comet on the 7th of O&tober 1793 ; which was found by her brother the following evening to precede the ift. (8) Ophiuchi 6° 34' in time, and to be 1° 25' more to the North than that ftar. Observations of a quintuple Belt on the Planet Saturn. By William Herschel, LL. D. and F. R. S. On the Rotation of the Planet Saturn upon its Axis. By the Same. In a paper published in the Transactions, vol. 1xxx. p. 1, &c. Dr. H. established the spheroidical figure of the planet Saturn, and pointed out the motion of a spot on its disk. From the figure of the planet, we may infer that it has a confiderable rotation on its axis, and the reality of such a motion is ascertained by actual observation : but the period of its rotation was still undetermined. From fome late observations, the Doctor is led to conclude that this period is not of long duration. The phenomenon described in this memoir suggests, on the first view of it, a strong presumption in favour of this conclusion. Since Saturn has numerous belts on its disk, 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 short like that of the latter. This argument will be confirmed by considering that no such phenomena as parallel belts have been observed in the disks of Mars and Venus; and there are known to have a slower rotation on their axes than Jupiter. Dr. H. however does not content himself with this kind of reasoning. He has pursued a series of observations, 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 less variable than those of Jupiter ; and, as no material change occurred during the course of two months, his observations were more accurate; consequently, the period which he assigns must have been af certained with a very considerable degree of exactness. Another circumstance deserves to be noticed. While Dr. H. was making his observations, he purposely avoided any calculations, or even surmises, as to the length of a rotation, in order to be perfectly free from every bias that might mislead the eye. The instrument which he generally used in this series of observations was a seven-feet reflector with a power 287. The Shadow of the ring of Saturn, when it passed the body of the planet, was very narrow and black; and immediately south of the shadow there appeared a bright, uniform, and broad belt. Close to this belt there was broad, darker belt, divided by two narrow white freaks, so that it thus became fiye belts, three of which were dark and two bright. The phenomenon is illustrated by a drawing. The method, by which Dr. H. determined the rotation of the planet from his observations, and by which he evinced the correspondence of the appearances deduced from calculations with those that were actually observed, cannot be intelligibly explained without the figure and tables. We can therefore only ftate the result, 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 10% 16' 0".4; and this period is so exact, that it cannot err so much as two minutes either in excess or defect ; for, if the error amounted to this quantity, the calculations and observations would be totally at variance. Account of some Particulars observed during the late Eclipse of the Sun. By the Same. The attention of Dr. H., in observing this eclipse, was not directed to those particulars which are usually noticed in phenomena of this kind; such as the beginning, the end, and the digits eclipsed. It was his wish to avail himself of the power and distinctness of his telescopes, in order to determine whether any' appearances would occur which might deserve to be recorded, and which would furnish any additional knowlege with regard to the nature and condition of the moon, or of the sun, or of both these heavenly bodies. The most remarkable appearances, which our author noticed at the commencement and during the progress of this eclipse, were the mountains of the moon, These he has delineated ; and he has subjoined a conjectural estimate of their beight. On drawing several of them on the segment of a large circle, so as to look like what they appeared when projected on the fun, he found them to be from the 1500dth to the 2coodth part of the diameter of that circle. Then assuming the moon's diameter to be what M. de la Lande states it, or 2151 English miles, he infers that the 1500dth part of this is lets than one mile and a half for the highest mountain, and the 200odth part pot quite one mile and a tenth for the lowest. In order to satisfy persons that the eye is able to ascertain the proportion of a quantity so little as the 1500dth or 200odth part of the diameter of the moon, he proposes the following exe periment; « On a line 6 or 8 inches long, drawn on a Meet of paper, make several small marks, representing mountains on the projected circumference of a large globe. The paper being then placed in a proper light and situation, withdraw the eye to the distance of 7, 8, or 9 feet, and take gotice which of the marks appear of the fame size, and dir tinctness, tincinels, with the mountains they represent. Then, from the known angular magnitude of the moon, calcuiate its diameter, at the distance of your acuation : this, multiplied by the power of the telescope, gives the diameter of a circle, to the circumference of which belongs the fine, upon which are placed the marks above described. Now, meafure the clevation of these 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. thews that fo fmall a mountain as the c5th, or not much more than the fixth part of a mile, may be perceived and estimated, by the telescope and the power that was ued upon this occafion; and that, conseguently, the estimation of mountains, near a mile and a half high, must becoine a very easy task.' On this subject fee a paper by the author in vol. Ixx. Part 2. p. 527, or our Review, vol. Ixiv. p, 4+1. 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 construsion of a pendulum which shall be al ways of the same length, whatever be the degree of cold or heat to which it is expoled. This is a defideratum of great importance in the science of mechanics; and there are many practical purposes to which it may be applied. It will assist in establishing a measure of lengths which may be always and universally ascertained. The difference of the lengths of two pendulums, vibrating different times, would furnith the most perfect standard for this purpose, if we were in poflefion of an easy and certain method for keeping the pendulum of the fame length when the heat varied. Mr. Whitehurst had contrived an apparatus for determining this difference: -but, though he bad endeavoured to keep his pendulum of the same degree of heat, bis mode of doing it was not adequate to the effect, nor were the experiments on which it was founded fatisfaciory. After the death of Mr. Whitehurit, his machine was purchased by Dr. Fordyce, who, with a view of rendering the pendulum in it always of the same length, in any degree of heat, discovered the principle and formed the apparatus which are described in this paper. Without the annexed figures, it is impossible to give any intelligible and interelling deiail or abridgment of the contents of this elaborate article, which occupiès 19 pages. We ihall only observe that, when the author had annexed his own apparaius 10 the machine of Mr.W. he proceeded to examine its effect; and he concludes that, notwithstanding some inconveniences to which it was subject, 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 used in fixed observations for keeping time with certainty, by easy and not very expensive means; and of determining, with the rest of Mr. W.'s apparatus, the different diameters, in any two given different simes.' This paper terminates with observations necessary to be made, in order to enable workmen to construct clocks according to the author's principle, and with some reflections on its operation. Observations on the fundamental Property of the Lever, with a Proof of the Principle assumed by Archimedes, in his Demonftration. 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 same as if they were placed in the middle point between them.” This is the principle affumed by Archimedes : but, as it is not self-evident, the demonstration founded on it has been rejected as imperfect. Huygens, Newton, Maclaurin, Hamilton, and others, have proposed different modes of demonstration, liable to various objections, the chief of which are fuggested by Mr. Vince. The principles allumed by Mr. Landen, in his memoirs, and his reasoning 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 use of learners, in which simplicity and conciseness are of the greatest importance. To the demon. ftration of Arihimedes there can be no objection, if his fun. damental principle be admitted. The proof of it here fubjoined is concise, clear, and satisfactory. We tall give it in the au. thor's own words.' The reader will easily supply the necessary figures : • Let A, C, be two equal bodies placed on a straight lever, A P, moveable about P; bisect AC in B, produce P A to Q, and take BQ=B P, and suppose the end to be sustained by a prop. Then as A and C are similarly fituated in respect to each end of the lever, chat is A P=CQ, and A Q=CP, the prop and fulcrum mult bear equal parts of the whole weight; and therefore the prop at Q will be pressed with a weight equal to A. Now take away the weights A and C, and put a weight at B equal to their sum ; and then the weight at B being equally distant from Qard P, the prop and fulcrum mult fultain equal parts of the whole weight; and therefore the prop will now allo Tustain a weight equal to A. Hence if the prop Obe taken away, the moving force to turn the lever about P in both cases mult evidently be the same; therefore the effects of A and C upon the lever to turn it about any point are the same as when they are both placed in the middle point between them. And the same is manifestly true if A and C be placed without the fulcrum and the prop. If gherefore A C be a cylindrical lever of uniform denlity, its effect to furn itself about any point will be the same 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 laminæ perpendicular to its axis, of equal thickDelles. turn • The principle therefore assumed by ARCHIMEDES is thus esta, blished upon the mott self-evident principle, that is, that equal bodies at equal distances must produce equal effects; which is manifeft from ebis consideration, that when a!l the circumstances in the cause are equal, the effects must be equal. Thus the whole demonstration of ARCHIMEDES is rendered perfe&tly complete, and at the same time it is very short and simple.' The other part of the demonstration will readily occur to those who are acquainted with the subject. Mr. V. has subjoined it. The Latitudes and Longitudes of several Places in Denmark; cal culated from the Trigonometrical Operations. By Thomas Bugge, F. R. S. Regius Professor of Astronomy at Copenhagen. This article contains a table of the latitudes of 35 different places, and also of their longitudes from the Royal Observatory at Copenhagen. The trigonometrical operations from which they are calculated, and the instruments and surveys on which these operations depend, were described by the author in a crea. zise published in the Danilh language at Copenhagen in 1779, and translated into German by Major After at Dresden 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 easily understood ; and it seems to be very well adapted to the purpose. The geometrical survey of Denmark was begun in 1762 ; and the angles of the triangles, on which it is founded, were observed with a circular instrument of a foot radius, the divisions of which inftrument are double, in 90 and 56 degrees. The angles were oblerved with it to a less error than 8", and the sum of all the angles in every triangle seldom had a difference of 15 from 180°. Inftru. ments of this kind have been used for 31 years by the Danith astronomers 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 exactness as well as the excellence of the engraving, The author closes with observing that, in the best inaps of the Kattegat, the pofition of Anholt is very erroneous : • The light house of Anholt, (he says,) and the whole ise is from 7 to 9 minutes too much weiterly; and the distance from the lightboute to the Swedish coast, in a direction perpendicular to the meridan of the light-houle, is, in all maps hitherto published, nearly four have very |