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- 4. Observation of the fame transit, by MECHAIN.
. 5. On the construction and the accuracy of a new regular
tor, by Mr. SEYFFERT of Dresden,

6. On Geographical Mensurations, by Prof. HENNERT: The most interesting part of this memoir, is the problem, to ascertain, from the given polar elevation of one place, and the distance of another from the meridian of the former, the polar elevation of the latter.

-7. Observations and calculations respecting the opposition of Uranus, (Georgium Sidus) by Mr. DERFFLINGER, Of Krems-Munfter.

8. Perturbations of Mars by Venus, the Earth, and Mer çury, calculated by Pastor Wurm, of Gruibingen, in the Duchy of Wirtemberg.

9. Astronomical observations by Messrs. FRIĘSNECKBR and BURG, at Vienna. , ** 10. On Comets which take their course near our globe: from the papers of the late Professor LAMBERT, at Berlin, comets of this description deserve to be carefully observed and calculated by astronomers, because an accurate knowledge of them may furnish us with the best method of finding the paral. lax of the sun; and consequently the proper scale for the whole planetary system. It may be added, that, if such comętę were sufficienrly weighty and bulky, they would manifest con. siderable influence on the solid and fuid parts of our globe. Lambert considers the earth at rest, 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 increases, as the comet approaches to the globe. The general standard by which he has made his calculations, is the hourly motion of the earth, and that of a comet equally distant from the sun, expressed in parts of the radius of the earth. From the figure of an hyperbola tbus delineated, Lambert infers, that a comet, moving in a very eccentrical ellipsis, never will become a satellite of the earth, or any other planet. .

II. On the motions of planets, in an ethereal medium, by

M. SCHOBART of St. Petersburg. The author of this memoir .: explains and demonstrates La Place's formulâ on the fame

subject. This astronomer had already remarked, that no re fistance 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 secular equation, M, S. adds, that the mean distance from the fun will, in confequence of any resistance of the medium, continually and uniformly decrease; and this in a more rapid manner, when the planet is nearer the sun. The mean motion will annually

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

12. General Tables for calculating the greatest digreffion of Venus from the fun; the upper and lower conjunctions, and the greatest brightness of that planet, for all succeeding centuries, by M. WURM. Venus appears in her greatest brightness nineteen days before or after her most confiderable eastern digression, which, as well as her conjunctions, and greatest brightness, have a regular, Cyclus, amounting to near, ly 2,922 days.

13. On the second comet in the year 1798, by Dr. OLBERS of Bremen. Dr. O. discovered this comet, December 8, in the constellation of Cerberus. It was visible but few days. It is the g2d comet; the orbit of which has been calculated. The mist round the comet, Dr. O. estimates at five minutes, or equal to four and an half semi-diameters of our globe. The nucleus did not appear to be greater than 2" 1., for which reason the diameter of the globe of that comet could not exceed twenty-seven geographical miles, 1. 14. Astronomical observations by M. CASSELLA, astrono. mer at Naples.

15. Some observations on the moon made during the lunar eclipse, between the 3d and 4th of December, 1797 ; by Chevalier De Hawn of Remplin. From these and other obServations M. de Hahn endeavours to prove, by a variety of strong arguments, that the moon is in a perpetual ftate of phosphorescence, and that nature seems to have fupplied by these means the defect of water and air with respect to vege fation; but that the vegetables of the moon on that account will be of a more volatile changeable quality than those of the earth. . * 16. Astronomical observations by Mr. KOHLER, astrono. mer at Dresden.

17. Astronomical observations by Dr. Koch at Dantzig. Dr. Koch finds the periodical return of light, with regard to the sign of the Cygnus, to be 407 days'; two days more than were allowed. MARALDI' and LE GENTIL:

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

Io. Some observations on the spots of the sun, by M. Fritsch, Paftor of Quedlenbury, M. Fritsch pretends to have observed with a reflector of two and an half feet, executed by Ramsden, a chain of mountains in the sun, similar to that in the moon.

20. On the nebulous Itar near the sign of Hydra, by Che. yalier De HAHN, This nebulous ftar appears to be rather one

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extensive

waters feems to perpetualariety of

extenfive celeftial body than a colle&tion of stars; though con trary to the opinion of Dr. Herschel. De Hahn thinks his hypothesis is supported by the observation, that this nebulous body has its peculiar motion contiguous to the Hydra, and that it appears to have an obscure and an illumined side.

21. Astronomical accounts by LA LANDE. ;

22. The great solar eclipse which will be visible the lith of 't ebruary, 1804, calculated for several parts of Europe, by the Rev. Father INIGO KAUTSCH of Leutomilh-l, in Bohe mia. This eclipse will be annular in the south-east of Germany, and in Hungary; it will appear in the former country of a size of ten or eleven inches. - 23. Astronomical oblervations by M. Bode, astronomat Berlin." * 24. Various astronomical articles of intelligence,

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Art. XIII. Beyträge zur Hydraulischen Architecture; i. c. - Esays. on Hydi aulič Architecture. By Reinhard Woltmann

of Ritzebüttel, 1799. Pp. 424. gr. 8vo. Price Two

Rix Dollars. Gottingen. Dieterich. : : .
T E read with regret, that the ingeniqus author pro,

VV poses to conclude his useful labours with the present volume. He begins with some corrections and improvements relative to the first and second volumes. He begins with some cofrections and improvements relative to the first and second volumes. He next communicates to us the obfervations made by him on a hydraulic journey, from thç mouth of the Scheldt to that of the Weser. These are aco companied by instructive reflections, for which no country could afford materials more diversified and interesting than that comprehended between the mouths of those two rivers. The volume is concluded with a theoretical and practical essay on the best construction of walls for supporting earth-banks and dykes. This essay is one of the most ingenious ever published on this important subject. In every instance we discover the judicious practical writer, who is aided by a compétent share of mathematical knowledge,

ART. XIV. Louise, Raugräfinn' zu Pfalz, &c. i.e. The Hisy

tory of Louisa, "Countess of the Palatinate, by birth, Baronefs of Degenföld. "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, Gölhen. 1798.

VAL UABLE

ITALUABLE historical documents, exhibited in elegant

V and perspicuous language, strongly recommend this work to all attentive readers ; cfpecially as it contains the characters and vicissitudes of a family, described with a lively degree of interest; while we may learn from it, that even the most complicated incidents of human life, if clearly and faithfully related, become equally entertaining and instructive,

fully remplicated in while we maamily, defcrinita

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, Mem, ber of the Royal Academy of Sciences, rin Lisbon), and Mathematical Professor of that of the Marine, Lisbon, &c.

1800. MAR, STOCKLER had given the Theory of Fluxions,

Ve mentioned in the title, in the memoirs of the Portuguese Academy of Sciences. As his original paper is not before us, the merits of this mode of elucidating their principles cannot be here fully considered : it is the objections to it in the Monthly Review alone, and the answers given to them, that are the proper subject of this article. We shall find some convenience in giving our opinion on each of these separately.

The author of the article, in the Monthly Review, censures the theory of Mr. S. Affirms that " in the first place, the objection juftly made against the method of Newton and Ma. claurin, &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 subject.”. And again, that « Mr. Stockler fupposes quantity to be generated by motion.” Here we must obserye, 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 considered first be extension; extension is of lines, superficies, and solids ; how just the objection is, to applying the principles of motion to determine their magnitudes and relations, must now be shown.

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

methods

Let, there other thie: now in the relatior motion at Mr.

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by the montepresent increase, that without tie augm

methods of Newton and Maclaurin, “ as grounded on the principle of motion," is equally valid against the Elements of Euclid. The postulates of geometry speak of nothing, but lines described by the motion of a point : the legitimacy of confidering fuperficies, as described by the motion of a line or a folid, by that of a superficies, is equally indisputable. And the demonstrations of the fuxional theorems by Maclaurin, are all purely geometrical, the principle of motions being fuch...

It is next to be considered, whether it be consistent with the accuracy of the geometrical method, to reason of quantity in the abstract, as if generated by motion. Now if abftrati quantity or magnitude may be represented by a line, and a particular line, if such quantity be conceived to be increased, the same will be true if it be diminithed, converso, in any given mode or law, the line representing it must be inereased or lengthened by the same law; and if the augmentation of the quantity be successive, and without intermiffion in the whole time of its increase, that of the line multibe the same duly to represent it ; but the line cannot be augmented but by the motion of one of its extreme points. It may be said that magnitude in the abstract, is here represented by one par ticular species of magnitude ; that of lines, and even an inu dividual line, the object, even fuch as it is, lays equally againft the whole of the fifth book of the Elements; where:Euclid, considering magnitude in the abstract, represents it constantly by a particular line; for wherever he speaks of a magnitude, it is to be understood of any magnitude, or in general ; and, on the assumption that it is so juftly to be considered, he de duces all the doctrine of the relation of magnitudes therein delivered. And one particular líne is taken as the representa tive of magnitude, or quantity in general, by the same opera tion of the mind, as one particular circle or triangle, in the the other parts of the elements, is taken as the representative of all possible circles or triangles : and in the fame manner all magnitudes may be represented by a füperficies, or a solid; 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 superficies : and in this manner allo things relating to magnitudes, and their increments, may be legitimately deduced from the nature of motion.

The purest geometry has taught us, that lines may be taken as generated by motion, and that magnitude, in the abstract, may be considered as represented by lines fo generated ; and ponsequently increasing quantity by increasing lines: the

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