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cated) air, is a very effectual and commodious agent in the ope. rations of refining and assaying, and will considerably accelerate the cupellation of gold and silver, as the imperfect metals are speedily dilipated by the fire it produces, while the perfect ones resist it much more powerfully. This method, however, though very expeditious, cannot furnish results which are strictly accu. rare, because a small portion of the gold and silver is diffipated in the operation.

Two objections may be made against experiments of the kind which we are now considering. The first is, that as the bodies, on which these experiments are made, are in contact with burning coal, the metals are revivified, and the greater part of the neutral falts or mineral substances, in the composition of which there is an acid, is decomposed. The second is, that we are not sure, that the coal does not furnish the bodies, which undergo this operation, with alkali and earch, - circumstance which, if it takes place, may contribute to their fusibility. For M. Lavoilier's solution of these objections we refer our readers to the volume.

VII. Concerning Vitriolic Ammoniacal Salt, or Secret Sal Am. moniac of Glauber. By M. CORNETTE. VIII. Concerning Nitrous Sal Ammoniac. By the same.

ANATOMY. Mem. I. Concerning some Particularities in the Structure of the Medulla Spinalis. By M, SABATIER.

II. Continuation of the Researches of M. Vice D’AZYR, con. cerning the Structure of the Brain. This interesting Memoir contains a comparative view of the structure of the brain, in men and other animals. The ingenious Academician is too judicious and modest to aspire to the knowledge of the mechanism of the intellectual functions in man, for the wiseft philosopher must aca knowledge his ignorance in this matter. The Author, therefore, only proposes to investigate the arrangement, which is peculiar to the human brain, and which diftinguishes it from that of the animal species, wherein fenfibility is, generally speaking, less vigorous and less extensive. He points out these diversities by an accurate inspection of the brain in quadrupeds, birds, fishes, reptiles, and insects; and bis observations are illuftrated by a great number of plates, elegantly engraved. Though it be evidently beyond the reach of human investigation, in the present state of our intellectual facullies, to point out the nexus, or efficient principles, that render a certain structure favourabie to a more perfect exertion of sensibility and intelligence, yet, from our Author's anatomy of the human brain, we see in it something peculiar, and analogous to man's superior 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 Dimic nution. By M. LE GENTIL. This is the third time that the subject here announced has been treated by inis laborious Aca. demician. He here gives a farther account of his observations, compared with those of the eminent men who have preceded bim in the same line.-This Memoir is followed by two observations of the solsticial heights of the sun in June 1782 and 1783, which he made at the Royal Observatory.

II. On the Figure of the Earth.' By M. DE LA PLACE. The figure of our globe, that of its frata, and the law according to which their density varies from the center to the surface, have not been hitherto accurately ascertained. Nature feems to have placed unfurmountable obstacles in the way of inquirers into this difficult subject. What then is to be done ? All we can do, says this Academician, is, to deduce from the phenomena, which depend on the constitution of the earth, and which are observable at its surface, the limits between which the true ele. ments of the physical theory of our planet are comprehended, if we cannot arrive at the direct and accurate knowledge of these elements.

These inquiries are not only interesting in themselves, but useful in astronomy. The Author exhibits, in this Menoir, all That is known, with respect to the conftitution of our globe, from observations, and from theory; and endeavours to determine, with all posible precision, the figure which it muft be supposed to have, by calculating the principal phenomena depending upon its confticution, such as the variation of gravity from the Equa. tor to the Poles, the parallaxes, eclipses, the procession of the equinoxes, and the nutation of the earth's axis.

111. Concerning the Use of Marine Clocks relative to Navigation, and more especially to Geography. In this Memoir, the Marquis DE CHABERT determines ihe difference of longitude between some points in the Leeward Inands--in the Coasts of North America, - at Fort Royal in Martinico, and at Cape François in St. Domingo, by Observations made during the campaign of D'Efaing, in the years 1778 and 1779, and that of Count de Grolle, in 1791 and 1782.

IV. On an Eclipse of the Moon, March 19th, 1783, and alla on the Dimenfions of the Moon's Shadow. -- V. Corierning ile Change of Inclinatiön that must take place in te Orlits of th: Planets. By M. DE LA LANDE.

VI. Observations on two total Eclipses of the Moon in 1783.VII. On ibe Cemet of 1983. By M MESSIER.

VIII. Neiu analytical Methods for the Solution of different allr9. nomical Quejtions: XVilleh Memoir.-In which the analitical formula that were demonstrated in the pieceding Memoirs are ap

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plied to the Determination of the Parallax of Mars. By M. DioNIS DU SEJOUR.

IX. X. XI. XII. XIII. On the total Eclipse of the Alccr, the 7315 of March, 178 3.--Occultations of porne Stars of the Flriades, observed at Paris, February orh 1783, and compared with the icrrepond nt Occultations, observed at !ude, Drontheim, and Bagdal. On the Cornet of 10;83. By M. MECHAIN.

MATHEMATICS and MECHANICS. Mem. I. Splerical Trigonometry, deduceid, in a compendious and complete Vianner, from the algebraical Solution of t'e molt simple of its general Problems, by means of the different Transformations, of which, the Proportions of Sines and Co-fines, of I angents and Cotangents, Seionts and Co fecants of the jame frch, or the same plane

Angle, render that Solution (usceptible, and containing fome new and useful Formule and Observations. By the Abté GUA

II. Different Measures of Spherical Areas and fo'id Angles, triangular and polygonal, of which a sufficient Num'er of the Elements is supposed to be known. By the Same.

M New Propositions not less useful than curious, relative to the Terraëdron, or an Ejay on Tetraë drometry. By the Same.

IV. Concerning the Approximations of Formule, which are FunElions of great Numbers. By M. DE LA PLACE.

V. Concerning the Calculation of Probabilities. Part IV. containing Reflections on the Method of determining the Probability of future, by the Observation of past Events. By the Marquis DE CONDORCET.

VI. Theoren on Equations in finite Differences. By M. CHARLES.

VII. Remarks on the Banner of interrating, 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, l'arriages, and Deaths at Paris, from the Year 1771 to 1784, and through the whole Extent of France, during the Years 1781 and 1782. By M. DE LA PLACE. This Memoir contains an ingenious method of calculating the population of a country. There are annexed to it Two Tables, furnilhed by a learned magistrate, who has been much occupied in this subject, with a view to public utility. From the first, which takes in a series of fourteen rears, and regards only the ciry of Paris, it appears that the total lift, during that period, of birihs, marriages, and diaths, was ás foilows:

App. Rev. Vol. LXXVI.

Births Births Marriagesil Deaths Foundlings Males Females

Males | Females Males Females 151,859 | 145,159 75,353 ||156,204 133,466|| 48,036 46,941

Yearly 1 Yearly Yearly Yearly | Yearly || Yearly Yearly Ann. Com. ; Ann. Com. Ann. Com. 10,121 | 9,6771 5,023 | 10,4131 8,890|| 3,202 3,130

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 results : For 1781, 970,406 Births male and female; 236,503 Marriages ; 881,138 Deaths.- For 1782, 975,-03 Births ; 224,890 Marriages ; 948,502 Deaths. The rules which the Academician lays down, to estimate, from such materials as these, the population of a country, are learned and ingenious. There are many contingent circumstances, that render it impossible to come to a rigorous accuracy in calculations of this kind, and these M. de la Place points out with his usual penetration. He thews, 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 shall 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 Cases, 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.

970, s. - Forubs? The smaterials as. There as come to M. de la 948oLimate, foarned and in der it impokind, and ch thews, howa

ART. III. The Norwegian Account of Haco's Expedition against Scotland, A. D.

1263, now first published in the original Mandic from the Fla. teyan and Frisan Manuscripts, with a literal English Verfion and Notes. By the Rev. James Johnstone, A. M. Chaplain to his Britannic Majesty's Envoy at the Court of Denmark. 8vo. 38. Copenhagen printed, 1782, and sold by Cadell, in London. 1786. THE publication of manuscripts tending to illustrate the obI scure parts of history, is a work which Mr. Johnstone has been encouraged to undertake, from the peculiar advantages he enjoyed in having access to a number of inedited fragments of northern historians. It was his intention to have given a succinct detail of the descents made by the northern nations on the Britilh isles; but a vast increase of materials obliged him to defer that work to a future period; in the mean time, he favours the antiquary and the historian with such detached parts as he hath been able to collect.

The

The situation of the kings of the illes was peculiarly delicate ; for though their territories were extensive, yet they were by no means a match for the neighbouring states. On this account, allegiance was extorted from them by different sovereigns. The Hebridian princes considered this involuntary homage as implying protection; and when this was not granted to them, they were under the necessity of forming such new connexions as they supposed, or hoped, would be more conducive to their safety and protection.

The Norwegians were in posseflon 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 designs, they first secured the Somerlid family, and gained over the insular chiefs. Haco, the Norwegian monarch, was no less anxious to attach every person of consequence to his party : all his pacific efforts were however ineffectual. Disappointed in his negotiations, he had recourse to the sword; and failing from Norway with a very numerous armament, he defeared the Scots in many skirmishes, and died at Kirkwall in the winter following.

The publication before us contains a minute detail of this expedition, according to the Flateyan and Frisian MSS. the first of which belongs to the library of his Danish majesty, and the other to the Magnæan collection. Of these, Mr. Johnstone obtained copies. By the help of one he was enabled to supply, reciprocally, the imperfections of the other; and to correct many errors of transcribers. These MSS. have also furnished him with several emendations of a former publication, “The anecdotes of Olave the Black* ', which corrections he has in. serted in the preface to this performance.

As antiquaries may be desirous of knowing something of these MSS. Mr. Johnstone has given the following description of them :

• The Frisian MS. is a vellum Quarto of the largest size in a beautiful hand, and the character resembles thae 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 che fourteenth age. It contains a collection of poems; excerpts from Adam Bremenfis ; a dissertation on the first inhabitants of Norwey; the life of Eric the traveller; Olave Trygvason; of St. Olave; of the Earls of Orkney; of Suerir ; of Haco che aged; of his ron Magnus ; of Magnus the Good; of Harald the Imperious; of EinaSockafon of Greenland; and of ölver the Mischievous; it contains also a general chronology down to A. D. 1394, the year in which the MS. was completed. The initial letters, in some places, are or.

* See Review, vol. LXV. p. 95.

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