MEMOIRS III. and IV. Enquiries concerning the Motions of a Planet, on the Hypothefis of diffimilar Meridians. By M. D'Alembert.

Thefe inquiries were begun in the volume of the Academy for the year 1754; where the Author confidered the motions of a fuppofed planet, whofe equator and parallels are circles, and all its meridians fimilar. He here examines what would be the motions of another planet, whofe equator and paral lels are elliptical, and its meridians unequal or diffimilar. He applies his principles, in particular, to the determining the Jaws of the libration of the moon, as refulting from the figure of her equator and meridians, the pofition of the plane of her equator and axis, and the motions of that axis. All these subjects are here treated of with the greatest accuracy, depth, and minutenefs. It will however be fufficient for us to give only the outlines or refult of this inquiry.

From analytical calculations, and reafonings founded on the Newtonian theory of gravitation, the Author deduces the following particulars; that the lunar equator is elliptic; and that, in confequence of this figure, the moon is fubjected to a phyfical and real libration, as well as to that other which he calls an optical libration, depending on the figure of her orbit, and on the irregularity of her motion in it: that her axis, on which the turns round in a time nearly equal to that of her periodical motion, is inclined to her orbit; and that consequently the lunar equator forms with the faid orbit two nodes or equinoetial points, refembling thofe of the earth's equator; and laftly, that these points, and the axis itfelf, have a motion contrary to the order of the figns, and fenfibly equal to that of the nodes of the lunar orbit on the ecliptic.

MEMOIR V. On the greatest Inclination of the Orbit of the Moon to the Plane of the Eliptic; and on the Parallax of that Planet: First Memoir. By M. Le Monnier.

An accurate knowledge of the moon's motions is become an object of the greatest importance to astronomy and navigation, fince the late fuccefsful application of it to the interefting problem of difcovering the longitude at fea, by obfervations made on the distance of that planet from the various fixed ftars, which it approaches in its courfe round the earth. This confideration determined the Author of this memoir to endeavour to afcertain, by actual observation, how far the best tables of the moon's motion, now extant, were to be confided in, with respect to the particular cafe which forms the fubject of this article; and from thence to difcover and correct the errors of the tables. Now one of the most neceffary elements of the said tables is the quantity of the greatest inclination of the plane of the

moon's

moon's orbit to that of the ecliptic. This inclination, as is indeed, implied by the very terms of the problem, is variable; being fubject to a difference or variation of about 18 minutes: the greatest inclination taking place, when the fun is in the Jine of the nodes; and the leaft, when he is about 90 degrees distance from thence: as, in this laft fituation, his attractive power tends most forcibly to draw the moon nearer to the plane of the ecliptic.

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Two obfervations, taken fome years ago, of the moon when on the meridian, when he was accurately compared with fome.. fixed ftars, appeared to him very proper for this inquiry. By the first, made on the rt of January, the moon was found to be in her greatest fouthern latitude, which was determined by, the common methods to be 5°. 16. 18". fuppofing the horizontal parallax to be 54, 33. and diminishing the parallax of; altitude about 8 feconds, on account of the fpheroidical figure. of the earth and fam

In the fecond obfervation, taken on the 14th of the fame, month, the moon was at her greateft limit of northern latitude, which was found, to be 5. 17. 36". differing above a whole minute from that which had been found in the preceding. obfervation. This error M. le Monnier attributes to the parallax, as her two greatest northern and fouthern latitudes ought to have been exactly equal, and as he was convinced of the accuracy of the divifions of the mural quadrant, with which thefe, obfervations were made. He accordingly infers that the pa-, rallax requires correction, fo as to reduce the two inclinations, to an equality, and that we may be well affured of the exact quantity of that important element.

There are the most important articles comprehended under the class of Aftronomy; excepting perhaps a memoir, in which, M. Bailly difcufles fome important points relating to the theory, of Jupiter; and the continuation of M. Du Sejour's new Ana-, lytical Methods of calculating eclipfes of the fun, and occultations of the fixed ftars and planets by the moon; being the fixth memoir which he has given on this fubject. It will be fufficient to give barely the titles of the remaining articles, which are of Jefs fignificance, Thefe are, 1; Aftronomical Obfervations made to determine the Geographical Position of the City of Manilla, by M. le Gentil; and 2. Of, the Capes Finisterre and Ortegal, by M. de Bory. 34, 35. Calculations and Obfervations of the Op. pofition of Jupiter to the Sun, on April 6, 1768, by Meff. Jeurat, De la Lande, and Bailly. 6. Hints with regard to the (then). approaching Tranfit of Venus, by M. de la Lande; and fome few particular obfervations.

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HYDRAULICS.

HYDRAULICS.

In the fingle memoir contained in this clafs, the Chevalier de Borda inquires into the cause, and endeavours to ascertain the quantity, of a very obfervable diminution of the effects expected, from theory, to be produced by certain hydraulic machines, and particularly pumps. It appears that one of the principal caufes of this diminution is a certain obftruction, or ftrangulation, as he terms it, which the afcending column of water undergoes in paffing through the apertures of the valves neceffarily employed in thefe machines, and which is produced by the converging direction of the different columns, and by fome circumstances in the conftruction of these valves. In the cafe, for instance, of a particular fire-engine which he examines, he finds that the force neceffary to move the pump, is to the force which would be sufficient, if this contraction, or obftruction, did not fubfift, as 65.88 is to 61; and that accordingly the effect of the machine is diminished, from this caufe, more than a thirteenth part.

For his proofs and calculations we must refer to the memoir itself; from which, however, we fhall extract the fubftance of an obfervation at the end of it, as it is of a practical kind, and appears to be of fome importance. This is, that as the refiftance caufed by this ftrangulation is proportional to the square of the velocity of the pifton; by diminishing the latter a certain quantity, we may diminish the former in a much more confiderable degree. For example, if inftead of employing four piftons, having each a play or range of fix feet, eight were to be ufed, which played only three feet each, the machine would not be more loaded in the latter cafe than in the former; and at the fame time, the refiftance caused by the ftrangulation of the fluid would be reduced to a fourth part of what it was before. Accordingly, in practice, and particularly in the pumps ufed at fea, it is more advantageous to increase the number of pumps, than to augment the play and velocity of the piftons.

In the Hiftory of the Arts, published this year, the fix following have been defcribed: 1. The Art of forging Iron, and the making of the various Utenfils of that Metal; by M. du Hamel. 2. The Art of making Shoes; by M. Garfault: and, 3. Of making Bricks and Tiles; by M. Jars. 4. The Art of dividing Mathematical Inflruments; by the Duke de Chaulnes. [We have formerly given fuma remarkable inftances of the great improvements which have been lately made in this new art, by this noble mechanician †, which depends not on the fingular talents

+ See the Appendix to our 42d volume, page 500, &c. and that to our 46th volume, page 680.

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or address, as has hitherto been the cafe, of fome particular and rare individual; but on certain curious mechanical contrivances, by means of which the accurate divifion of mathematical inftru ments may be executed with the greatest ease and certainty, by almost any person who beftows a moderate share of attention on the work.] 5. The Art of making Wire; by M. du Hamel: and, 6. That of working Coal Mines; by M. Morand. The Eloges of M. Baron, of M. Camus, M. Deparcieux, and M. de l'lfle, terminate the volume.

AR T. II.

Delli Viaggi D'Enrico Wanton, &c.-The Travels of Henry Wanton, to the Terra Auftralis. 8vo. 4 Vols. London, 1772. OUR paffion for ideal narratives is founded on that innate curiofity which is the instinctive inftrument of knowledge Were a school boy asked why he fhould lofe his fleep to read Robinson Crufo, he could only answer that it was because he liked the book. A philofopher would acquaint him with the reason why he liked it. He would tell him that, as a human being, who had originally that being to fupport by his own industry, he would naturally find himself interested in the dif treffes of another human being, who was represented as caft on a defolate ifland, and obliged to fubfift by the expedients of invention; because he would lay up thofe expedients for his own use, in cafe of the like circumstances befalling himself.

The book before us is quite as ideal as Robinson Crufo, but it has a very different ftyle of merit. It abounds with character, fentiment, and philofophical obfervation.

The traveller is the fon of an English merchant, who being imprudent enough not to confult his boy's genius and temper with refpect to his education and his future appointment in life, threw him into a fituation that was extremely difagreeable to him, in confequence of which, at a very early period, he makes his efcape from his pedantic tutor, and goes on board a veffel bound for the Eaft Indies.

Naturally fenfible and affectionate, the diftreffes which, he conceives, his family muft feel from this elopement, affect him as he lofes fight of his native fhore. With little provifion, and without profpect of more, he suffers too for himself, and gives way to melancholy and despair.

This conduct is obferved by a benevolent young gentleman, the fon of a capital English merchant, who, by his kind folicitations, obtains a perfect knowledge of his fituation, and offers his friendship and affiftance.

The philofophical confolations he offers him, when afflicted with the idea of leaving his family and his country, do honour

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to his understanding. Obferve, my dear Henry, faid he, the immenfity of this ocean on which we fail, and the vault of hea- · ven above us. One would imagine, that we were the only created beings, the only inhabitants of this wide extent of space. Alas! we are but at a little distance from the Continent, which the feebleriefs of our eyes and the curvity of the fea make us unable to discover. From hence conceive the vast size of this our globe, or rather of the univerfe; for this earth is, in comparifon of that, no more than a grain of fand. The researches of the philofophical mind, however, adds he, end not here: they stretch beyond the weakness of the fenfes, and by the analogy of geometrical reafoning have travelled far beyond the sphere of fight. In this inacceffible variety of real, or poffible exiftence, the mind at length is loft. It may ftretch far forward by the measure of proportions, but it knows not where either to seek or fix the limits of creation.

And in this immenfity of being what then is man?—The object of the univerfal Creator's providence? The object of his care, as if he were the only work of his hands?-Aftonishing !. but true-What fentiments of gratitude, what impreffions of humility towards the father of nature should not this confideration fuggeft?-Think then, my dear friend, how little you have loft by leaving your father's houfe, and putting yourfelf in the hands of Providence, who has the minifters of his bounty in every department of the creation, and can make them the inftruments of your fupport into whatever region you may go, as much as your father was that inftrument at home.'

The fame fpirit of virtue and good fenfe appears in the obfervations he makes, when the two friends are thrown by ship-. wreck on a defart ifland, and are obliged to fubfift on fish, wild fruits, and water.

**We are now, my dear Henry, in the fituation of the first race of men, whofe food was the produce of the chace, or of the net, and whofe only beverage was the fpring. Strangers, however, they were to ambition, to rapine, and diforderly inclinations. They had no defires but fuch as were dictated by the. voice of nature, and when those were fatisfied, their spirit was at reft. We cannot therefore call ourfelves lefs happy than they were. On the contrary, we enjoy the advantages which affociated life has, in the long procefs of ages, produced, (the advantages of knowledge and invention, I mean) without fuf fering the inconveniences that fociety brings along with it. Happy fhould we be, could this eafy tranquillity attend us to the clofe of life. But that, I fear, is inconfiftent with human inconftancy. To live long fatisfied within the limited purfuits of nature will hardly be posible for thofe, on whom the improvements of fociety have impreffed ftrong ideas of artificial wants.

Yet