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The Conversations of Emily,

Journal of W. Dowsing, Parliamentary Visitor, in 1643 and 1644, 237

History of Henry VII. King of England,

238

Rope's End for Hempen Monopolists,

ibid.

Dr. M.Farlan's Tracts on Subjects of National Importance, ibid.

Abstract of Public Acts passed from Jan. 26, to Oct. 27, 1786, 239

Prowne's Method to preserve Peach and Nectarine Trees, ibid.
Wright's Art of Conversing,

ibid.
Macbeth r'e-considered ; an Esay,

jbid.
Hancock's Astronomy of Comets,

ibid.

Bigland's Historical, Monumental, and Geological Collections re.

lative to the County of Gloucester,

240

Joannis Brunonis, M. D. Elementa Medicinæ,

241
Dr. Adams's Defence of the Constitutions of Government of Ame.
rica,

248

Whiteley's Essay on the Advantages of Revelation,

261

Evidence that the Relation of Josephus concerning Herod's having

new built the Temple at Jerusalem is false, &c.

263

The Asiatic Miscellany,

266

Sylva ; or, the Wood,

269

Pou Rou: or, an Enquiry into the Physiology and Pathology of

Parliaments,

272

The Maid of Orleans,

276

Des Carrieres' Essay on Pronouncing and Reading French, 279

Dr. Price's Sermons on the Christian Doctrine,

280

Holcroft's Seductivn, a Comedy,

Wollstonecraft's Thoughts on the Education of Daughters,

287

: Chemical Discoveries,

Continuation of the Dispute on the Composition of Water, 292

Extract of. a: Lester from M. Crell,

293

Tertia Differtatio Botanica de Ruilia, &c.

ibid.

Dr. Rees's Sermon on the Benefit of early Instruction in Religion, 298

Housman's Sermon on the Doctrines of the Gospel,

ibid.
Lottec.fo.the Rev. Mr. R. Housman,

ibid.

Charge and Sermon, &c. at the Ordination of Mr. Birley, 299

Wright's Sermon on the Union of Love to God and Love to Man, ib.

Dr. Paterson's Sermons,

300

A Discourse on Baptism,

301

Reader's Remarks on the three first Chapters of the Revelations, 302

Hawkins's Appeal to Scripture, &c.

ibid,

Ormerod's Remarks on Dr. Priestley's Disquisitions, &c. 303

Hampton's Answer to Dr. Priestley,

304

Bath’s Essay on the Medical Character,

Dr. Buchan's Caution concerning Cold Bathing,

ibid.

William of Normandy, an Historical Novel,

307

Child of Chance; or Adventures of Harry Hazard,

ibid.

The Minor; or History of George O'Nial, Esq.

ibid.

Louisa; or, the Cottage on the Moor,

308

History of Henrietta Mortimer,

ibid.

Reuben; or, the Suicide,

ibid.

History of Captain and Miss Rivers,

309

The Distressed Nabob,

ibid.

Cartwright's Platonic Marriage,

310

The Generous Attachment,

ibid.

Peter Pindar's Ode upon Ode,

ibid.

Congratulatory Epiltle to Peter Pindar, Esq.

311

General View of the Bill for preventing the illicit Exportation of

British Wool and Live Sheep,

ibid.

:

306

Pigott's New Information and Lights on the Late Treaty, 312

Alarming Progress of French Politics,

ibid.

Case of the Protestant Dissenters,

ibid.

Appeal to the Candor, &c. of those in Power,

314

Oblervations upon the Case of the Protestant Diflenters, ibid.

Substance of Mr. Beaufoy's Speech,

315

Bishop Sherlock's Arguments against a Repeal of the Corporation

and Test Acts,

316

Bishop Hoadly's Refutation of Bishop Sherlock's Arguments, 317

Riglie of Protestant Dissenters to a complete Toleration afferted, ibid.

Letter to the Deputies of the Protestant Disenting Congregations, ib.

Dr. Priestley's Letter to the Right Hon. William Pitt,

318

Berington's Address to the Protestant Dillenrers,

319

Philosophical Transactions, Vol. LXXVI. Part II..

321

Douglas's Nenia Britannica,

327

Berington's History of the Lives of Abeillard and Heloisa,

332

Sir John Hawkins's Life of Dr. Samuel Johnson,

339, 417

Tarleton's History of Campaigns in North America,

Hunt's Observations on the Circulation of the Blood,

352

Jabet's Sermons,

354

Polwhele's Transation of the Idyllia, &c. of Theocritus, &c.

355

Joseph; Translated from the French of M. Bitaub,

362

Landmann's Elements of Tactics,

Millar's Historical View of the English Government,

Effects of Electricity on Minerals, &c.

Powerful Effects of the Gastric juice as a Menstruum,

380

M. Chaptal's Observations on the Use of the Vesiculæ Seminales, 386

Dr. Walter's Annotationes Anatomicæ,

+382 :

Burns' Poems chiefly in the Scottish Dialect,

The Vision, a Poem, to the Memory of Jonas Hanvay, Esq. • 388

The Farrago, a Pick-penny,

ibid,

Harwood's Death of Dion, a Tragedy,

fbich

Exceffive Senfibility,

389

The Curse of Sentiment,

ibid,

Georgina ; or, Memoirs of the Belmour Family,

joid.'

Henrietta of Gerstenfield,

ibid.

The Sultan; or, a Peep into the Seraglio,

ibid.

Caroline; or, the Diversities of Fortune,

390

The Village of Martindale,

ibid.

Retaliation, a Novel,

ibid.

Orlando and Seraphina, a Turkish Tale,

Lumley-house, a Novel,

ibid.

Vanbrugh's Sermon at the Drum-head,

392

Thoughts on the Progress of Socinianism,

ibid.

Dr. Perkins's Essay for a Nosology and Comparative View of the

Cynanche, or Putrid Sore Throat,

393

Dr. Smyth's Account of the Effects of Swinging,

ibid.

Elay on the Virtues and Properties of the Ginseng Tea, 394

The Natural History of Birds,

395

The Theatre of Eucation. A New Translation,

ibid.

An Apology for Negro Slavery. Second Edition,

ibid.

Critical Review of the Works of Dr. Samuel Johnson,

ibid.

Belchier's Essays on various Subjects,

A Panegyrie on Great Britain. Second Edition,

ibid.

Anticipation of the Speeches intended to be spoken in the House of

Commons, on the Motion relative the Prince of Wales, 397

Kearsley's Tables of Trades. A new Edition,

ibid.
Some Hints towards a Revisal of the Penal Laws,

ibid.

Stone's Suggestions for rendering the Inclosure of Common Fields,

&c. a Source of Population and Riches,

398

Uther's Elements of Englith Grammar,

ibid.

Reformation, or, a Plan for abolithing Christianity,

ibid.

Dr. Trusler's Country Lawyer,

399

Trial at large, the King against Mr. Amery and Ms. Monk, ibid.

Amusements in High Life,

ibid.

Trial of the Hon. John Townshend,

ibid.

Clater's Every Man his own Farrier,

ibid.

Account of the Conduct of Mr. Levy,

ibid.

The Mystical Initiations; or Hymns of Orpheus,

401

Experiments and Observations on Light and Colours,

The History of Mexico,

Commentaries and Essays, No III, IV, and V,

424

The Tatler,

429

Bell's System of Surgery, vol. V.

435

Dr. Cooper's One great Argument for the Truth of Christianity, 437

Consolation to the Mourner, &c.

440

Strictures on Dr. Cooper's Two Discourses,

440, 442

Hewlett's Sermons,

443

The Ladies' Calling,

445

Brief Account of the Hospital of St. Elizabeth,

Fenn's Original Letters written during the Reign of Henry VI. Ed--

ward IV. and Richard III.

447

Observations on the Land-Revenue of the Crown,

454

Reflections on a late Resolution respecting the Peerage of Scotland,457

Account of a Map of France, descriptive of its Mountains, 460

A Scientific Map of the Franche-Compté and its Frontiers, 461

Prizer.p;opoled by the Imperial Academy at Petersburgh, 463

Distribution of former Prizes, and new ones proposed by the Royal

Society of Medicine at Paris,

464

Memoirs of the Royal Academy of Sciences of Stockholm,

465

Urrion of England and Ireland proved to be practicable, 469

Chuis of the Colonies, Second Edit.

ibid.

Cupsory Remarks on Dr. Priestley's Letter to the Chancellor of the
Exchequer,

ibid.

Martin's Marriage Law of Scotland, stated,

470

Speech of the French King to the Assembly of Notables, ibid.

The Final Farewell, a Poem,

ibid.

The Loufiad, Canto II.

472

Diamond cut Diamond, a Comedy,

473

The Midnight Hour; or, War of Wits. A Farce,

ibid.

Stuart's Distressed Baronet,

ibid.

Dr. Duncan's Medical Commentaries, Decad II. Vol. I. 474

Fontana's Treatise on Poisons,

ibid,

Thompson's Treatise on the Intermittens Febris,

475

Charge and Sermon at the Ordination of Mr. John Deacon, ibid.

Ramsay's Manual for African Slaves,

ibid.

Weddred's Thoughts on various Causes of Error,

ibid.

Peters's Sermon on the Death of Dr. Moffatt,

476

Sketch of a Tour through Swifferland,

ibid.

The Gentleman's Guide in his Tour through Italy,

477

'The Gentleman's Guide in his Tour through France,

Gray's Supplement to the Tour through Great Britain,

479

Blanchard's Complete Instructor of Short-Hand,

ibid.

Select Passages from various Authers,

ibid.

Mrs. Steele's Memoirs of Mrs. Baddeley,

ibid.

THE

CRITICAL REVIEW.

For JANUARY, 1787.

Tracts, Mathematical and Philofophical. By Charles Hutton,

LL. D. F.R. S. &c. and Profesor of Mathematics in the Royal Military Academy at Woolwich. 410. 145. in Boards. Robinsons.

T

THE volume now before us is of a miscellaneous nature,

being partly mathematical and partly philosophical. The mathematical parts consist of discoveries and improvements in algebra and infinite series, and in fpeculative geometry; and the philosophical part in experiments and differtations in artillery, relating to projectiles, gunpowder, the nature of guns, the refiftance of the air, the doctrine of forces and angular motion, &c. all treated with a degree of perspicuity and elegance which would seem to be the result of lohg and careful polishing, inftead of being executed on the spur of the occafion, as it appears was really the case.

Our author obferves, that the preference given of late, even among profesied philofophers, to studies of a less abtract kind, has too frequently diverted the pursuits of mathema ticians into paths less suited to their talents, from the desire of a vain and fleeting popularity, instead of the more laudable ambition of making real improvements in the sciences which they had profeffed to cultivate. The humble consciousness which the author has ever entertained of his own abilities, has, he hopes, preserved him from this common and pernicious vanity. However-solicitous to extend and diversify his own acquirements, he can only hope to add, and that a little, to the public stock of knowlege, in those parts of science to which his early habits, and subsequent occupations, have led him peculiarly to consecrate his studies,' And again, • The very honourable distinction paid to the author by the Royal Society, for his former experiments in gunnery, as well as their general indulgence to his attempts in other mathematical fubjects, would perhaps have given an obvious destination to these papers, had he not thought their publication in a colVol. LXIII. Jan. 1787.

B

lective

lective form better adapted, from the connection of their sufru jedt, to extend their utility.'--A sentiment which, if real, muit appear uncommonly modest to those who are aware of the unphilosophical disturbances which lately agitated that body. But, whatever may be the motives which produced this volume in its present form, it is our duty only to give an account of the Tracts according to their merit.

The firt is intitled "A Differtation on the Nature and Value of Infinite Series. This Tract, it appears, is delivered as preparatory to those that follow in this volume, and that are promised in future volumes of the work; and enumerates the different acceptations annexed to the terms sum or value, &c. of an infinite series, and the controversies that have taken place concerning them, among the mathematicians of the last and present age. And here our author, to avoid such discordant opinions and sentiments, has adopted the new term radix, intead of the sum or value of a series, as more general and unexceptionable, applying to all series, under the very natural idea of its being the finite expression from whence the series might properly arise by evolution, and which, therefore, may be substituted as an equivalent instead of it, in any mathematical operation.

The second Tract is 'A New Method for the Valuation of Numeral Infinite Series, whose Terms are alternately plus and minus.' This is one of those happy discoveries which, from their obviousness and fimplicity, both charm and surprise us, and make us wonder they had not been discovered before. The generality of this method is such, that it is equal applicable to all feries of alternate figns, whether they be converging or diverging, or what the author calls neutral, leaving all the terms equal. In case and simplicity, it far excels any other ; as it confifts only in collecting the successive sums of a few of the initial terms of the series, and then taking continual sets of arithmetical means between those fuccellive fums, by which the radix or value is presently and accurately found, when it is rational, or else a very quick approximation to it in all other cases. The truth of this method is demonstrated, independently of any other, from the nature of the series itself, and a general expression for the value is given in all cases; from which also the famous differential series is here deduced, and thereby shewn to be of the same degree of convergency with it. One excellence of this method is, that the flower a given series converges or diverges, the sooner and easier is its fum found; and by it the value is instantly found in all cases of neutral series. This method is illustrated by an application to a variety of series, the last of which is a very difficult

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