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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,
Rope's End for Hempen Monopolists,
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,
Macbeth r'e-considered ; an Esay,
Hancock's Astronomy of Comets,
Bigland's Historical, Monumental, and Geological Collections re.
lative to the County of Gloucester,
Joannis Brunonis, M. D. Elementa Medicinæ,
Dr. Adams's Defence of the Constitutions of Government of Ame.
Whiteley's Essay on the Advantages of Revelation,
Evidence that the Relation of Josephus concerning Herod's having
new built the Temple at Jerusalem is false, &c.
The Asiatic Miscellany,
Sylva ; or, the Wood,
Pou Rou: or, an Enquiry into the Physiology and Pathology of
The Maid of Orleans,
Des Carrieres' Essay on Pronouncing and Reading French, 279
Dr. Price's Sermons on the Christian Doctrine,
Holcroft's Seductivn, a Comedy,
Wollstonecraft's Thoughts on the Education of Daughters,
: Chemical Discoveries,
Continuation of the Dispute on the Composition of Water, 292
Extract of. a: Lester from M. Crell,
Tertia Differtatio Botanica de Ruilia, &c.
Dr. Rees's Sermon on the Benefit of early Instruction in Religion, 298
Housman's Sermon on the Doctrines of the Gospel,
Lottec.fo.the Rev. Mr. R. Housman,
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,
A Discourse on Baptism,
Reader's Remarks on the three first Chapters of the Revelations, 302
Hawkins's Appeal to Scripture, &c.
Ormerod's Remarks on Dr. Priestley's Disquisitions, &c. 303
Hampton's Answer to Dr. Priestley,
Bath’s Essay on the Medical Character,
Dr. Buchan's Caution concerning Cold Bathing,
William of Normandy, an Historical Novel,
Child of Chance; or Adventures of Harry Hazard,
The Minor; or History of George O'Nial, Esq.
Louisa; or, the Cottage on the Moor,
History of Henrietta Mortimer,
Reuben; or, the Suicide,
History of Captain and Miss Rivers,
The Distressed Nabob,
Cartwright's Platonic Marriage,
The Generous Attachment,
Peter Pindar's Ode upon Ode,
Congratulatory Epiltle to Peter Pindar, Esq.
General View of the Bill for preventing the illicit Exportation of
British Wool and Live Sheep,
Pigott's New Information and Lights on the Late Treaty, 312
Alarming Progress of French Politics,
Case of the Protestant Dissenters,
Appeal to the Candor, &c. of those in Power,
Oblervations upon the Case of the Protestant Diflenters, ibid.
Substance of Mr. Beaufoy's Speech,
Bishop Sherlock's Arguments against a Repeal of the Corporation
and Test Acts,
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,
Berington's Address to the Protestant Dillenrers,
Philosophical Transactions, Vol. LXXVI. Part II..
Douglas's Nenia Britannica,
Berington's History of the Lives of Abeillard and Heloisa,
Sir John Hawkins's Life of Dr. Samuel Johnson,
Tarleton's History of Campaigns in North America,
Hunt's Observations on the Circulation of the Blood,
Polwhele's Transation of the Idyllia, &c. of Theocritus, &c.
Joseph; Translated from the French of M. Bitaub,
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,
M. Chaptal's Observations on the Use of the Vesiculæ Seminales, 386
Dr. Walter's Annotationes Anatomicæ,
Burns' Poems chiefly in the Scottish Dialect,
The Vision, a Poem, to the Memory of Jonas Hanvay, Esq. • 388
The Farrago, a Pick-penny,
Harwood's Death of Dion, a Tragedy,
The Curse of Sentiment,
Georgina ; or, Memoirs of the Belmour Family,
Henrietta of Gerstenfield,
The Sultan; or, a Peep into the Seraglio,
Caroline; or, the Diversities of Fortune,
The Village of Martindale,
Retaliation, a Novel,
Orlando and Seraphina, a Turkish Tale,
Lumley-house, a Novel,
Vanbrugh's Sermon at the Drum-head,
Thoughts on the Progress of Socinianism,
Dr. Perkins's Essay for a Nosology and Comparative View of the
Cynanche, or Putrid Sore Throat,
Dr. Smyth's Account of the Effects of Swinging,
Elay on the Virtues and Properties of the Ginseng Tea, 394
The Natural History of Birds,
The Theatre of Eucation. A New Translation,
An Apology for Negro Slavery. Second Edition,
Critical Review of the Works of Dr. Samuel Johnson,
Belchier's Essays on various Subjects,
A Panegyrie on Great Britain. Second Edition,
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,
Some Hints towards a Revisal of the Penal Laws,
Stone's Suggestions for rendering the Inclosure of Common Fields,
&c. a Source of Population and Riches,
Uther's Elements of Englith Grammar,
Reformation, or, a Plan for abolithing Christianity,
Dr. Trusler's Country Lawyer,
Trial at large, the King against Mr. Amery and Ms. Monk, ibid.
Amusements in High Life,
Trial of the Hon. John Townshend,
Clater's Every Man his own Farrier,
Account of the Conduct of Mr. Levy,
The Mystical Initiations; or Hymns of Orpheus,
Experiments and Observations on Light and Colours,
The History of Mexico,
Commentaries and Essays, No III, IV, and V,
Bell's System of Surgery, vol. V.
Dr. Cooper's One great Argument for the Truth of Christianity, 437
Consolation to the Mourner, &c.
Strictures on Dr. Cooper's Two Discourses,
The Ladies' Calling,
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.
Observations on the Land-Revenue of the Crown,
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,
Memoirs of the Royal Academy of Sciences of Stockholm,
Urrion of England and Ireland proved to be practicable, 469
Chuis of the Colonies, Second Edit.
Cupsory Remarks on Dr. Priestley's Letter to the Chancellor of the
Martin's Marriage Law of Scotland, stated,
Speech of the French King to the Assembly of Notables, ibid.
The Final Farewell, a Poem,
The Loufiad, Canto II.
Diamond cut Diamond, a Comedy,
The Midnight Hour; or, War of Wits. A Farce,
Stuart's Distressed Baronet,
Dr. Duncan's Medical Commentaries, Decad II. Vol. I. 474
Fontana's Treatise on Poisons,
Thompson's Treatise on the Intermittens Febris,
Charge and Sermon at the Ordination of Mr. John Deacon, ibid.
Ramsay's Manual for African Slaves,
Weddred's Thoughts on various Causes of Error,
Peters's Sermon on the Death of Dr. Moffatt,
Sketch of a Tour through Swifferland,
The Gentleman's Guide in his Tour through Italy,
'The Gentleman's Guide in his Tour through France,
Gray's Supplement to the Tour through Great Britain,
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.
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.
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