at the Court of Denmark. 8vo. 38. Copenhagen printed, 1782, and fold by Cadell, in London. 1786. THE HE publication of manufcripts tending to illuftrate the obfcure parts of hiftory, is a work which Mr. Johnftone has been encouraged to undertake, from the peculiar advantages he enjoyed in having access to a number of inedited fragments of northern hiftorians. It was his intention to have given a fuccinct detail of the defcents made by the northern nations on the British ifles; but a vaft increafe of materials obliged him to defer that work to a future period; in the mean time, he favours the antiquary and the hiftorian with fuch detached parts as he hath been able to collect. The The fituation of the kings of the ifles was peculiarly delicate; for though their territories were extenfive, yet they were by no means a match for the neighbouring ftates. On this account, allegiance was extorted from them by different fovereigns. The Hebridian princes confidered this involuntary homage as implying protection; and when this was not granted to them, they were under the neceffity of forming fuch new connexions as they fuppofed, or hoped, would be more conducive to their fafety and protection. The Norwegians were in poffeffion of the Hebrides when the Alexanders of Scotland, after having added Galloway (then a powerful maritime ftate) to their dominions, attempted to expel the Norwegians from the Hebrides. In order to effect their defigns, they firft fecured the Somerlid family, and gained over the infular chiefs. Haco, the Norwegian monarch, was no less anxious to attach every perfon of confequence to his party all his pacific efforts were however ineffectual. Difappointed in his negotiations, he had recourfe to the fword; and failing from Norway with a very numerous armament, he defeated the Scots in many fkirmishes, and died at Kirkwall in the winter following. The publication before us contains a minute detail of this expedition, according to the Flateyan and Frifian MSS. the firft of which belongs to the library of his Danifh majefty, and the other to the Magnæan collection. Of thefe, Mr. Johnstone obtained copies. By the help of one he was enabled to fupply, reciprocally, the imperfections of the other; and to correct many errors of tranfcribers. Thefe MSS. have alfo furnished him with feveral emendations of a former publication, The anecdotes of Olave the Black*', which corrections he has inferted in the preface to this performance. As antiquaries may be defirous of knowing fomething of the fe MSS. Mr. Johnftone has given the following defcription of them: The Frifian MS. is a vellum Quarto of the largest size in a beautiful hand, and the character refembles that which prevailed in the end of the thirteenth century. The book of Flatey is a very large vellum volume in folio, and appears to have been compiled in the fourteenth age. It contains a collection of poems; excerpts from Adam Bremenfis; a differtation on the first inhabitants of Norwey; the life of Eric the traveller; Olave Trygvafon; of St. Olave; of the Earls of Orkney; of Suerir; of Haco the aged; of his fon Magnus; of Magnus the Good; of Harald the Imperious; of EinaSockafon of Greenland; and of ölver the Mifchievous; it contains alfo a general chronology down to A. D. 1394, the year in which the MS. was completed. The initial letters, in fome places, are or See Review, vol. LXV. p. 95. namented |