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jects affords. Dr. Waring's labours in analytics are well known;
of these a Paper * appeared, in the Transactions of 1784, on the
Summation of Series, in which is given a method of finding the
fum of a series whole general term (P = 2, a fraction reduced
to its lowest terms) is a determinate algebraical function of the
quantity (Z), the distance from the first term of the series. The
Doctor's pretent performance is of a fimilar kind with the for-
mer, and Thews how the methods there exhibited may be applied
or extended to several cases not enumerated before.

In the second part of this paper Dr. Waring considers the
several methods for approximating the value of quantities, whose
exact value could not be obtained by any other means. The
reader will here meet with many useful methods of resolving
equations of higher exponents, together with observations on the
writings of former analysts., Much has been advanced on this
subject; the present labours of Dr. Waring are rather illustra-
tions of the algebraical inquiries of preceding authors, than any
new improvements of the art,

The third part contains some observations in order to deter.

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mine the cases in which the series for finding the fluent of axi,

or the area of a curve whole ordinate is a x" and abscissa x,
converges or diverges; this is a useful inquiry, because the series
is of no use if it diverges, and of very little except the convergency
is quick. We cannot lay the particulars of this long Paper be-
fore our Readers : the above account will inform them what it
chiefly concerns, and what parts of the extenfive subjects of in-
finites the Doctor has here elucidated.
Art. 9. Observations and Remarks on these Stars which the Astro-

nomers of the last Century suspected to be changeable. By Ed-
ward Pigott, Esq.

lo this Paper Mr. Pigott has given a catalogue of such fixed
ftars as have been observed to be variable in size and lustre, and
also such as are suspected, from the accounts of former astrono-
mers, to be so. The catalogue contains 50 fixed stars, with their
right ascension and declination reduced to the beginning of the
year 1786. Mr. Pigott then enumerates the particular observa-
tions on each of these stars, and the reasons why he supposes
Some of them variable, although their changes have not yet been
ascertained.

· The establishing of facts is the first step toward the advance.
ment of science ; and though these discoveries do not seem to be
of any real use at present, yet they may, at some future period,
throw fresh light on astronomy. The causes of the appearances

* For an account of which, see Rev. vol. Ixxiii. p. 197.

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are undoubtedly a just object of inquiry; what has been conjectured concerning them wants as yet much confirmation.

(The Philosophical and Chemical Papers in this part *, as

soon as possible.)
* N. B. The ad Part of vol. Ixxvi. is just published.

2-m Art. VI. Chemical Elays. By R. Watson, D.D. F. R. S. and

Regius Professor of Divinity in the University of Cambridge.
Vol. IV.

45. sewed. Cadell, &c. 1786.
E are sorry to find that this is the last chemical perform-

ance we have to expect from the right reverend author. Though convinced, by the uncommon sale of the former voJumes, that they met with general approbation, and that they have contributed greatly to the promotion of chemical knowledge, he now resigns, for ever, these pleasing and useful purfuits ; but not without fingular reluctance, and doing violence to his own feelings. "Above two thousand copies' (he says) of the former volumes of my Chemical Eliays have been fold in less than five years. I mention not this circumstance out of vanity, or as if I thought it contained any proof of their merit; but I produce it as a solid proof of the difpofition of the Public to become acquainted with chemical subjects when they are treated in a popular way. This disposition has been long prevalent in foreign countries; it seems to be gaining ground in our own; and if I have endeavoured to contribute a little towards its establishment amongst us, I hope the utility of the defign will plead my excuse with those, who, in the severity of their judgments, may think that I have contributed more than, from the nature of my profession and fituation, I ought to have done.

" When I was elected Professor of Divinity in 1771, I determined to abandon for ever the study of chemistry; and I did abandon it for several years : but the-veteris veftigia fiamnestill continued to delight me, and at length seduced me from my purpose. When I was made a Bishop, in 1782, I again determined to quit my favourite pursuit; the volume which I now offer to the Public is a sad proof of the imbecility of my resolution. I have on this day, however, offered a sacrifice to other people's notions, I confels, rather than to my own opinion of episcopal decorum-I have destroyed all my chemical manuscripts. -A prospect of returning health might have persuaded me to pursue this delightful science; but I have now certainly done with it for ever; at least I have taken the most effectual step I could to wean myself from an attachment to it, for with the holy zeal of the idolaters of old, who had been addicted to curious arts, - I have burned my books!'

The

The remainder of the Preface, about 15 pages, is employed in recommending an institution at our universities, for instructing young men of rank and fortune in the elements of agriculture ; in the principles of commerce; and in the knowledge of our manufactures. This kind of study, the Author observes, would agreeably solicit, and might probably secure, the attention of that part of our youth, which, in being exempted from the discipline of scholaltic exercises, has abundant leisure for other pursuits; which, in being born to opulence, is unhappily deprived of one of the strongelt incentives to intellectual exertion,-narrowness of fortune : it would prepare them for becoming intelligent legislators of their country; and it would inipire them with such a taste for husbandry, as might constitute the chief felicity of their future lives.

His notion of national strength, security, and happiness, tends not so much to the extending of our commerce, or increasing the number of our manufacturers, as to the multiplication of an hardy, and, comparatively speaking, innocent race of peasants, by making corn to grow on millions of acres of land where none bas grown before. Let us but once have as many Britons in the kingdom, as the well-cultivated lands of Great Britain are able to support (at least twice the present number), and we shall have little to regret in the loss of America; nothing to apprehend from the partitioning policy of all the continental despots in Europe.- In thus fixing the bafis of our strength on the improved cultivation of our lands, he does not mean to exclude manufaclures, but on the contrary, considers agriculture and manu. factures as mutually subservient to each other. With regard to commerce, he thinks the present state of the finance of this king, dom requires it to be cheriched with fingular indulgence; and that we fall not sufficiently avail ourselves of the inestimable advantages of our insular situation, if we do not consider our glory and our safety as closely connected with the number of our feamen, which will ever be in proportion to the extent of our foreign and domestic commerce. Perhaps the advantages of commerce, and of manufactures as its basis, are here estimated below their real value to the national strength and importance; nevertheless, the observations respecting the education of young men of fortune are certainly just, and deserve the most serious attention.

The essays which compose this volume are written on the same plan as those of the three preceding; not with a view to enrich science with any considerable new discoveries, but to promote a general taste for these useful ftudies, and to engage the attention of those who are but little acquainted with chemical subjects, by describing, in a clear and pleasing manner, the succelsive discoveries made in some of the principal branches of chernical knowledge, and the consequent improvements in the arts depending on them. The subjects are, Rev. Jan, 1787.

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Essay I. Lapis calaminaris, blende, zinc, brass; containing the natural history of the iwo first-mentioned substances, the history of the discovery of their being ores of zinc, the methods of extracting zinc from them, the preparation of them for the brassmaker, the manufacture and commerce of brass, &c.

JI. On Orichalcum ; an enquiry into the orichalcum of the ancients; from which it appears, that the art of making brass was known to the Romans, but was derived to them from some other country; that brass was made, in the most remote ages, in India and other parts of Asia, of copper and calamine, as at present; and that in the early ages, when iron was little known, it was valued higher than gold *

III. Of gun metal, ftatuary-metal, bell-metal, pot-metal, and Speculum-metal. The compaclness of a mixture of copper and tin, which adapts it for making speculums, is attributed, with great probability, to the thinness of its fulion. 'I have observed' (fays the Author) at Sheffield, that the same weight of melted Ilcel will fill the fame mould to a greater or less height, accord. ing to the degree of fusion the steel has been in; if it has been in

a Itrong heat and thin fusion, the bar of cast steel will be an inch in thirty-fix thorter than when the fusion has been less perfect. On breaking one of the bars made from steel in an imperfect fufión, its inside was full of blebs; a shorter bar of the same weight and diameter, which had been in a thin fufion, was of a cloler texiure,'

IV. Of tinning copper, tin, pewter.
V. Of tinning iron. Plating and gilding copper.

VI. Of gilding in or moulu. Of the use of quicksilver in extracting gold and filver from earths. Boerhaave's experiments on quicklilver. Silvering looking-glasses; and of the time when that art was discovered. Though this art is commonly suppored to be of modern discovery, we here find it to have been known, probably in the first century, and with certainty in the fecond. A paslage in Pliny gives good ground to believe that it had been discovered before his time, by the Sidonians.

VII. Of the transmutability of water into earth. The facts and arguments on both sides are stated, but the point is left undetermined.

· VIIH. Of Westmoreland flate, and some other forts of ftones. From a particular examination of the gravities of different forts of the flate, and a comparison with lead and copper as used for covering buildings, it is concluded that 42 square yards will be covered by 4 hundred weight of copper, 26 of fine flate, 27 of lead, 36 of coarser Aate, and 54 of tile. By Atrong fire, the flate was reduced into a black celular glass, so hard as to frike

* This Essay is similar to that in the Manchefter Transactions; see our Rev. for Oct. lait, p. 252.

fire with steel. Very good glass, the Author observes, might probably be made from the date alone, for the cellular texture would disappear by continuance of fire; but certainly it might be made from the late mixed with fern alhes, or with kelp alhes, or with other substances containing fixed alcali.' We hope, with the Bishop, that this hint will not be given in vain; and we beg leave to hint also, that if the certainty of vitrification with alcalies has been only inferred from the known effect of those salts upon some other earthy bodies, such conclufion cannot be depended on. There are earthy compounds, fusible by themselves, which refuse to unite with alcalies: we have mixed vitrescible Itone with glass itself, and found the vitrification impeded, and the alcali of the glass (pued out. Whether the Weftmoreland Nate is, or is not, of this nature, can be ascertained only by trial; but, in either case, we persuade ourselves that the candid Author will be rather pleased, than offended, with our remark.

To this volume is added a very useful appendage, - a general Index to all the four.

Chire Art. VII. A System of Surgery. By Benjamin Bell, Member of

the Royal College of Surgeons, one of the Surgeons to the Royal Infirmary, and Fellow of the Royal Society of Edinburgh. Vols. III. and IV. 8vo. 125. Boards. Illustrated with Copper. plates. Elliot, Edinburgh ; Robinsons, London. 1786. " HE continuation of this useful work, fully supports and

confirms the reputation Mr. Bell had acquired by the two preceding volumes.

The third volume contains, in the former part of it, the theory and practice in affections of the brain from external violence. The very intricate nature of these disorders has excited the attention of practitioners from the time of Hippocrates downward; but although some material improvements have been introduced into this branch of practice, by the industry and observations modern Surgeons, yet whoever is accustomed to the treatment of these complaints, muft allow that our knowledge of them is Hill very deficient. Our Author, sensible of the great difficul. ties of attaining a certain knowledge concerning the nature and treatment of them, points out the means best calculated to extricate this part of practice from such uncertainty; but before he proceeds to do so, he gives a concise anatomical description of those parts which are more apt to suffer from injuries done to the head.

Mr. Bell considers all the symptoms of diseases of the brain from external violence, to originate from one of these three cirCumstances, from compreffion of the brain, from commotion or concuffion, or from inflammation.' Of these he creats in D 2

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