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comet on the 7th of October 1793; which was found by her brother the following evening to precede the rft. (8) Ophiuchi 6′ 34′′ in time, and to be 1° 25′ more to the North than that ftar.

Obfervations of a quintuple Belt on the Planet Saturn. By William Herfchel, LL. D. and F. R. S.

On the Rotation of the Pianet Saturn upon its Axis. By the

Same.

In a paper published in the Tranfactions, vol. lxxx. p. 1, &c, Dr. H. established the spheroidical figure of the planet Saturn, and pointed out the motion of a spot on its difk. From the figure of the planet, we may infer that it has a confiderable rotation on its axis, and the reality of fuch a motion is afcertained by actual observation: but the period of its rotation was ftill undetermined. From fome late obfervations, the Doctor is led to conclude that this period is not of long duration. The phenomenon described in this memoir fuggefts, on the first view of it, a ftrong prefumption in favour of this conclufion. Since Saturn has numerous belts on its difk, resembling those of Jupiter, and placed in the direction of its longest diameter, we may argue, from analogy, that the period of the rotation of the former is fhort like that of the latter. This argument will be confirmed by confidering that no fuch phenomena as parallel belts have been obferved in the difks of Mars and Venus; and these are known to have a flower rotation on their axes than Jupiter. Dr. H. however does not content himself with this kind of reafoning. He has purfued a series of obfervations, in which Saturn has been traced through 154 revolutions of its equator; and by means of these he determines the precise period of its rotation. The belts of Saturn were lefs variable than those of Jupiter; and, as no material change occurred during the course of two months, his obfervations were more accurate; confequently, the period which he affigns muft have been afcertained with a very confiderable degree of exactnefs. Another circumftance deferves to be noticed. While Dr. H. was making his obfervations, he purposely avoided any calculations, or even furmifes, as to the length of a rotation, in order to be perfectly free from every bias that might mislead the eye. The inftrument which he generally ufed in this feries of obfervations was a feven-feet reflector with a power 287.

The shadow of the ring of Saturn, when it paffed the body of the planet, was very narrow and black; and immediately fouth of the fhadow there appeared a bright, uniform, and broad belt. Clofe to this belt there was a broad, darker belt, divided by two narrow white freaks, fo that it thus became

five belts, three of which were dark and two bright. The phenomenon is illuftrated by a drawing.

The method, by which Dr. H. determined the rotation of the planet from his obfervations, and by which he evinced the correfpondence of the appearances deduced from calculations with those that were actually obferved, cannot be intelligibly explained without the figure and tables. We can therefore only flate the refult, and refer to his own account of the ingenious process by which it was investigated. The true period of the rotation of Saturn on its axis is fixed at 10h 16′ 0′′.4; and this period is fo exact, that it cannot err fo much as two minutes either in excess or defect; for, if the error amounted to this quantity, the calculations and obfervations would be totally at variance.

Account of fome Particulars obferved during the late Eclipfe of the Sun. By the Same.

The attention of Dr. H., in obferving this eclipfe, was not directed to thofe particulars which are ufually noticed in phenomena of this kind; fuch as the beginning, the end, and the digits eclipfed. It was his wifh to avail himself of the power and diftinctness of his telescopes, in order to determine whether any appearances would occur which might deferve to be recorded, and which would furnish any additional knowlege with regard to the nature and condition of the moon, or of the fun, or of both these heavenly bodies. The moft remarkable appearances, which our author noticed at the commencement and during the progress of this eclipfe, were the mountains of the moon, Thefe he has delineated; and he has fubjoined a conjectural estimate of their height. On drawing feveral of them on the fegment of a large circle, fo as to look like what they appeared when projected on the fun, he found them to be from the 1500dth to the 2000dth part of the diameter of that circle. Then affuming the moon's diameter to be what M. de la Lande ftates it, or 2151 English miles, he infers that the 1500dth part of this is less than one mile and a half for the higheft mountain, and the 2000dth part not quite one mile and a tenth for the lowest.

In order to fatisfy perfons that the eye is able to ascertain the proportion of a quantity fo little as the 1500dth or 2000dth part of the diameter of the moon, he propofes the following experiment;

On a line 6 or 8 inches long, drawn on a sheet of paper, make feveral fmall marks, reprefenting mountains on the projected circumference of a large globe. The paper being then placed in a proper light and fituation, withdraw the eye to the diftance of 7, 8, or 9 feet, and take notice which of the marks appear of the fame fize, and dif

tinctness,

tincnefs, with the mountains they reprefent. Then, from the known angular magnitude of the moon, calculate its diameter, at the distance of your fituation: this, multiplied by the power of the telescope, gives the diameter of a circle, to the circumference of which belongs the line, upon which are placed the marks above defcribed. Now, meafure the elevation of thefe marks above that line, and you will obtain the proportion they bear to the diameter of the circle.'

By means of this experiment, Dr. H. fhews that fo fmall a mountain as theth, or not much more than the fixth part of a mile, may be perceived and eftimated, by the telescope and the power that was fed upon this occafion; and that, confequently, the eftimation of mountains, near a mile and a half high, mult become a very eafy task.'

On this fubject fee a paper by the author in vol. Ixx. Part 2. p. 507, or our Review, vol. lxiv. p. 441.

MATHEMATICS, MECHANICS, &c.

Account of a new Pendulum. By George Fordyce, M. D. F. R.S. being the Bakerian Lecture.

Dr. F.'s principal object is to contrive the conftruction of a pendulum which fhall be always of the fame length, whatever be the degree of cold or heat to which it is expofed. This is a defideratum of great importance in the fcience of mechanics; and there are many practical purpofes to which it may be applied. It will affift in establishing a meafure of lengths which may be always and univerfally afcertained. The difference of the lengths of two pendulums, vibrating different times, would furnifh the moft perfect ftandard for this purpose, if we were in poffeffion of an eafy and certain method for keeping the pendulum of the fame length when the heat varied. Mr. Whitehurft had contrived an apparatus for determining this difference: -but, though he had endeavoured to keep his pendulum of the fame degree of heat, his mode of doing it was not adequate to the effect, nor were the experiments on which it was founded fatisfactory. After the death of Mr. Whitehurst, his machine was purchafed by Dr. Fordyce, who, with a view of rendering the pendulum in it always of the fame length, in any degree of heat, difcovered the principle and formed the apparatus which are defcribed in this paper. Without the annexed figures, it is impoffible to give any intelligible and interefting detail or abridgment of the contents of this elaborate article, which occupies 19 pages. We fhall only obferve that, when the author had annexed his own apparatus to the machine of Mr.W. he proceeded to examine its effect; and he concludes that, notwithstanding fome inconveniences to which it was fubject, and which are capable of being obviated, it certainly performed better than any other time-piece that has been made; and per

haps affords a principle which may be ufed in fixed obfervations for keeping time with certainty, by eafy and not very expenfive means; and of determining, with the reft of Mr. W.'s apparatus, the different diameters, in any two given different times.'

This paper terminates with obfervations neceffary to be made, in order to enable workmen to conftruct clocks according to the author's principle, and with fome reflections on its operation.

Obfervations on the fundamental Property of the Lever, with a Proof of the Principle affumed by Archimedes, in his DemonAtration. By the Kev. S. Vince, A. M. F. R. S.

"If two equal bodies be placed upon a lever, their effect to turn it about any point is the fame as if they were placed in the middle point between them." This is the principle affumed by Archimedes but, as it is not felf-evident, the demonftration founded on it has been rejected as imperfect. Huygens, Newton, Maclaurin, Hamilton, and others, have proposed different modes of demonftration, liable to various objections, the chief of which are fuggefted by Mr. Vince. The principles affumed by Mr. Landen, in his memoirs, and his reafoning on them, Mr. V. approves but he objects to his investigation as too complicated and tedious for an elementary treatise of me. chanics, adapted to the ufe of learners, in which fimplicity and concifenefs are of the greatest importance. To the demonftration of Archimedes there can be no objection, if his fundamental principle be admitted. The proof of it here fubjoined is concife, clear, and fatisfactory. We fhall give it in the au thor's own words. The reader will eafily fupply the neceffary figures:

Let A, C, be two equal bodies placed on a ftraight lever, A P, moveable about P; bifect A C in B, produce P A to Q, and take BQ=BP, and fuppofe the end Q to be fuftained by a prop. Then as A and C are fimilarly fituated in refpect to each end of the lever, that is A P=CQ, and A Q=CP, the prop and fulcrum must bear equal parts of the whole weight; and therefore the prop at Qwill be preffed with a weight equal to A. Now take away the weights A and C, and put a weight at B equal to their fum; and then the weight at B being equally diftant from Qard P, the prop and fulcrum muit fuftain equal parts of the whole weight; and therefore the prop will now alfo fuftain a weight equal to A. Hence if the prop Qbe taken away, the moving force to turn the lever about P in both cafes muft evidently be the fame; therefore the effects of A and C upon the lever to turn it about any point are the fame as when they are both placed in the middle point between them. And the fame is manifeftly true if A and C be placed without the fulcrum and the prop. If therefore AC be a cylindrical lever of uniform denlity, its effect to

turn

turn itself about any point will be the fame as if the whole were collected into the middle point B; which follows from what has been already proved, by conceiving the whole cylinder to be divided into an infinite number of lamina perpendicular to its axis, of equal thicknelles.

The principle therefore affumed by ARCHIMEDES is thus eftas blished upon the mott felf-evident principle, that is, that equal bodies at equal distances must produce equal effects; which is manifeft from this confideration, that when all the circumftances in the cause are equal, the effects must be equal. Thus the whole demonstration of ARCHIMEDES is rendered perfectly complete, and at the fame time it is very fhort and fimple.'

The other part of the demonftration will readily occur to thofe who are acquainted with the fubject. Mr. V. has fubjoined it. The Latitudes and Longitudes of feveral Places in Denmark; calculated from the Trigonometrical Operations. By Thomas Bugge, F. R. S. Regius Profeffor of Aftronomy at Copenhagen. This article contains a table of the latitudes of 35 different places, and also of their longitudes from the Royal Obfervatory at Copenhagen. The trigonometrical operations from which they are calculated, and the inftruments and furveys on which thefe operations depend, were defcribed by the author in a treatife published in the Danish language at Copenhagen in 1779, and tranflated into German by Major After at Drefden in 1787. Mr. B. has introduced the table with a new method of computing the longitude and latitude of such places as are laid down by trigonometrical operations. By the help of the annexed figure it may be eafily understood; and it feems to be very well adapted to the purpofe. The geometrical furvey of Denmark was begun in 1762; and the angles of the triangles, on which it is founded, were obferved with a circular inftrument of a foot radius, the divifions of which inftrument are double, in 90 and 96 degrees. The angles were oblerved with it to a lefs error than 8", and the fum of all the angles in every triangle have very feldom had a difference of 15" from 180°. Inftruments of this kind have been used for 31 years by the Danish aftronomers and geographers; and they now begin to be more generally employed. We learn from this paper that nine geographical maps have been published in Denmark, which are highly commended for geometrical exactnefs as well as the excellence of the engraving, The author clofes with obferving that, in the best maps of the Kattegat, the pofition of Anholt is very erroneous:

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The light-houfe of Anholt, (he fays,) and the whole ifle is from 7 to 9 minutes too much wefterly; and the diftance from the lighthoufe to the Swedish coaft, in a direction perpendicular to the meridan of the light-houfe, is, in all maps hitherto published, nearly

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