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MEMOIRS III. and IV. Enquiries concerning the Motions of a
Planet, on the Hypothesis of difimilar Meridians. By M. D'Alembert.
These inquirie. were begun in the volume of the Academy for the year 1754 ; where the Author considered the motions of a supposed planct, whose equator and parallels are circles, and all its meridians similar. 'He here examines what would be the motions of another planet, whose 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 impon, as resulting from the figure of her equator and meridians, the position 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 minuteness. It will however be sufficient for us to give only the outlines or result of this inquiry.
From analytical calculations, and reasonings founded on the Newtonian theory of gravitation, the Author deduces the following particulars; that the lunar equator is elliptic; and that, in consequence of this figure, the moon is subjected to a physical 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 ļunar equator forms with the faid orbit two nodes or equinoe. ţial points, resembling those of the earth's equator; and lastly, that these points, and the axis itfelf, have a motion contrary to the order of the signs, and sensibly equal to that of the nodes of the lunar orbit on the ecliptic. MEMOIR V. 'On the greatesi Inclination of the Orbit of the Moon
to the Plane of the E-liptic; 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, since the late successful application of it to the interesting problem of discovering the longitude at fea, by observations made on the distance of that planet from the various fixed stars, which it approaches in its course round the earth. This confideration determined the Author of this memoir to endeavour to ascertain, 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 case which forms the fubject of this article ; and from thence to discover and correct the errors of the tables. Now one of the most necessary elements of the said tables is the quantity of the greatest inclination of the plane of the
moon's orbit to that of the ecliptic. , This inclination, as is indeed, implied by the very terms of the problem, is variable; being subject to a difference or variation of about 18 minutes : ; the greatest inclination taking place, when the sun is in the Jine of the nodes; and the least, when he is about go degrees distance from thence : as, in this last fituation, his attractive power tends most forcibly to draw the moon nearer to the plane of the ecliptic.
Two observations, taken some years ago, of the moon when on the meridian, when she was accurately compared with some fixed stars, appeared to him very proper for this inquiry. By the firit, made on the ilt of January, the moun was found to be in her greatest southern latitude, which was determined by the common methods to be so: 16'. 18". supposing the horizontal parallax to be 54,433". and diminishing the parallax of altitude about:8-secondson account of the spheroidical figure, of the earth,
In the second observation, taken on the 14th of the same month, the moon was at her greatest limit of northern latie rude, which was found to be 5. 17. 36". differing above a: whole minuie from that which had been found in the preceding. obfervation. This error M. le Monnier attributes to the parallax, as her two greatelt northern and southern latitudes ought to have been exactly equal, and as he was convinced of the , accuracy of the divisions of the mural quadrant, with which these observations were made. . He accordingly infers that the pa-, rallax requires.correction, so as to reduce the two inclinations to an equality, and that we may be well a!lured of the exact quantity of that important element.
There are the inost important articles comprehended under the class of Aftronomy; excepting perhaps a memoir, in which, M. Bailly difcufies some 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 sun, and occultations of the fixed Itars and planets. by the moon; being the sixth
memoir which he has given on this subject. It will be fufficient • to give barely the title of the remaining articles, which are of
dels fignificance. These are, 1: Aflronomical Observations made to determine the Geographical Pobtion of the City of Manilla, by M. le Gentil; and 24 Of the Capes Finisterre and Ortegal, by M. de Bory. 34, 35, Calculations and Observations of the Op. position of Jupiter to the Sun, on April 6, 1768, by Mess. Jeurat, De la Lande, and Bailly. 6. Hints with regard to the (then). approaching Transit. of Venuse by M. de la Lande; and some few particular observations.
HYDRAULICS. In the single memoir contained in this class, the Chevalier de Borda inquires into the cause, and endeavours to ascertain the quantity, of a very observable diminution of the effects expected, from theory, to be produced by certain hydraulic machines, and particularly pumps. It appears that one of the principal causes of this diminution is a certain obstruction, or Arangulation, as he terms it, which the ascending column of water undergoes in pafling through the apertures of the valves necessarily employed in these machines, and which is produced by the converging direction of the different columns, and by some circumstances in the construction of these valves. In the case, for instance, of a particular fire-engine which he examines, he finds that the force necessary 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 cause, more than a thirteenth part.
For his proofs and calculations we must refer to the memoir itself; from which, however, we shall extract the substance of an observation at the end of it, as it is of a practical kind, and appears to be of some importance. This is, that as the refiftance caused by this strangulation is proportional to the square of the velocity of the piston; by diminishing the latter a certain quantity, we may diminish the former in a much more confiderable degree. For example, if instead of employing four pistons, having each a play or range of fix feet, eight were to be used, which played only three feet each, the machine would not be more loaded in the latter case than in the former; and at the same time, the resistance caused by the strangulation of the Auid would be reduced to a fourth part of what it was before. Accordingly, in practice, and particularly in the pumps used at sea, it is more advantageous to increase the number of pumps, than to augment the play and velocity of the pistons.
In the History of the Arts, published this year, the fix following have been described : 1. The Art of forging Iron, and the making of the various Utensils of that Metal; by M. du Hamel. 2. The Art of making Shoes ; by M. Garsault: and, 3. Of making Bricks and Tiles ; by M. Jars.' 4. The Art of dividing Mathematical Instruments ; by the Duke de Chaulnes. [We have formerly given fume remarkable instances of the great improvements which have been lately made in this new art, by this noble mechanician t, 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.
or address, as bas hitherto been the case, of some particular and rare individual; but on certain curious mechanical contrivances, by means of which the accurate division of mathematical inftrue ments may be executed with the greatest case and certainty, by almost any person who bestows a moderate thare of attention on the work.] s. 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 Ilde, terminate the volume.
ART. 11. Delli Viaggi D'Enrico Wanton, &c. - The Travels of Henry Wanton,
to the Terra Australis, 8vo. 4 Vols. London, 1772. OUR paffion for ideal narratives is founded on that innate
curioficy which is the instinctive inftrument of knowledge. Were a school boy asked why he lould lose his sleep to read Robinson Cruso, he could only answer that it was because he liked the book. A philosopher 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 support by his own induftry, he would naturally find himself interested in the dif. trelles of another human being, who was represented as cast on a desolate ifland, and obliged to sublift by the expedients of invention; because he would lay up those expedients for his own use, in case of the like circumstances befalling himself.
The book before us is quite as ideal as Robinson Cruso, but it has a very different style of merit. It abounds with character, sentiment, and philosophical observation.
The traveller is the son of an English merchant, who being imprudent enough not to consult his boy's genius and temper with respect to his education and his future appointment in life, threw him into a fituation that was extremely disagreeable to him, in consequence of which, at a very early period, he makes his efcape from his pedantic tutor, and goes on board a vessel bound for the East Indies,
Naturally fenfible and affectionate, the distresses which, he conceives, his family must feel from this elopement, affect him as he loses fight of his native shore. With little provision, and without prospect of more, he suffers too for himself, and gives way to melancholy and despair.
This conduct is observed by a benevolent young gentleman, the son of a capital Englidh merchant, who, by his kind solicitations, obtains a perfect knowledge of his situation, and offers his friendthip and ashitance.
The philosophical confolations he offers him, when afflicted with the idea of leaving his family and his country, do honour
to his understanding: Observe, my dear Henry, said he, the immensity of this ocean on which we sail, 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 sea make us unable to discover. From hence conceive the vaft Tize of this our globe, or rather of the universe; for this earth is, in comparison of that, no more than a grain of sand. . The researches of the philosophical mind, however, adds he, end not here: they stretch beyond the weakness of the senses, and by the analogy of geoinetrical reasoning have travelled far beyond the sphere of fight. In this inaccessible variety of real, or poffible existence, the mind at length is loft. It may stretch far forward by the measure of proportions, but it knows not where either to seek or fix the limits of creation.
. And in this immensity of being what then is man? - The object of the universal Creator's providence? The object of his care, as if he were the only work of his hands ? Astonishing !. but true-What sentiments of gratitude, what impressions of hu. mility towards the father of nature should not this consideration saggeft!--Think then, my dear friend, how little you have lost. by leaving your father's house, and putting yourself in the hands, of Providence, who has the ministers of his bounty in every department of the creation, and can make them the inftruments of your support into whatever region you may go, as much as your father was that inftrument at home.'
The same spirit of virtue and good sense appears in the obfervations he makes, when the two friends are thrown by thipwreck on a desart island, and are obliged to fubfitt on fith, wild fruits, and water,
• We are now, my dear Henry, in the fituation of the first race of men, whose food was the produce of the chace, or of the net, and whose only beverage was the spring. Strangers, however, they were to ambition, to rapine, and disorderly inclinations. They had no desires but such as were didated by the voice of nature, and when those were satisfied, their spirit was at rest. We cannot therefore call ourselves less happy than they were. On the contrary, we enjoy the advantages which affociated life has, in the long process of ages, produced, (the advantages of knowledge and invention, I mean) without fuffering the inconveniences that fociety brings along with it. Happy should we be, could this easy tranquillity attend us to the clore of life. But that, I fear, is inconfistent with human inconstancy. To live long satisfied within the limited pursuits of nature will hardly be poßible for those, on whom the improvements of society have impressed krong ideas of artificial wants.