when the distance between the two points about which the vibrations were performed being measured, the length of a simple pendulum, and the time of its vibration, will at once be known, uninfluenced by any irregularity of density or figure."

Having thus discovered an unexceptionable principle, Captain Kater's next object was to discover the best mode of suspending his pendulum. After studying the relative advantages and disadvantages of diamond points, spheres working in a conical aperture, and knife edges, he gave a decided preference to the latter, notwithstanding the supposed difficulty of forming a perfectly straight edge, and of preventing it from suffering any change during the experiment. The first of these difficulties was soon found to be merely imaginary, and if any error arose from the second, it would have become perceptible in Captain Kater's mode of observation every ninth minute; but independent of that circumstance, he proposed to detect any change in its form, by measuring the distance of the knife edges, both before and after the experiments. The following description of the pendulum is so minute and easily understood, that we can neither abridge it nor make it more perspicuous:

"The pendulum constructed upon these principles is formed of a bar of plate brass, one inch and a half wide, and one eighth of an inch thick. Through this bar, two triangular holes are made, at the distance of 39,4 inches from each other to admit the knife edges. Four strong knees of hammered brass of the same width as the bar, six inches long, and three quarters of an inch thick, are firmly screwed by pairs to each end of the bar, in such a manner, that when the knife edges are passed through the triangular apertures, their backs may bear steadily against the perfectly plane surfaces of the brass knees, which are formed as nearly as possible at right angles to the bar. The bar is cut of such a length, that its ends may be short of the extremities of the knee pieces about two inches.

"Two slips of deal 17 inches long, and of the same thickness as the bar, are inserted in the spaces thus left between the knee pieces, and are firmly secured there by pins and screws. These slips of deal are only half the width of the bar; they are stained black, and in the extremity of each, a small whalebone point is inserted for the purpose of indicating the extent of the arc of vibration.

"A cylindrical weight of brass, three

inches and a half diameter, one inch and a

quarter thick, and weighing about two pounds seven ounces, has a rectangular opening in the direction of its diameter, to

admit the knee pieces of one end of the pendulum. This weight being passed on the pendulum, is so thoroughly secured there by means of a conical pin fitting an opening made through the weight and knee pieces, as to render any change of position impossible. A second weight of about seven ounces and a half, is made to slide on the bar near the knife edge at the opposite end; and this weight may be fixed at any distance on the bar by two screws with which it is furnished.

It

"A third weight, or rather slider of only four ounces, is moveable along the bar, and is capable of nice adjustment by means of a screw fixed to a clamp, which clamp is included in the weight. This slider is intended to move near the centre of the bar. has an opening, through which may be seen divisions, each equal to one twentieth of an inch, engraved on the bar; and a line is drawn on the edge of the opening to serve as an index to determine the distance of the slider from the middle of the bar.

"We now come to the most important part, the knife edges. These are made of that kind of steel which is prepared in India, Their and known by the name of wootz. form is triangular, and their length one inch and three quarters. Mr Stodart was so obliging as to forge them for me: they were made as hard as possible, and tempered by immersing them merely in boiling water.

"The knife edges were ground on a plane tool, which necessarily ensured a perfectly straight edge. This was ascertained by bringing the edge of the one in contact with the plane of the other, when, if no light was perceptible between them in any position, it was inferred that the edge was a right line. They were then carefully finished on a plane green hone, giving them such an inclination as to make the angle on which the vibrations are performed about 120 degrees.

"Previously to the knife edges being hardened, each was tapped half way through, near the extremities, to receive two screws, which being passed through the knee pieces, drew the knife edges into close contact with them, the surfaces of both having been previously ground together to guard against any strain which might injure their figure."

Captain Kater next proceeds to describe the supports of the pendulum, and the other part of his apparatus, for an account of which we must refer our readers to the paper itself; but we cannot restrain ourselves from giving an account of a simple and beautiful little instrument, used by Captain Kater, and invented by our countryman, Mr Hardy, now the first clock-maker in Great Britain, for the purpose of detecting and rendering visible the slightest vibration in the support of the clock. This little instrument, resembling a small inverted pendulum,

with the point of suspension lowermost, consists of a steel wire, the lower end of which is inserted in a piece of brass, which serves as its support. The wire is flattened so as to form a delicate spring. A small weight slides on the wire, by the shifting of which the wire may be made to vibrate round its lower extremity, in the same time as the pendulum to which it is to be applied as a test. When this adjustment is effected, so that the pendulum and the wire perform their vibrations in the same time, the machine is placed on the solid body to which the pendulum is attached; and if this body should not be perfectly firm, its motion will be communicated to the wire, which, in a short time, will accompany the pendulum in its vibrations. This contrivance, posses; sed of extreme sensibility, afforded Captain Kater the most complete proof of the stability of the point of suspen

sion.

The next step in the investigation was to determine the number of vibrations made by the pendulum in 24 hours, or a mean solar day. This result could obviously have been obtained by actually counting the vibrations; but this method, even if it could be adopted without error, would be too laborious for any person to undertake. He therefore suspended his brass pendulum in front of an excellent clock made by Arnold, the pendulum of which performed nearly

The

86400 vibrations in 24 hours. pendulum of the clock was a gridiron one, and was suspended by a spring, the strength of which was so adjusted that the vibrations in different arcs were performed in equal times. A circular white disk, pasted on a piece of black paper, was attached to the ball of the pendulum of Arnold's clock; and this disk was of such a diameter, that when both pendulums were at rest, it was just hid from an observer (standing on the opposite side of the room) by one of the slips of deal which form the extremities of the brass pendulum suspended in front of it.

"A firm triangular wooden stand, as high as the ball of the pendulum, was screwed to the floor at the distance of nine feet in front of the clock. This served as a support, to which was attached a small telescope, magnifying about four times, which was capable of a horizontal motion on its axis, a vertical motion, and a motion at right angles to the line of sight. In the focus of the eye-glass was a diaphragm form

ing a perpendicular opening, the sides of which were parallel, and capable of being placed nearer, or further asunder. The edges of this diaphragm were adjusted so as to form tangents to the horizontal diameter of the white disk, and consequently to coincide with the edges of the slip of deal. When, therefore, both pendulums were at rest, nothing was visible through the telescope, excepting the divided are for ascertaining the extent of the vibrations, and which was seen through a horizontal opening made for that purpose in the top of the diaphragm.

If both pendulums be now set in motion, the brass pendulum a little preceding that of the clock, the following appearances may be remarked. The slip of deal will first pass through the field of view of the telescope at each vibration, and will be followed by the white disk. But the distance between the centres of suspension and oscilthe longer, the pendulum of the clock will lation, in the brass pendulum, being rather gain upon it, the white disk will gradually approach the slip of deal, and at length, at a certain vibration, will be wholly concealed by it. The minute and second at which this total disappearance is observed, must be noted. The pendulums will now be seen to separate, and after a time will again approach each other, when the same phenomenon will take place. The interval between the two coincidences in seconds, will give the number of vibrations made by the pendulum of the clock; and the number of oscillations of the brass pendulum, in the same interval, may be known by considering that it must have made two oscillations less than the pendulum of the clock. Hence, by simple proportion, as the vibrations made by the pendulum of the clock are to the

number of vibrations made by the brass pendulum, so are the vibrations made by the pendulum of the clock in 24 hours, to those of the brass pendulum in the same period.

The distance between the knife edges was then measured with great ingenuity, and by methods in which every probable source of error was anticipated and corrected, and the mean result, obtained by three successive measurements, was 39,44085 inches, suited to a temperature of 62°.

The experiments were now made, and the moveable weights were at last shifted to such a position, on the pendulum rod, that a mean of the number of vibrations, in 24 hours, when the great weight was above the

In order to render the calculation more easy, the clock has always been supposed to keep mean time, or to make 86,400 vibrations in 24 hours, and the variation from this number, or the rate of the clock (being a very small quantity), has been afterwards applied as a correction."

centre of suspension, was 86058.71; while the mean of the number of vibrations, when the great weight was placed under the centre of suspension, was 86058.72-a coincidence so great as to prove, that the distance of the knife edges, or 39,44085, was the exact distance between the centres of suspension and oscillation, and the true length of a pendulum, which performed 86058.715 vibration, in a mean solar day.

But as 86058.715 is 341.285 seconds less than a mean solar day, which consists of 86.400 seconds, we must reduce the length of 39.44085 by means of the known relation be tween the lengths of different pendulums, and the number of their vibrations. This will give 39,13329 for the true length of a pendulum vibrating seconds at the place where the experiments were made, namely, at the house of H. Browne, Esq. F.R.S. in Portland-place, situated in latitude 51° 31' 8" 4. When this is reduced to the level of the sea, which is eightythree feet lower than the place of observation, it gives 39.1386 inches for the true length of the pendulum.

Captain Kater's valuable paper is terminated with an appendix, consisting of a letter from Dr Thomas Young, containing a demonstration of a new property of the pendulum recently discovered by Laplace, namely, that if the pendulum vibrates upon a cylindrical surface, the length of the pendulum is the exact distance between the cylindrical surface, whatever be its radius and the centre of oscillation. M. Laplace had previous ly given a very elaborate demonstration of this property, founded upon mechanical principles; but Dr Young has conducted his investigation in a more simple and intelligible manner, and deduces the property immediately from a general theorem for finding the curvature of trochoids. It is impossible not to regret, after the perusal of this letter, that Dr Young has any other occupations than those of physical and mathematical researches. If the whole force of his powerful and cultivated mind had been directed to the advancement of his favourite studies, England would not have had the mortification of yielding to foreigners the palm of mathematical skill.

In concluding this notice of Captain Kater's labours, we feel ourselves bound, in justice to his reputation, to

notice the attempt which has been made to deprive him of the honour of an invention, which, in so far as our information goes, belongs exclusively to himself. Whenever a man of genius either invents or discovers, he must prepare himself for the mortification of having the honour of his labours claimed for some obscure individual, who may have accidentally performed some rude experiment, or uttered some ambiguous conjecture remotely connected with the subject of his investigations. These claims are commonly urged by a set of inferior and halflearned individuals, who derive all their importance from the accidental association of their names with those of superior men; and we regret to say, that men of genius themselves give too much countenance to these inroads upon the reputation of their rivals.

These remarks, though generally applicable to claims of this kind, by no means apply to the case of Captain Kater. The honour of having suggested the idea of a pendulum vibrating on two axes, has been claimed by M. Prony, a member of the Institute of France, and one of the most eminent mathematicians and civil engineers of which any country can boast. From the high character and respectability of this distinguished individual, we are convinced that, when he states, that he had proposed the same method in 1790, he had either mistaken the nature of Captain Kater's invention (probably from having heard of it in conversation), or, what is more likely, that he had made a nearer approach to the invention than appears in his writings. Our readers will be better able to form their own opinions on this subject, from the following statement of Captain Kater.

"In the Connoissance des Temps for 1820, is an article by M. de Prony on a new method of regulating clocks. At the conclusion of this article is a short note, in which the author adds, J'ai proposé en 1790 à l'Academie des Sciences un moyen

de déterminer la longueur du pendule en faisant osciller un pendule composé sur deux ou trois axes attahés à ce corps (voyez mes Leçons de Mécanique, art. 1107 et suivans). Il paroit qu'on a fait ou qu'on va faire usage de ce moyen en Angleterre.' On referring to the Leçons de Mécanique, as directed, I can perceive no hint whatever of the possipendulum by means of a compound penbility of determining the length of the seconds dulum vibrating on two axes; but it appears that the method of M. de Prony con

sists in employing a compound pendulum having three fixed axes of suspension, the distances between which, and the time of vibration upon each, being known, the length of three simple equivalent pendulums may thence be calculated by means of formulæ given for that purpose. M. de Prony indeed proposes employing the theorem of Huygens, of which I have availed myself, of the reciprocity of the axis of suspension and that of oscillation, as one amongst other means of simplifying his formula, and says, 'J'ai indiqué les moyens de concilier avec la condition à laquelle se rapportent ces formules, celle de rendre l'axe moyen le reciproque de l'un des axes extrêmes; J'emploie pour les ajustemens qu'exigent ces diverses conditions un poids curseur dont j'ai exposé les proprietés dans un mémoire publié avec la Connoissance des Temps de 1817.' Now, it appears evident from this passage, that M. de Prony viewed the theorem of Huy gens solely with reference to the simplification of his formula; for had he perceived that he might thence have obtained at once the length of the pendulum without further calculation, the inevitable conclusion must instantly have followed, that his third axis and his formula were wholly unnecessary."

Since Captain Kater has completed his experiments for determining the length of the seconds pendulum in the latitude of London, he has been employed, at the expense of government, in measuring the length of the pendulum at various stations in the great trigonometrical survey of this country. By means of an invariable pendulum, which vibrates seconds in London, he has this summer determined the relative length of the pen dulum at Unst, one of the Shetland Islands; at Portsoy in Banffshire; at Leith Fort near Edinburgh; and at Clifton in Yorkshire; and we have no doubt, that before the season is finished, he will have completed his observations at Arbury-hill and Dunnose. The zeal which he has displayed in carrying on these experiments, and the cheerfulness with which he has encountered the hardships which are incident to operations of this kind, lead us to indulge the hope, that in "some future season he will repeat his experiments at the North Cape, and even extend them to the Equator itself. Such a series of results, obtained by such accurate methods, and by means of the same pendulum and the same observer, will give us more correct information respecting the figure of the earth, than could have been obtained from the insulated observations of half a century.

The present goverment will, we have no doubt, cheerfully furnish the means of completing such a great work. Since the termination of the late war, they have extended their patronage to science with a zeal and liberality which was never exhibited by any of their predecessors. While the operations of the great trigonometrical survey have been carried on with activity and success, they have, in the short period of a year, remodelled the Board of Longitude, and added to it, with suitable salaries, the names of Dr Wollaston, Dr Young,* and Captain Kater; they have carried on the experiments on the length of the pendulum, which we have already mentioned; and have equipped four ships of discovery on the most interesting expedition which has ever left the British Islands.

ANALYSIS OF MR BARROW'S CHRONOLOGICAL HISTORY OF VOYAGES INTO THE ARCTIC REGIONS.

"How shall I admire your heroicke courage, ye marine worthies, beyond all names of worthiness! that neyther dread so long eyther presence or absence of the sunne; nor those foggy mysts, tempestuous winds, cold blasts, snowes and hayle in the ayre: nor the unequall seas, which might amaze the hearer, and amate the beholder, where the Tritons and Neptune's selfe would. quake with chilling feare, to behold such monstrous icie ilands, renting themselves with terrour of their owne massines, and disdayning otherwise both the sea's sovereigntie, and the sunne's hottest violence, mustering themselves in those watery plaines where they hold a continual civill warre, and rushing one upon another, make windes and waves give backe; seeming to rent the eares of others, while they rent themselves with crashing and splitting their congealed PURCHAS.

armours.

THE public have taken such a deep interest in the fate of the two expeditions of discovery, under the command of Captains Ross and Buchan, that they have looked forward with no inconsiderable anxiety for the appearance of the present work. The very able articles connected with this subject, which we have already received, from the pen of Mr Barrow, through the medium of the Quarterly Review, have indicated his peculiar qualification

* In consequence of Dr Young's recent appointment as Secretary to the Board, his place as commissioner has been filled by Colonel Mudge.