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1797*] Important Proceedings cf the National Injlitute. zSxtitude of the Inftitute will, doubtlefs, not forget their names in the futire collection of its labours. Let thole, in the mean time, who chcriih letters and humanity, know, that nor only private individuals—not only numerous coniine us of enlightened men, but ^ven foreign governments, -particularly that of Spain, have given frcili proofs of eitcjm to the french nation, by applying to the Xnfti-tute for its dccifion upon ievernl fubjedts relating to Arts and.Sciences.—Let them know, that war id elf has not proved an impediment to thole men, in whom Europe prides itfelf; .that- country which gave birth to a Newton,' ftili fees fevcrai members of its Royal S ciety, especially its celebrated prefident, endeavouring, by his trulyffraternal communications, to dimimlh the horrors of that fcourgc which has fallen fo long, and fo heavily! on two great and iliullrious nations,— Thanks to the Genius of frit nee, which is alfothat of nature, peace, and virtue I May this fcntimental alliance—this fa-cred union of ail thofe who have dedicated themlelves to literature, become daily clofer, and contribute to refture peace to unhappy Europe i May France become the centre of this pacific. ufeful, and glorious inrercourle 1 After having received fo many laurels from the hands of victory, let her only holdout the olive to the furrounding nations—let her be ambitious of no .other triumphs, than thole of labour over time—cf intelligence over fpacc—and of art over nature.NoTrcE of Mathematical Memoirs by Phony, on*e of the Secret aries.Laplace read a memoir on thefe-cular equations of- the motion of the nodes of the apogee of the lunar orbit, and on the abberration of the liars.— This learned member had, in a preceding memoir, published in 1786, obferved, that the motions of the nodes, and of the apogee, were fubjedt to inequalities fimiiar to thofe of the mean motion of the moon—inequalities that are very exactly determined for this latter motion, regard being had only to the terms depending on the hrft power of the pertur-bating force ; but in refpett to the mo-iion^ of the apogee, a half of it-only is obtained through fthe means of this firft power, and the other half is principally due to the terms depending on the fe~ cond power. Laplace has accordingly found, that the refults proceedingfrom each of thefe powers, do not differ from each other , and that.rheir total produces nearly 2^t the morion obferved.It follows,-from his rcfearches, that while the morion of the moon is accelerated. that of its apogee is leffened, a de-lay, which is 2* of the acceleration of the mean motion of the moon; and that the lecular equation of the anomaly is 3L of the equation, of the mean motion ; which mmt have a very fenfibie influence on the calculation of ancient obfervations.By introducing the fquare of the per-turbating force into the calculation of the morions of the' nodes, Laplace finds their lecular equation to be Rof that-of the mean motion, and to coincide with the obfervation within, nearly TJ,35. The motion of the nodes, and that of the apogee, are leffened?, when the mean motion is accelerated ; and thefe three motions are to each other in the conftant proportion of n, 36, and 16.Thefe great inequalities muft one day produce variations, equal at leaft to the 40th of the circumference in the fecular motion of the moon, to the iSrh in the fecular motion of its apogee, and the primitive order, or fituation, will not return for millions of years.Paft obfervations have made known the fecular equation of the mean motion, fuch as it is concluded to be from univer-fal gravity 5 but notice has not been taken of the fecular equation of its ano-~ m.-dy, cf which the exiftence is afcer-tained by the calculations that Bouvard has made of all the eclipfes, tranfmirced by Ptolemy and the Arabians, and of which, the introdudlion evinces the ne-ceifity of an alteration in calculating the motion of the moon’s anomaly. La-flACE, applying to former obfervations the confiderations refulting from his re-fearches, finds that thele obfervations prove inconteftibly the exiftence of the lecular equations of the moon’s motion and of its anomaly, .the necdfity of attending to it, and of accelerating the motion of the anomaly given by the tables. He does not hefitate to propofe to affronomers, to increafe this motion about 5' 49,; every hundred years, and to apply it to an additional fecular equation, equal to 3^, which is that of the mean motion. Thefe correions will infallibly conduce to augment the exaft-nefs of the lunar tables, which are of fuch importance to navigation and geography.La?lag«;
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Monthly Magazine
London, Middlesex, GB
Sun, Oct 01, 1797
Page 19
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