4. Obfervation of the fame tranfit, by MECHAIN. 5. On the conftruction and the accuracy of a new regula tor, by Mr. SEYFFERT of Drefden,

6. On Geographical Menfurations, by Prof. HENNERT. The moft interefting part of this memoir, is the problem, to afcertain, from the given polar elevation of one place, and the diftance of another from the meridian of the former, the polar elevation of the latter.

7. Obfervations and calculations refpecting the oppofitioni of Uranus, (Georgium Sidus) by Mr. DERFFLINGER, of Krems-Munfter.

8. Perturbations of Mars by Venus, the Earth, and Mer cury, calculated by Paftor WURM, of Gruibingen, in the Duchy of Wirtemberg.

9. Aftronomical obfervations by Meflrs. FRIESNECKER and BURG, at Vienna.

10. On Comets which take their courfe near our globe: from the papers of the late Profeffor LAMBERT, at Berlin, comets of this description deserve to be carefully obferved and calculated by aftronomers, because an accurate knowledge of them may furnish us with the best method of finding the paral lax of the fun; and confequently the proper fcale for the whole planetary fyftem. It may be added, that, if fuch comes were fufficiently weighty and bulky, they would manifeft confiderable influence on the folid and fluid parts of our globe. Lambert confiders the earth at reft, and transfers its motion to the paffing comet. Hence the line exhibiting the relative motion will be a kind of hyperbola, the curve of which increafes, as the comet approaches to the globe. The general ftandard by which he has made his calculations, is the hourly motion of the earth, and that of a comet equally diftant from the fun, expreffed in parts of the radius of the earth. From the figure of an hyperbola thus delineated, Lambert infers, that a comet, moving in a very eccentrical ellipfis, never will become a fatellite of the earth, or any other planet.

II. On the motions of planets, in an ethereal medium, by M. SCHUBART of St. Petersburg. The author of this memoir explains and demonftrates LA PLACE's formulâ on the fame fubject. This aftronomer had already remarked, that no refiftance of any medium will affect the aphelia of planets; but that the axis major of the orbit, the eccentricity, and the mean motion of the planet will have a fecular equation. M, S. adds, that the mean distance from the fun will, in confe quence of any refiftance of the medium, continually and uniformly decrease; and this in a more rapid manner, when the planet is nearer the fun. The mean motion will annually

increase,

increafe, and the orbits of planets, as well as comets, will tend to a circular form.

12. General Tables for calculating the greateft digreffion of Venus from the fun; the upper and lower conjunctions, and the greatest brightnefs of that planet, for all fucceeding centuries, by M. WURM. Venus appears in her greatest brightnefs nineteen days before or after her moft confiderable eaftern digreffion, which, as well as her conjunctions, and greatest brightnefs, have a regular Cyclus, amounting to nearly 2,922 days.

13. On the fecond comet in the year 1798, by Dr. OLBERS of Bremen. Dr. O. difcovered this comet, December 8, in the conftellation of Cerberus. It was vifible but few days. It is the 92d comet; the orbit of which has been calculated. The mift round the comet, Dr. O. eftimates at five minutes, or equal to four and an half femi-diameters of our globe. The nucleus did not appear to be greater than 2" I., for which reason the diameter of the globe of that comet could not exceed twenty-seven geographical miles.

14. Aftronomical obfervations by M. CASSELLA, aftronomer at Naples.

15. Some obfervations on the moon made during the lunar eclipfe, between the 3d and 4th of December, 1797; by Chevalier DE HAHN of Remplin. From these and other obfervations M. de Hahn endeavours to prove, by a variety of ftrong arguments, that the moon is in a perpetual state of phofphorefcence, and that nature seems to have fupplied by thefe means the defect of water and air with respect to vegetation; but that the vegetables of the moon on that account will be of a more volatile changeable quality than those of the earth.

16. Aftronomical obfervations by Mr. KOHLER, aftrono mer at Drefden.

17. Aftronomical obfervations by Dr. KocH at Dantzig. Dr. Koch finds the periodical return of light, with regard to the fign of the Cygnus, to be 407 days; two days more than were allowed. MARALDI and LE GENTIL.

18. Equations for correfponding altitudes of the fun, taken between ten and two o'clock, by M. SCHAUBACH, at Meinungen,

19. Some obfervations on the spots of the fun, by M. Fritsch, Paftor of Quedlenbury, M. Fritsch pretends to have obferved with a reflector of two and an half feet, executed by Ramfden, a chain of mountains in the fun, fimilar to that in the moon.

20. On the nebulous ftar near the fign of Hydra, by Chevalier DE HAHN. This nebulous ftar appears to be rather one

extenfive

extenfive celeftial body than a collection of ftars; though contrary to the opinion of Dr. HERSCHEL. DE HAHN thinks his hypothefis is fupported by the obfervation, that this nebulous body has its peculiar motion contiguous to the Hydra, and that it appears to have an obfcure and an illumined fide. 21. Aftronomical accounts by LA LANDE.

22. The great folar eclipfe which will be vifible the 11th of tebruary, 1804, calculated for feveral parts of Europe, by the Rev. Father INIGO KAUTSCH of Leutomifhel, in Bohe mia. This eclipfe will be annular in the fouth-eaft of Germany, and in Hungary; it will appear in the former country of a fize of ten or eleven inches.

23. Aftronomical obfervations by M. BODE, aftronomat Berlin.

24. Various aftronomical articles of intelligence.

ART. XIII. Beyträge zur Hydraulischen Architecture; i. e Effays on Hydraulic Architecture. By Reinhard Woltmann of Ritzebüttel, 1799. PP. 424. gr. 8vo. Price Two ; Rix Dollars. Gottingen. Dieterich.

WE

9

E read with regret, that the ingenious author propofes to conclude his ufeful labours with the prefent volume. He begins with fome corrections and improvements relative to the firft and fecond volumes. He begins with fome corrections and improvements relative to the firft and second volumes. He next communicates to us the obfervations made by him on a hydraulic journey, from the mouth of the Scheldt to that of the Wefer. Thefe are ac companied by inftructive reflections, for which no country could afford materials more diverfified and interefting than that comprehended between the mouths of thofe two rivers. The volume is concluded with a theoretical and practical effay on the beft conftruction of walls for fupporting earth-banks and dykes. This effay is one of the most ingenious ever published on this important fubject. In every inftance we difcover the judicious practical writer, who is aided by a competent share of mathematical knowledge.

ART. XIV. Louife, Raugräfinn zu Pfalz, &c. i. e. The Hif tory of Louifa, Countess of the Palatinate, by birth, Barenefs of Degenfeld. By the Author of the Life of Frederick of Scomberg. 3 Vols. 8vo. Vol. I. PP. 155. Vol. II. PP. 165. Vol. III. Pp. 168. Seipzig. Göthen. 1798. VAL UABLE

V

'ALUABLE historical documents, exhibited in elegant and perfpicuous language, ftrongly recommend this work to all attentive readers; efpecially as it contains the characters and viciffitudes of a family, defcribed with a lively degree of intereft; while we may learn from it, that even the moft complicated incidents of human life, if clearly and faithfully related, become equally entertaining and inftructive.

ART. XV. Lettre, &c. i. e. A Letter to the Editor of the Monthly Review: or an Answer to the Objections in that Journal, to the Methods of the Limits of Hypothetic Fluxions. By Mr. Stockler, Colonel of the Corps of Artillery, Member of the Royal Academy of Sciences, fin Lifbon], and Mathematical Profeffor of that of the Marine, Lisbon, &c. 1800.

MR.

R. STOCKLER had given the Theory of Fluxions, mentioned in the title, in the memoirs of the Portuguefe Academy of Sciences. As his original paper is not before us, the merits of this mode of elucidating their principles cannot be here fully confidered: it is the objections to it in the Monthly Review alone, and the answers given to them, that are the proper fubject of this article. We fhall find fome convenience in giving our opinion on each of these separately.

The author of the article, in the Monthly Review, cenfures the theory of Mr. S. Affirms that "in the first place, the objection justly made against the method of Newton and Maclaurin, &c. is equally valid against that of Mr. Stockler, which is grounded in the principle of motion; a principle foreign to the nature of the fubject." And again, that " Mr. Stockler fuppofes quantity to be generated by motion." Here we muft obferve, that quantity is the relation of a magnitude to the common measure: now that magnitude may be extenfion, or any other thing variable in measure or proportion. Let, therefore, the magnitude confidered first be extenfion; extension is of lines, fuperficies, and folids; how just the objection is, to applying the principles of motion to determine their magnitudes and relations, muft now be shown.

Against the clearness and rigorous accuracy of the foundations of the elements of geometry no objections can be justly made: to the most accurate reasonings, we can give no higher praise as fuch, than to fay they have all the evidence and juftice of geometry; but this fatal objection brought against the

003

methods

methods of Newton and Maclaurin, "as grounded on the principle of motion," is equally valid against the Elements of Euclid. The poftulates of geometry fpeak of nothing, but lines defcribed by the motion of a point: the legitimacy of confidering fuperficies, as defcribed by the motion of a line or a folid, by that of a fuperficies, is equally ind fputable. And the demonftrations of the fluxional theorems by Maclaurin, are all purely geometrical, the principle of motions being

fuch.

It is next to be confidered, whether it be confiftent with the accuracy of the geometrical method, to reafon of quantity in the abstract, as if generated by motion. Now if abftratt quantity or magnitude may be reprefented by a line, and a particular line, if fuch quantity be conceived to be increased, the fame will be true if it be diminished, converfo, in any given mode or law, the line representing it must be increased or lengthened by the fame law; and if the augmentation of the quantity be fucceffive, and without intermiffion in the whole time of its increase, that of the line mult be the fame duly to reprefent it; but the line cannot be augmented but by the motion of one of its extreme points. It may be faid that magnitude in the abstract, is here represented by one par ticular fpecies of magnitude; that of lines, and even an individual line, the object, even fuch as it is, lays equally against the whole of the fifth book of the Elements; where Euclid, confidering magnitude in the abstract, reprefents it conftantly by a particular line; for wherever he speaks of a magnitude, if is to be underflood of any magnitude, or in general; and, on the affumption that it is fo juftly to be confidered, he deduces all the doctrine of the relation of magnitudes therein delivered. And one particular line is taken as the reprefentative of magnitude, or quantity in general, by the fame operation of the mind, as one particular circle or triangle, in the the other parts of the elements, is taken as the representative of all poffible circles or triangles: and in the fame manner all magnitudes may be reprefented by a fuperficies, or a folid; and the increase of the former be duly represented by that of the latter, which may be conceived to be generated by the motion of a line or a fuperficies: and in this manner also things relating to magnitudes, and their increments, may be legitimately deduced from the nature of motion.

The pureft geometry has taught us, that lines may be taken as generated by motion, and that magnitude, in the abftract, may be confidered as represented by lines fo generated ; and onsequently increafing quantity by increafing lines: the

crude