THE

MONTHLY REVIEW,

For SEPTEMBER, 1787.

RT. I. Philofophical Tranfactions of the Royal Society of London. Vol. LXXVII. For the Year 1787. Part I. 4tó. 8s. fewed. Davis. 1787.

ASTRONOMICAL and MATHEMATICAL PAPERS.

An Account of a new Comet. By Mifs Caroline Herfchel.

ON

N the firft of Auguft 1786, Mifs Herschel discovered a comet between the 54th and 53d Urfæ Majoris, and the 14th, 15th, and 16th Coma Berenices, and makes an obtufe triangle with them, the vertex of which is turned to the south.'

Remarks on the new Comet. By William Herfchel, LL.D. From the defcription which his fifter gave of the comet, Dr. Herschel endeavours to afcertain its place.

Obfervations on Mifs Herfchel's Comet. By the Rev. Francis Wollafton, LL.B.

Mr. Wollafton recites a number of observations of the comet's place, from Aug. 5, to Sept. 21, 1786. The telescope that he ufed was fitted up with his new invented fyftem of wires, which he recommended in a former article *.

Determination of the Heliocentric Longitude of the defcending Node of Saturn. By Thomas Bugge, Profeffor of Aftronomy at Copenhagen.

This accurate obferver hath here given us an account of a series of obfervations on Saturn, in order to afcertain the longitude of that planet's node.

The culmination of Saturn was obferved with a fix-feet achromatic tranfit inftrument, and the planet was compared with o and of Sagittarius; the meridian altitude was taken with a fix-feet mural quadrant: from thefe the Author calculates the right afcenfion and declination, and the geocentric longitude and latitude, which are true, within 4 or 6 feconds: as thefe longitudes and latitudes are compared with the tables of Halley and De la Lande, the errors of the tables are corrected. The

* See Rev. vol. lxxv, p. 216.
O

VOL. LXXVII.

heliocentric

heliocentric longitudes and latitudes are deduced from the obferved geocentic longitudes and latitudes; and from thefe the place of the node is determined.

The Profeffor began his obfervations on July the 12th, and continued them to Oct. 8th, 1784. Saturn's paffage through the node was on Auguft 21ft, at 18h 20' 10" when his heliocentric longitude was 9' 21° 50′8′′. The errors in the place of the node are relative to Halley's Tables + 19′ 39′′, to Caffini's +16'4" and to De la Lande's +1'31'. Should the Profeffor, in the fame accurate manner, determine the nodes of the other planets, the fcience would receive much improvement, and the valuable Tables already published would be brought nearer to perfection.

Obfervations on the Tranfit of Mercury, May 4th, 1786, at Drefden. By M. Köhler, Infpector of the Mathematical Repofitory of the Elector of Saxony.

Obfervations on the fame at Petersburg. By M, Rumovski. To record obfervations is of vaft ufe in aftronomy. Befide determining the longitudes, thefe obfervations ferve to correct the tables, and to improve the elements of the planets.

On finding the Values of algebraical Quantities by converging Seriefes, and demonftrating and extending Propofitions given by Pappus and others. By Edward Waring, M.D. Profeffor of Mathematics at Cambridge.

Dr. Waring begins this Paper with a method of finding the roots or values of any given algebraical quantity by converging infinite feriefes; fuppofing the roots of this equation x+1=0 (where the b denotes any whole number or fraction) to be given. The problem includes many cafes, and has occupied much of the Author's attention; and though it afford ample entertainment to the curious reader on account of the intricacy of the investigation, yet it can be ufeful only in a very few cafes. For inftance, we shall take the Doctor's firft cafe, in which he finds the roots of this general expreffion+A; the roots are Д × a + λ √ — 1, Aa × ß + μ 1, 4 × 8+ √ √ — 1, &c.

I

I,

I

I, & + v√—1, &c, are the

- I,

where a+a, ß+μ roots of the equation "+=0; it will be + if it was -A, and -1 if + A. Now all the roots of "+1=0 are not poffible; when indeed n=2, then the roots are +1 and namely both poffible, but in other cafes many roots will be impoffible, as, when n=3, the roots are +1, −1+✔=}, -I-V, the two laft of which are impoffible, so that in this cafe the theorem cannot be used; and many others might be produced where the fame impoffibility would occur.

-

In the fubfequent part of this Paper, Dr. Waring gives a geheral method of demonftrating certain propofitions in which one equation, as o, involving r unknown independent quantities, is predicated of another equation containing the fame quantities. Of this fort are many of thofe propofitions given by Pappus; as, if the ratio a+b: b be greater than c+d: d, then b: a- b will be less than d:c- d.

The Author has added a brief account of the labours of former algebraifts with respect to the method of finding the number of affirmative and negative, and of poffible and impoffible roots, in any given equation. This is truly valuable, efpecially to the tyro, who is here directed to feveral authors that have given rules for determining these circumstances. No perfon is fo thoroughly acquainted with this fubject as Dr. Waring, and his information concerning it is, without doubt, much to be depended on.

An Account of the Discovery of Two Satellites revolving_round the

Georgian Planet. By William Herschel, LL.D.

On the 11th of January 1787, this indefatigable observer saw two small stars near to his lately difcovered planet; fubfequent obfervations have proved them to be moveable, and confequently fatellites. Dr. H. has not yet feen them long enough to determine their periodical times with accuracy; he supposes that the first performs its revolution in about 8 days and 4, and the fecond in nearly 13 days and . Their orbits,' he fays, ' make a confiderable angle with the ecliptic, but to affign the real quantity of this inclination, with many other particulars, will require a great deal of attention and much contrivance.' We truft, however, that Dr. Herfchel's unremitting diligence and ardour for making difcoveries, will fhortly enable him to prefent the Public with a perfect description of these moons, which, in all probability, would have remained unknown to the inhabitants of our globe, if the penetrating eye of an Herschel had fuffered them to pafs unnoticed.

Concerning the Latitude and Longitude of the Royal Obfervatory at Greenwich; with Remarks on a Memorial of the late M. Caffini de Thury. By the Rev. Nevil Mafkelyne, D.D. Astronomer Royal.

Caffini's Memoire was undoubtedly a grofs affront on Dr. Mafkelyne, and his learned predeceffors. The French Aftronomer fays, "Il paroit que l'on n'eft point d'accord fur la longi tude de Greenwich à onze seconds près, et fur fa latitude à quinze feconds." It may furely be pronounced impoffible that the latitude of Greenwich Obfervatory, which is furnished with the best and moft accurate inftruments in the world, fhould not have been ascertained to a fecond. M. Caffini fays it is not within. 15 feconds of the truth. Dr. Mafkelyne proves that his predeceffor, Dr. Bradley, made the latitude of the Obfervatory .0 2

519

51° 28′ 40.7. And Dr. M. from 246 obfervations on the equinoxes for fix years, befide a number of others, makes it 51° 28′ 413, differing from the former only of a fecond. From the whole then,' fays the Author, I conclude that the latitude of the Royal Obfervatory at Greenwich is firmly established from Dr. Bradley's obfervations and my own, at 51° 28′ 40′′, probably without the error of a single fecond.' Dr. M. then gives feveral obfervations that have been made at the Paris Obfervatory, whence he concludes its latitude to be 48° 50′ 14′′, and the difference of latitude of the two Obfervatories is 2° 38′ 26′′. A question naturally arifes; On what foundation was M. Caffini's fuppofition of an uncertainty of 15" built? This, the Author fhews, is in confequence of a paffage in De la Caille's refearches into the aftronomical refractions and latitude of Paris, contained in the Memoirs of the Paris Academy for 1755, where De la Caille takes the differences of zenith diftances of 14 ftars obferved by Dr. Bradley, as publifhed in the Memoirs for 1752, and the fame obferved by him at Paris, and, correcting them for the difference of the refractions at the refpective zenith diftances according to his own table of refractions, finds the mean to be 2° 37′ 23′′.9, which added to 48° 51′ 29′′.3, his Jatitude at the College of Mazarine, gave 51° 28′ 53".2, for the latitude of Greenwich, exceeding Dr. Bradley's latitude by almoft 13". The Author adding many learned remarks on refractions, and the errors of inftruments, proceeds to fhew, which he does in a fatisfactory manner, that Caffini is wrong alfo in his affertion concerning the longitude of Greenwich. It appears, from many obfervations made at both Obfervatories, that the true difference of longitude between Paris and Greenwich is 9' 20" within two or three feconds.

This is an excellent Paper, and does honour to its Author. Why it was not given to the Public fooner, does not appear, and we regret that the Aftronomer Royal fhould have with-held his ufeful remarks fo long. The French Memoir was prefented to Dr. M. on the 28th April, 1785.

An Account of the Mode propofed to be followed in determining the relative Situation of the Royal Obfervatories of Greenwich and Paris. By Major General William Roy.

In our 75th volume, p. 217, we gave an account of General Roy's meafurement of the bafe on Hounflow Heath. We are in this Paper informed how the operations are to be carried on, by a series of triangles, from that measured bafe to the neighbourhood of Dover, and thence to Calais, in order to determine the difference of latitude and longitude of the two Obfervatories of Greenwich and Paris. In the map accompanying this Paper the ftations are laid down, and the triangles are defcribed. The execution of the plan is poftponed until Mr. Ramfden finishes

the inftrument for measuring the angles, which, we are told, is new of its kind,' and by which angles may be determined to a degree of precifion hitherto unexampled.' This is certainly a valuable contrivance, and we hope the General will, in fome future Paper, explain its conftruction. The ftations are, in our opinion, well chofen; the chief object being to obtain triangles. with their fides as long as poffible, in order to make few ftations, and by that means avoid the calculations of more triangles than may be neceffary.

The General has added two tables, one containing a comparifon of the observed length of the celeftial arc of the meridian, comprehended between the parallels of Greenwich and Perpig nan, with the computed and measured lengths of the correfponding terreftrial are between thefe parallels. Thefe computations must have coft no small labour and time; they are made on ten different hypotheses of the earth's figure. The other table has also been a work of great labour: it contains the lengths of the degrees of latitude, and longitude in different latitudes, and the length of the degrees of a great circle perpendicular to the meridian, and likewife fuch as are oblique to it for the other feven points of the quadrant..

The determination of the figure of the earth is a material point both in navigation and geography, and every attempt to afcer-. tain it, or even to correct former measurements, deferves the highest encouragement.

(The PHILOSOPHICAL and other Papers, in a future Article.)

ART. II. A Courfe of Phyfico-Theological Lectures on the State of the World, from the Creation to the Deluge. By Robert Miln, A. M.. 8vo. 6s. Boards. Faulder. 1786.

'CON

ONVINCED that reafon and revelation mutually fupport each other, and that true philofophy is the beft defence against scepticifm and infidelity, I have ventured,' fays the writer, on these principles, to contribute my mite to the fupport of facred hiftory.' Such is the profeffed defign of this volume; and it muft be allowed, that the defign is profecuted in a rational, ingenious, and inftructive manner. Whether, or not, the Author has thrown any new light on that part of these ancient records which falls under his review, Mr. Miln obferves, I flatter myself that I have freed it from fome vifionary com ments, which can neither be reconciled to the rectitude of the Divine Nature, nor to that uniformity of government, which is exercifed over the natural and moral world.'

It does not confift with the limits of our work to furnish our Readers with fpecimens of our Lecturer's reasonings and decifions on the different points, with their various difficulties, which

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occur