eftablishment in Scotland, feems to found his work on the Scotch confeffion of faith: but furely he will acknowledge that there may be very pious and good Chriftians who, after very ferious and careful attention, cannot confent to every article which he appears to confider as effential.

With fome exceptions of this kind, the publication before us may be confidered as calculated for general benefit. The account of the Chriftian spirit and character, the obligations to virtue and piety, their neceffity, and their advantage, is in general, very commendable: but all is, in fome meafure entangled with the aforefaid confellion. Mr. Dalgliesh confiders, judiciously and properly, the duties which mankind owe to each other, but we have not obferved, that he takes particular notice of that fpecies of benevolence and charity which confifts in candid and friendly difpofitions to thofe of very different religious fentiments. The work will, no doubt, be acceptable to thofe with whofe fyftem it concurs; and a great part of it may be ferviceable to others, and to all, though they should not entirely correspond, in fome inftances, with the opinion of the writer.

Art. 68. Efay on the Chriftian Character: being an Attempt to afcertain the Nature of that Affection which the Author of Christianity hath made. the Characteristic of his Difciples. By Samuel Copland, D. D. Minister of the Gospel at Fintray. 8vo. fewed. Dilly. 1785.

35.

"A new commandment give I unto you, that ye love one another, &c. By this fhall all men know that ye are my difciples, if ye have love one to another." John, xiii. 34, 35. This being a capital principle in the fchool of Christ, it must, Dr. Copland obferves, be of great importance for every Chriftian to acquire a diftinct knowledge of this grace of love, and attain an habitual eafe in its practice. With this view he here communicates the refult of an enquiry begun and carried on for his own private instruction. In purfuit of his defign he inveftigates the object of this love and its qualities; whence he infers, that, though univerfal good-will and beneficence are warmly inculcated by the Author of our holy religion, this is not the principle which he immediately recommends as the badge of his followers: What then is it? fome of our readers are inclined to afk. The anfwer is, It is a particular affection to our fellow Chriftians, to thofe who are pious and virtuous, increasing in proportion as they excel in fuch a temper and habit. This concurs with the fentiment of our Lord,-" Whofoever doth the will of my Father who is in heaven, the fame is my mother, my fifter, and brother." Had fuch a fentiment, fays this writer, proceeded from the lips of fome perfon of rank and opulence, or had it been uttered by an ancient Greek or Roman, all the stores of rhetoric had been ranfacked to difplay its grandeur, &c.

Dr. Copland profecutes his fubject in a fenfible manner, but with a detail of words, and of reafoning, more than appears to us to have been neceffary; by which means he may be thought, by fome readers, to have rendered his performance fomewhat tedious,-not to Lay dull,

SER

SERMONS.

1. Preached at St. Peter's, Colchefter, June 26, 1787, for the Benefit of the Sunday Schools in that Town. By Thomas Twining, M. A. Vicar of White Notly, Effex. 8vo. 15. Robinfons.

From Solomon's words, The rich man's wealth is his ftrong city: the deftruction of the poor is their poverty, Mr. Twining forcibly recommends to the attention and encouragement of his hearers, a charitable inftitution, whofe object is, to refcue the poor, as far as human means can do it, from that worst evil to which their poverty exposes them, the want of a proper education; and, in doing this, to rescue the Public alfo, from the bad effects of that want.

The difcourfe is very well written, and happy it is for the inftitution of Sunday Schools, that it has found, among the number of its able advocates, fo very able an one as Mr. Twining.

II. The Duty of a Minifter: Preached at the Vifitation at Leeds, June 24, 1784. By the Rev. Miles Atkinfon, B. A. 8vo. 6d. Wallis, &c.

According to Mr. A. the doctrines which Chriftian teachers should continually enforce, are, the fall of man; his moral depravity; the neceffity of converfion; the facrifice and interceffion of our Redeemer; the willingness of God to forgive, &c.; the eternal happiness of those who believe and are converted; and the everlasting mifery and torment which must be the inevitable portion of all who will not come to Chrift, that they may have life.

We leave it to our Readers to determine, whether this mode of preaching is agreeable to the Apoftolic injunction: Thefe things I will that thou affirm conftantly, that they which have believed in God maintain good works—but avoid foolish questions."

Thanks to Oxonienfis.-The Reviewers are obliged to him for his hint; the purport of which is under confideration.

+++ Our Conftant Reader's letter is tranfmitted to the continent, for an answer to his inquiries concerning articles of Foreign Literature. With respect to the domeftic publication which he mentions, it certainly never was criticised in the M. R. The omiflion was occafioned by the long, lingering illness, and, at last, the death of the Gentleman to whom the confideration of that work was referred; by which means, both the tract, and fome account of it, which he had prepared, were loft: and it was deemed too late to put the subject into other hands.

$15 Bishop Newcome's Reply to Dr. Prieftley's fecond Letter, on the duration of our Saviour's miniftry, was published in 1781, or 1782, by G. Robinson, price 25.

The Letter concerning Dr. Franklin's invitation of the Swimming Ancher, will be answered in our next.

THE

MONTHLY REVIEW,

For SEPTEMBER, 1787.

ART. I. Philofophical Transactions of the Royal Society of London. Vol. LXXVII. For the Year 1787. Part I. 4to. 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 Herfchel difcovered 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 obfervations 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 these 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 science 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 +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 useful only in a very few cafes. For inftance, we shall take the Doctor's first cafe, in which he finds the roots of this general expreffion+ A; the roots are AX

« + λ √— 1‚Âa × ß + μ √ = 1, 1a × g + √ √ =

1,

ß

xy+v√ 1, &c. where a +λ=1, B + μ √ =1, &+1, &c. are the roots of the equation x+1=0; it will be + if it was -A, and if A. Now all the roots of "+1=0 are not poffible; when indeed n = 2, then the roots are +1 and -1, namely both poffible, but in other cafes many roots will be impoffible, as, when n=3, the roots are + 1, −1+✔=},

V, the two laft of which are impoffible, fo 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 general method of demonftrating certain propofitions in which one equation, as Ao, 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+bb be greater than c+d: d, then b: a b will be less than d: 6-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, especially 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 Herfchel, LL.D.

On the 11th of January 1787, this indefatigable observer saw two small ftars 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 fuppofes that the firft performs its révolution in about 8 days and, and the second 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 defcription of thefe moons, which, in all probability, would have remained unknown to the inhabitants of our globe, if the penetrating eye of an Herfchel had fuffered them to pals 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 Maskelyne, D.D. Astronomer Royal.

Caffini's Memoire was undoubtedly a grofs affront on Dr. Maskelyne, 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 feconds 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

O 2

51°