other time, Sir Ifaac Newton and M. Leibnitz, both claimed the invention to give his readers a juft view of this noble dif pute, and the pretenfions of each party, the Editor lays before them the origin of the discovery, marks where each claim commenced, and how it was fupported, and concludes, after examining a number of witneffes, and reviewing the controversy among the mathematicians of that time, that Sir Ifaac Newton was the first inventor.' Dr. Rees then proceeds to explain the doctrine, and exemplify the theory by a number of practical applications of it to many ufeful problems, in a concife and (as is ufual with him) perfpicuous manner. In examining thefe, we find a typographical error in one of them, which we think it our duty to mention. The Editor makes the fluxion of b x2 · + ca x2 + e a2 • √x2+ a2 to be 3 b x3 +2 a c x2 + e a2x+ 2 √ x2 + a2 2 ba2x + ca3x.x, which fhould be 36x3+2 acx2 + ea2x √x2 + a2 +2ba2+ca3. x. The doctrine of Fluxions leads us to the confideration of infinity. Infinite in mathematics, fays the Editor, is applied to quantities which are either greater or smaller than any affignable ones.' Metaphyficians have cavilled at this definition, and at the whole doctrine of infinites; but Dr. Rees judiciously confutes their arguments, and fhews the truth of the reasonings uled by mathematicians, in this abftrufe fubject. Although the objects of infinity are in themfelves beyond our comprehenfion, yet we cannot refift the force of demonstration concerning their powers, effects, and other properties, which, under certain conditions, may be truly explained. With respect to infinite feries, we think the Editor rather too fhort; he has greatly increased the article which appeared in the former editions; yet much remains to be added. The variety, indeed, of infinite feries, is fo great, that no bounds can be fet to it; and the work might have been filled with more matter on this fubject, than would have been confiftent with the original plan, or any way ufeful to the generality of readers. The fummation of feries makes a confiderable part of the employment of our modern mathematicians, and it is with pleafure that we perufe their works, as they abound with feveral admirable contrivances for the fums of feries, as well thofe that are infinite, as thofe whole number of terms is finite. Though De Moivre, and others, of whofe labours Dr. Rees has very properly availed himfelf, are authors of great merit, and acknowledged abilities, yet Dr. Waring's meditations would have afforded the Editor much affiftance: but thefe are matters rather of curiofity than ufe. We would not however have it understood, that we condemn or flight what at prefent seem to be matters of curiofity only; fince at fome future period, perhaps, these curious inveftigations may be of material fervice. In aftronomy, thofe improvements which chiefly depend on the perfection of inftruments, afford the Editor ample matter for increafing the Cyclopædia. The divifion of quadrants and the conftruction of telescopes have, within these few years, been brought to a confiderable degree of perfection. The hiftory of the telescope is in this edition much enlarged, where Dr. Rees with great feeming probability makes it appear, that Roger Bacon, who died in 1294, was perfectly acquainted with the methods of combining optical glaffes, fo as to form an inftrument fimilar to our telescopes, though he perhaps never made use of it for aftronomical purposes. Having finished the hiftory of this inftrument, from which the reader will receive much information as well as amusement, the Editor defcribes the various conftructions of telescopes from the time of Galileo, and gives a particular account of the method of grinding lenfes and fpecula for them. The great improvement in refracting telescopes by Mr. Dollond is particularly attended to, and a minute description is given of every contrivance that has been used for overcoming the errors produced by the aberration of the rays. Dr. Rees has not neglected to mention the confiderable and truly aftonishing perfection to which Mr. Herfchel has brought reЯecting telescopes; and the many difcoveries he has, by their means, been able to make in the heavens. In order to find the parallax of the fixed ftars, various methods have been proposed: thefe are particularly defcribed, and the errors to which they are liable are clearly pointed out. In this part of the work the learned aftronomer will receive much fatisfaction, and meet with many original and judicious remarks. Confiderable articles appear under the names of each conftellation, as Taurus, Bootes, Aries, &c. in which are inferted the longitudes, latitudes, names, &c. of the several stars that compofe each, as fixed by Mr. Flamftead, in his Britannic Catalogue. The longitudes of the fixed ftars varying annually 50 feconds, render these tables unfit for ufe at this day without a correction to adapt them to the present time: the Editor has not mentioned this circumftance, nor informed us to what year Mr. Flamftead has fixed his longitudes. By comparing them with fome catalogues lately published, the neceflary correction, to be added to each longitude in order to reduce it to the true longitude for the beginning of the year 1786, is one degree 20 minutes 15 feconds: but Mr. Flamftead's longitudes, though fixed with great attention and care, are not fo much to be depended on as thofe fettled in later years, fince the inftruments he ufed in making making his obfervations were much inferior to thofe in common ufe at prefent. In order, however, to compenfate for this inaccuracy, the Editor has given a catalogue of 307 of the most remarkable fixed ftars, with their magnitudes, right afcenfions, declinations, and annual variations, rectified for the beginning of the year 1750. Moft of them are taken from M. de la Caille's Ephemeris; and the reft according to the lateft obfervations made at Greenwich. The right afcenfions are fet down in degrees to tenths of feconds, and alfo in time to feconds;-the declinations to tenths of feconds alfo,-and the annual variations in both to feconds and hundredths of feconds of a degree. We have examined this valuable catalogue with attention, and have not discovered any errors in it; on which account we venture to recommend it. Thefe tables of the longitudes and latitudes, and of right afcenfion and declination of the fixed ftars, are of great confequence: they are uleiul, among other things, for the more eafily calculating the distance of the moon from any far, the observing which diftance is the prefent method of finding the longitude at fea. This method of determining the longitude by the obferved diftance of the moon from fome far was first recommended in the year 1514, but, for want of proper tables and accurate infruments, it was never put in practice till within thefe laft 30 years. The hiftory of this method we gave at large in our 48th volume: it has however been greatly improved fince that time, and is now brought to fo great a degree of perfection that the longitude may be determined with tolerable exactnefs, by a calculation that will not take up more than half an hour. The different methods of determining the longitude at fea are each of them recited by the Editor, and the advantages and difadvantages of each are clearly ftated. Time-keepers (an appellation now become fashionable among artifts, to diftinguith fuch watches as are made with extraordinary care and accuracy, for nautical or aftronomical obfervations) are undoubtedly better adapted to determine the longitude, than any other method that has yet been propofed, becaufe there would be no occafion for fuch extenfive tables, or calculations, as are neceffary in the other methods. We have in England ingenious artifts, who have already confructed watches, that the greatest daily difference of their rates of going amount only to 4 feconds of time, and we doubt not that they may be brought to a greater accuracy. Our Editor has not paffed over the improvements that navigation has received from the more accurately conftructing of quadrants; the divifion of which, and indeed of all aftronomi See our account of the going of Arnold's watch, Review, vol. LXIII. cal cal inftruments, Ramfden executes with a degree of accuracy that almoft exceeds belief. While these mechanical improvements are making, mathematicians have not been wanting to conftruct tables for rendering the neceffary calculations eafier, fhorter, or more to be depended on. Accurate logarithms, and trigonometrical canons have engaged the attention of fome of our most able philofophers; they have reviféd the old, and are daily publishing new ones, on a more extensive scale: all which tends in a great measure to bring the practical part of navigation to its utmoft perfection. [To be concluded in our next. ] R-m. ART. II. Dr. REID'S Eays on the Intellectual Powers of Man, concluded. See Review for last Month. HE account which we have given of the fecond effay in this valuable work, has been extended to fo confiderable a length, that we are under a neceffity of being more concise in mentioning those which remain. We fhall therefore fatisfy ourfelves with giving a general view of their contents, and extracting a few paffages from them. The third Effay is on Memory, and is divided into feven chapters. In the first of them, the Author lays down certain principles with regard to this faculty, which are obvious and certain. In the fecond, he fhews that it is an original faculty, bestowed on us by the Author of our being, of which we can give no account, but that we are so made as to poffefs it. In the third, he treats of duration, with a view to prove that our notion of it, as well as our belief of it, is got by the faculty of memory. In the fourth, he confiders identity, or continued exiftence. He fhews, that the evidence which we have of our own identity is grounded on memory, and gives undoubted certainty. The evidence we have of the identity of other perfons, or of objects of fenfe, is grounded on fimilarity, and on other circumftances, which in many cases are not so decifive as to leave no room for doubt. This account of our notions of duration and identity is very different from that which is given by Mr. Locke: and the origin which it affigns to them is inconfiftent with the doctrine of that great philofopher, which has been very generally embraced fince his time, that all our ideas are derived from fenfation and reflection. To obviate any prejudice that may arife from controverting a received opinion, Dr. Reid proceeds, in the fifth chapter, to examine Mr. Locke's account of the origin of our ideas, and particularly of the idea of duration and fhews that all our ideas are not reducible to fenfation and reflection, and that the notion we have of duration is not obtained, as Mr. Locke thought it was, from reflection upon the fucceffion of ideas in our own minds. In the fixth chapter, he examines Mr. Locke's account of perfonal identity, which has also been very fuccessfully attacked by the great Dr. Butler, to wit, that it confifts in confcioufnels. In the laft chapter of this Effay he confiders the theories that have been adopted by philofophers, both ancient and modern, with refpect to memory, and states various infuperable objections to all of them. The fourth Effay has for its title, 'Of Conception.' It conifts of four chapters. The firft of thefe treats, in general, of conception; or, as it is called by logicians, fimple apprehenfion; or, as it has often been expreffed fince the days of Mr. Locke, the having an idea of a thing. This operation of the underftanding is fimple, and, like other operations of the fame nature, cannot be defined. The Doctor therefore, without attempting any definition of it, only endeavours to explain fome of its properties. In the second chapter, he examines fome theories concerning conception, founded on the fuppofition that certain images of thofe things which we conceive exift in the mind, or in the brain, and are the immediate objects of the mind's attention; and fhews that they are grounded only on a diftant ana- * logy, and the figurative use of language. In the third chapter, he points out fome common mistakes relative to this subject; and has corrected fome errors, which have received the fanction of refpectable authority. The obfervations here made, not only mark the penetration of the Author, but alfo fhew what caution is requifite in adopting opinions on abstract subjects, even when they are fupported by men of the greateft literary eminence. But juftice could not be done to them, without transcribing the whole chapter. In the last chapter, the Author treats of the train of thought in the mind, in which not only the imagination, but various other mental powers are concerned, and points out certain laws according to which it is conducted. The importance of the subject confidered in this chapter is admirably stated by the Author, at the conclufion of it. I believe it will be allowed by every man, that our happiness or mifery in life, that our improvement in any art or science which we profefs, and that our improvement in real virtue and goodness, depend in a very great degree on the train of thinking that occupies the mind, both in our vacant and in our more ferious hours. As far, therefore, as the direction of our thoughts is in our power (and that it is fo in a great measure, cannot be doubted), it is of the last importance to give them that direction which is most fubfervient to those valuable purposes. What employment can be have worthy of a man, whofe imagination is occupied only about things low and bafe, and grovels in a narrow field of mean, unanimating, and uninteresting objects, infenfible to those finer and more delicate fentiments, and blind to thofe |