ed out the cure; but there were old habits and inveterate prejudices to be overcome; and the phantom of innovation, even in its most innocent shape, was sufficient to alarm governments, conscious that so many of their institutions had nothing but their antiquity to recommend them. At the commencement of the French Revolution the National Assembly was avowedly superior to the last of these terrors, and the Philosophers of France considered it as a favourable opportunity for fixing, with the support of Government, a new system of measures and weights, on the best and most permanent foundation.

Of the quantities which nature preserves always of the same magnitude, there are but few accessible to man, and capable at the same time of being accurately measured. The choice is limited to a portion of the earth's circumference, or to the length of the pendulum that vibrates a given number of times in the course of a solar or sideral day, or any portion of time accurately defined by some of the permanent phenomena of nature. The choice of the French mathematicians, falling on the first of these, was accompanied with this great benefit to science, that it enforced a very diligent and scrupulous examination into the magnitude and figure of the earth. The quadrant of the terrestrial meridian was the unit of linear extension which they proposed to assume, and the ten-millionth part of it was the standard to which all linear measures were to be referred. The series of difficult and nice observations undertaken with a view to this improvement, carried on in the midst of much intestine disorder with signal firmness and perseverance, and finished, in spite of every obstacle, with all the accuracy that the new instruments and new methods could afford, has raised to the men of science engaged in it, (DELAMBRE, MECHAIN, BIOT, ARAGO,) a monument that can never be effaced. The meridian of Paris, continued to Dunkirk, on the one hand, and Solieure on the other, and afterwards extending beyond the latter to the southernmost of the Balearic Isles, amounting nearly to an arc of 12 degrees, afforded means more than sufficient for computing the quadrant of the meridian, and thus fixing the standard on sure and invariable principles.

The extent of the arc of the meridian, thus determined, is also about to receive a great increase by the addition from the British survey, of an arc extending from the parallel of Dunkirk to that of the most northerly of the Shetland Isles; so that the distance between this last parallel and that of Fermentera, nearly a fourth part of the quadrant of the meridian will become known by actual measurement.

But while it is possible to interrogate Nature in two different ways concerning the same thing, curiosity is not to be satisfied without having both her responses. The pendulum, as is well known, affords the means of determining, not indeed the magni

tude, but the figure of the earth; that is, its compression at the Poles, or the oblateness of the spheroidal figure into which it is formed. At the Equator, gravitation is weaker than at the Poles; both on account of the centrifugal force, which is greatest at the former, and vanishes altogether at the latter, and of the greater distance of the circumference of the Equator from the centre of the mass. If the earth were quite homogeneous, NewNEWTON demonstrated, that the same fraction, viz. would denote the oblateness of the earth, and the diminution of gravity from the Pole to the Equator. There is, however, good reason to believe, that the earth is very far from being homogeneous, and is much denser in its interior than at its surface. CLAIRAUT, therefore, did an unspeakable service to this branch of science, when he showed, that in every case the two fractions just mentioned, though not equal to one another, must always, when added together, constitute the same sum, that is, or ris. Hence the oblatenesss appearing from the measurement of degrees to be, the increase of gravity from the equator to the poles, or, which is the same, the shortening of the pendulum, must be We must have recourse to experiment, then, to discover whether this be agreeable to the fact, or whether evidences thus brought together from such different regions, conspire to support the same conclusion. LAPLACE, accordingly, from an examination of 37 of the best observations made in different latitudes, from the equator as far as the parallel of 67 degrees, had obtained a result that agreed very well with the conclusions from the measurement of degrees. But these observations had been most of them made long ago, before the present extreme precision was introduced, and even before the means of comparing the lengths of two rules, or two rods of wood or of metal, was completely understood. It was therefore extremely desirable, that a series of new observations of the same kind should be made in different countries. The National Institute had begun the series at Paris; it had made a part of the Système Métrique, to determine the relation between the seconds pendulum and the metre; and a number of experiments for that purpose were made by BORDA and CASSINI, with every precaution that could insure exactness.

After quiet was restored to Europe, England had leisure to attend to other objects than those in which the ideas of defence or of conquest were concerned. France and a great part of the continent had adopted the scheme of uniform measures; in England a plan for the same had been often thought of; it had been more than once undertaken, but never on a right system; and had always, fortunately, though perhaps weakly, been abandoned.

The attention of the men of science about London was naturally turned to the experiments by which the length of the pendulum may be accurately determined. The nature of the appa

ratus best fitted for that object is by no means obvious. The French Academiciaus, just referred to, had indeed employed a very simple one, which seems capable of great exactness. It consisted of a ball of platina suspended by a fine wire, and vibrating about a knife edge, which served as its axis. The vibrations counted by the person who conducted the experiment, were compared with those of a clock, placed close by, and regulated according to mean solar time. After a sufficient number of such comparisons, the length of the pendulum, from the knife edge to the centre of oscillation of the ball, was partly measured and partly calculated; and thus the quantity required was determined.

Though this method is susceptible of great accuracy, and, in the hands of such men as BORDA and CASSINI, could not fail to lead to a satisfactory conclusion, yet it is right to have so important an element in our researches as the length of the pendulum, or the intensity of gravitation, ascertained by experiments made with different instruments; made according to different methods, and particularly not so dependent on the mathematical theory of the centre of oscillation as to be without the possibility of verification by experiment. It must not be supposed, that in laying down this last condition we mean any thing so absurd as to question the force of mathematical demonstration. A conclusion purely mathematical, when applied to an object that is also purely mathematical, one that partakes of the same immaterial and impassible nature with itself, is above receiving additional evidence from any source whatever, and despises alike all attempts to increase or diminish its authority. But the same is not exactly the case when the conclusion is applied to a material body; it then partakes of the imperfection of the subject; and thus, in a sphere even of gold or platina, the actual centre of oscillation may not coincide to the ten-thousandth part of an inch, with the point which the calculus has determined. In such instances the verification by experiment, if it cannot be called necessary, is at least highly satisfactory.

Among the Mathematicians who endeavoured to resolve the problem on a principle of this kind, the author of the paper which is the subject of this article, came soon to be particularly distinguished. Captain KATER, to the profession of a soldier, seems early to have united the pursuits of science, and to have acquired uncommon skill and accuracy both in philosophical experiment, and astronomical observation.

-He began to consider how the experiment of the pendulum might best be made in a way to admit of verification by a reverse experiment; and a cylindric rod of brass or of iron readily occurred to him, as a body well adapted to that purpose. The impossibility, however, of finding a rod or bar of metal so homogeneous that its centre of oscillation could be determined merely

from its dimensions, made him quickly despair of succeeding by such means. It happily occurred to him, in this uncertainty, that there was one property of the centre of oscillation by which its place might be made manifest, whatever were the irregularity in the figure, or the density of the vibrating body.

HUYGENS, the profound and original author of the Theory of the Pendulum, had demonstrated that the centres of suspension and oscillation are convertible with one another; or that, if in any pendulum the centre of oscillation be made the centre of suspension, the time of vibration will be in both cases the same. Hence, conversely, said Captain KATER, if the same pendulum, with different points of suspension, can be made to vibrate in the same time, the one of these points must be the centre of oscillation when the other is the centre of suspension; and thus their distance, or the true length of the pendulum, is found. It is curious to remark, that a proposition, so well known, and affording so direct a solution of the difficulty in which experimenters on this subject had always found themselves involved, was never before, at least in as much as we have been able to discover, applied to a purpose for which, now that the secret is known, it seems so excellently and so plainly adapted. But it is one of the prerogatives of true genius, to find the highest value in things which ordinary men are trampling under their feet.

To reduce the principle just mentioned into a tangible_form, some further contrivance was still necessary. We copy the author's description of his convertible pendulum.

'The Pendulum 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 that are to serve for 'the axes of suspension in the two opposite positions of the pendulum. Four strong knees of hammered brass, of the same 'width with the bar, six inches long, and three quarters of an 'inch thick, are firmly screwed by pairs to each one of the bar; 'so that when the knife edges are passed through the triangular apertures, their backs may bear steadily against the perfectly 'plane surface 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 fall short of the extremities of the knee'pieces about two inches.

'Two slips of deal, 17 inches long, are inserted at either end, in the spaces thus left between the knee-pieces unoccupied by 'the bar, and are firmly secured by screws. These slips of deal are only half the width of the bar; they are stained black, and ' a small whalebone point inserted at each end indicates the ex6 tent of the arc of vibration.

'A cylindrical weight of brass, three inches and a half in dia'meter, and weighing about two pounds seven ounces, has a rec'tangular 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 firmly screwed in its place as to render any change impossible.'

This weight, it must be observed, is not between the knife edges, but is very near to one of them. 'A second weight, of ' about seven ounces and a half, is made to slide on the bar, near the knife edges, at the opposite end; and it may be fixed at any point on the bar by two screws, with which it is furnished. 'A third weight, or slider, of only four ounces, is moveable along the bar, and is capable of nice adjustment, by means of a screw ' and a clasp. It is intended to move near the centre of the bar, ' and has an opening, through which may be seen divisions of ' twentieths of an inch engraved on the bar.'

It is by means of this moveable weight that the direction of the vibrations in the two opposite positions of the pendulum are adjusted to one another; after which it is secured immoveably in its place.

The knife edges, or prisms, which make so important a part of this apparatus, and are to serve alternately as the axes of motion, are made of the steel prepared in India, and known by the name of wootz. The two planes which form the edge of each prism are inclined to one another nearly at an angle of 120 degrees. Every precaution was used to render the edges true, or straight, and to give the hardest temper to the steel; and a long series of experiments proves fully that they have been successful. Every precaution was also taken to give stability to the axes of suspension, when the experiments were made: But for the details of these, we find it necessary to refer to the paper itself.

We come now to the very ingenious method which Captain KATER adopted for determining the number of vibrations made by his pendulum in twenty-four hours. It is, no doubt, sufficiently understood, from what has been already said, that the pendulum was not to be applied to a clock, nor to receive its motion from any thing but its own weight. When experiments of this kind were attempted, it was for a long time supposed that the pendulum might safely be permitted to receive the continuance of its motion from machinery; and that, as it was then in no danger of coming to rest, the results were more to be depended on. This conclusion, however, proceeded on a great mistake as to the part which the machinery of the clock performs on such occasions. That machinery is hardly ever, we believe, so nicely adjusted as accurately to restore to the pendulum the motion it loses in each vibration, (from friction about the centre, and from the resistance of the air,) without either allowing