I rofe and gave him entrance, mov'd

To pity by his pray'r

Warm'd his cold hands in mine, and fqueez'd

The dew-drops from his hair.'

The fimilarity in this, and in a few other paffages referred to by the tranflator, is not, in our opinion, fo ftrongly characte riftic as he imagines. If love be perfonified (and Anacreon was not indebted for this idea to Solomon), it might be represented as wet and cold and wandering, by a natural train of metaphor, without having recourfe, either for the original thought, or the embellishment and improvement of it, to any poets out of Anacreon's own country.

ART. V. PHILOSOPHICAL TRANSACTIONS of the Royal Society of London. Vol. LXXVI. for the Year 1786. 4to. Part I. 7s. 6d. Davis.

MATHEMATICAL PAPERS. Art. 1. Obfervations on the Graduation of Aftronomical Inftruments; with an Explanation of the Method invented by the late Mr. Henry Hindly of York, Clockmaker, to divide Circles into any given Number of Parts. By John Smeaton, F. R. S.

TH

HE accuracy of quadrants, and other aftronomical inftruments, is a matter of the utmost confequence to the practical aftronomer and navigator. When aftronomy was revived in Europe, the neceffity of having inftruments properly adapted for the obfervations that were requifite for determining the relative fituations, &c. of the heavenly bodies, obliged aftronomers to become inftrument-makers, in order to furnish themselves with a neceflary apparatus: thus we find Tycho Brahe, and others, in his time, applying themselves to the conftruction of quadrants, theodolites, &c. In later times, when navigation became more extenfive, the demand for inftruments was increafed; and fince their perfection depends chiefly on the accuracy with which they are graduated, ingenious artifts were encouraged both to contrive and execute inftruments of feveral kinds. It was long, however, before the divifion of circles, or quadrants, was brought to the perfection required. In the paper before us, Mr. Smeaton gives a fhort account of the labours of our most able artists, in improving these instruments, and then defcribes a method of dividing a circle into a given number of parts (se should have faid equal parts), which in his opinion is more accurate than any thing that has hitherto been propofed.

The method is, to drill a number of equidiftant holes in a long brafs bar; the bar is then to be bent into the form of a hoop, and fitted, tight, on a cylindrical block of wood ready turned to receive it, by means of which a circle is formed, whofe periphery is divided into a certain number of equal parts. From

this original circle the divifions are to be transferred to the plate of a dividing engine. The directions for all thefe operations are minute and plain, and Mr. Smeaton's ftyle, abounding with the proper technical terms, feems admirably adapted to the capacity of the working mechanic, for whom, differtations of this kind are chiefly intended.

As to the practicability of the plan, we, who are not workmen, can fay little about it: the idea is certainly an ingenious one, but we doubt the poffibility of executing it without error.

We cannot conclude, without obferving, that in quadrants, and other inftruments for meafuring angles without telescopes, there is no occafion for carrying the divifions farther than

a minute, for an angle lefs than 27 feconds is evanefcent to the naked eye*. Whence Mr. Smeaton's quadrant, divided in the manner he defcribes, fo as to read off an observation to 2 feconds, must be furnished with a telescope that magnifies a line at least 14 times, or a fuperfice 230 times.

Art. 2. A Series of Obfervations on, and a Discovery of the Period of the Variation of the Light of the Star marked & by Bayer, near the Head of Cepheus. In a Letter from John Goodricke, Efq. From thefe obfervations Mr. Goodricke has determined that this ftar has a periodical variation in its brightnefs of 5 days 8 hours 37 minutes, during which time it undergoes the following changes.

ift, It is at its greatest brightnefs about 1 day and 13 hours. 2d, Its diminution is performed in about 1 day and 18 hours. 3d, It is at its greatest obscuration about 1 day and 12 hours. 4th, It increafes about 15 hours.

In its greatest brightnefs it appears to be between the 38 and 4th magnitude, and in its leaft near the fifth.

To this Paper Mr. Goodricke has added a number of observations made on the fame ftar, by Mr. E. Pigott, from Oct. 25th, 1784, to May 23d, 1785, which confirm the period determined by our Author from the obfervations he made from Oct. 19, 1784, to June 26, 1785.

Art. 4. On Infinite Series. By Edward Waring, M. D. F. R. S. Lucalian Profeffor of Mathematics at Cambridge.

The great use of infinite feries in calculating logarithms, areas of curves, tangents, &c. &c. is a fufficient inducement to engage the attention of the mathematician, independent of the pleasure and fatisfaction which the contemplation of these abftrufe fub

*From this we must except luminous bodies, which are visible to the naked eye, though less than the fubtenfe of the angle here mentioned. Yet the diftances between luminous bodies is not visible when that distance fubtends a small angle, witnefs Dr. Herfchel's obfervations on double ftars, &c. the angular diftance between which appeared greater, and was measured by a greater quantity of a circle, in proportion as his magnifying power was increafed. 8

jects

jects affords. Dr. Waring's labours in analytics are well known; of these a Paper* appeared, in the Tranfactions of 1784, on the Summation of Series, in which is given a method of finding the fum of a feries whofe general term (P2, a fraction reduced to its lowest terms) is a determinate algebraical function of the quantity (Z), the distance from the first term of the feries. The Doctor's prefent performance is of a fimilar kind with the former, and fhews how the methods there exhibited may be applied or extended to feveral cafes not enumerated before.

In the fecond part of this Paper Dr. Waring confiders the feveral methods for approximating the value of quantities, whofe exact value could not be obtained by any other means. The reader will here meet with many ufeful methods of refolving equations of higher exponents, together with obfervations on the writings of former analyfts. Much has been advanced on this fubje&; the prefent labours of Dr. Waring are rather illuftrations of the algebraical inquiries of preceding authors, than any new improvements of the art.

The third part contains fome obfervations in order to deter

mine the cafes in which the feries for finding the fluent of axx,

or the area of a curve whofe ordinate is ax" and abfciffa x, converges or diverges; this is a ufeful inquiry, because the feries 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 before our Readers: the above account will inform them what it chiefly concerns, and what parts of the extenfive fubjects of infinites the Doctor has here elucidated.

Art. 9. Obfervations and Remarks on thofe Stars which the Aftronomers of the last Century fufpected to be changeable. By Edward Pigott, Eiq.

In this Paper Mr. Pigott has given a catalogue of fuch fixed ftars as have been obferved to be variable in fize and luftre, and alfo fuch as are fufpe&ed, from the accounts of former aftronomers, to be fo. The catalogue contains 50 fixed ftars, with their right afcenfion and declination reduced to the beginning of the year 1786. Mr. Pigott then enumerates the particular obfervations on each of thefe ftars, and the reafons why he supposes fome of them variable, although their changes have not yet been atcertained.

The establishing of facts is the first step toward the advancement of science; and though these discoveries do not feem to be of any real ufe at prefent, yet they may, at fome future period, throw fresh light on aftronomy. The caufes of the appearances

* For an account of which, fee Rev. vol. lxxiii. p. 197.

are

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

(The Philofophical and Chemical Papers in this Part *; as foon as poffible.)

*N. B. The 2d Part of vol. lxxvi. is just published.

ART. VI. Chemical Effays. By R. Watfon, D.D. F. R. S. and Regius Profeffor of Divinity in the Univerfity of Cambridge. Vol. IV. 12mo. 4s. fewed. Cadell, &c. 1786.

E are forry to find that this is the laft chemical performance we have to expect from the right reverend author. Though convinced, by the uncommon fale of the former volumes, that they met with general approbation, and that they have contributed greatly to the promotion of chemical knowledge, he now refigns, for ever, these pleafing and useful purfuits; but not without fingular reluctance, and doing violence to his own feelings. Above two thoufand copies' (he fays) of the former volumes of my Chemical Effays have been fold in lefs than five years. I mention not this circumftance out of vanity, or as if I thought it contained any proof of their merit; but I produce it as a folid proof of the difpofition of the Public to become acquainted with chemical fubjects when they are treated in a popular way. This difpofition has been long prevalent in foreign countries; it feems to be gaining ground in our own; and if I have endeavoured to contribute a little towards its eftablishment amongst us, I hope the utility of the defign will plead my excufe with those, who, in the severity of their judgments, may think that I have contributed more than, from the nature of my profeffion and fituation, I ought to have done.

When I was elected Profeffor of Divinity in 1771, I determined to abandon for ever the ftudy of chemistry; and I did abandon it for several years: but the-veteris veftigia flammeftill continued to delight me, and at length feduced me from my purpose. When I was made a Bishop, in 1782, I again determined to quit my favourite purfuit; the volume which I now offer to the Public is a fad proof of the imbecility of my refolution. I have on this day, however, offered a facrifice to other people's notions, I confefs, rather than to my own opinion of epifcopal decorum-I have deftroyed all my chemical manuscripts. A profpect of returning health might have perfuaded me to purfue this delightful fcience; but I have now certainly done with it for ever; at leaft 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 inftitution at our univerfities, 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 ftudy, the Author obferves, would agreeably folicit, and might probably fecure, the attention of that part of our youth, which, in being exempted from the difcipline of fcholaftic exercifes, has abundant leifure for other purfuits; which, in being born to opulence, is unhappily deprived of one of the ftrongest incentives to intellectual exertion,-narrowness of fortune: it would prepare them for becoming intelligent legislators of their country; and it would infpire them with fuch a tafte for husbandry, as might conftitute the chief felicity of their future lives.

His notion of national ftrength, fecurity, and happiness, tends not so much to the extending of our commerce, or increafing 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 has grown before. Let us but once have as many Britons in the kingdom, as the well-cultivated lands of Great Britain are able to fupport (at least twice the prefent number), and we fhall have little to regret in the lofs of America; nothing to apprehend from the partitioning policy of all the continental defpots in Europe. In thus fixing the bafis of our ftrength on the improved cultivation of our lands, he does not mean to exclude manufactures, but on the contrary, confiders agriculture and manufactures as mutually fubfervient to each other. With regard to commerce, he thinks the prefent ftate of the finance of this kingdom requires it to be cherished with fingular indulgence; and that we fhall not fufficiently avail ourselves of the ineftimable advantages of our infular fituation, if we do not confider our glory and our fafety as closely connected with the number of our feamen, which will ever be in proportion to the extent of our foreign and domeftic commerce. Perhaps the advantages of commerce, and of manufactures as its bafis, are ere eftimated below their real value to the national ftrength and importance; nevertheless, the obfervations refpecting the education of young men of fortune are certainly juft, and deferve the most serious attention.

The effays which compofe this volume are written on the fame plan as thofe of the three preceding; not with a view to enrich fcience with any confiderable new difcoveries, but to promote a general tafte for thefe ufeful ftudies, and to engage the attention of those who are but little acquainted with chemical fubjects, by defcribing, in a clear and pleafing manner, the fucceffive difcoveries made in fome of the principal branches of chemical knowledge, and the confequent improvements in the arts depending on them. The fubjects are,

REV. Jan. 1787.

D