differing from that just assigned by .00813; a considerable quantity, in a matter where it appears that a ten thousandth of an inch is a distinguishable magnitude.

To the paper which ends with the measures just given, is added, in an Appendix, a letter from Dr THOMAS YOUNG, CONtaining a demonstration of a very remarkable property of the pendulum recently discovered by M. LAPLACE. The property is, that if the supports of a pendulum, inverted as above described, be two cylindric surfaces, the length of the pendulum is truly measured by the distance of those surfaces. This applies immediately to the experiments we have been considering; because the knife edges, supposing them somewhat blunted, may be regarded as cylindric surfaces of very great curvature, or of very small diameter; and in this way, as Dr YOUNG very justly remarks, is removed the only doubt that can reasonably be entertained of the extreme accuracy of the conclusions. The theory of experiments made with the inverted pendulum, is therefore much indebted to the calculus of the profound mathematician above named. We have not seen his analysis; but a demonstration is sketched by Dr YOUNG, that seems sufficiently concise and simple, considering the recondite nature of the truth to be demonstrated.

Captain KATER's paper is dated in July 1817, the experiments described in it having been made previously to that time. The same apparatus that was thus perfected has been employed since, for the purpose of ascertaining the length of the seconds pendulum in different latitudes, with a view to the questions about the figure of the earth. That the precise object of the experiments may be the better understood, it may be proper to go back to the summer 1816.

After the bill for the equalization of weights and measures was thrown out, the attention of those who promoted the scheme of equalization, was naturally turned to the determination of the lengths of the pendulum; so that one of the good effects arising from the disappointment of the premature plan of equalization, was probably that of directing the ingenuity of the author of this paper to a subject in which it has been so successfully exerted. This other good effect also resulted from it. The French academicians were known to have directed a great deal of attention to this subject; the experiments of BORDA and CASSINI, SO often mentioned, were the most accurate that had yet been made; and the speculations of LAPLACE had deduced, from a collection of the best experiments that he could find, some very important conclusions concerning the figure of the Earth. On this subject, however, more information was still to be

expected, when experiments of equal accuracy with those made at Paris should be repeated in different latitudes. It would then be seen, whether the lengths of the pendulum agreed in giving the same figure to the Earth with the measures of degrees of the meridian, and, if they did not, in what respects they differed. This was the more desirable, that some inconsistencies had been found in the information derived from the last of these sources, and that there was reason to think that the same causes of inconsistency might not affect the experiments made with the pendulum. The pendulum measures the intensity of gravity; but its vibrations are little affected by the direction of that force. The measures of degrees, on the other hand, are extremely sensible to whatever affects the direction of gravity, but not much to what only changes its intensity. Hence, each of these methods of inquiring into the figure of the earth contains a remedy for the imperfections of the other; each by itself is incomplete; and both, of course, ought to be employed. It has been imagined, that the intensity of gravity suffers less alteration from the action of local causes, than the direction does; and that, on that account, the conclusions deduced from the I pendulum are more likely to be free from inconsistency than those that depend on the measurement of degrees. But it must not be supposed that, with the pendulum carried to its present state of sensibility and precision, the results will be free from inconsistency, or beyond the influence of the local irregularities that may exist immediately under the surface of the Earth. Were the pendulum the same inaccurate instrument that it was a few years ago, it might not feel the influence of such causes as only increase or diminish the intensity of gravity by a very small part of the whole. But, when the length of the pendulum can be determined to the ten thousandth of an inch, or to

1

134959

of its whole length, the force of gravity is measured with the same precision, and one part out of 134959 is rendered sensible. Now, it seems to us probable, that the variation in the density of the strata immediately under the surface, may produce a change in the intensity of gravitation, much more considerable than one part in 134959; the pendulum will not fail to be affected by this irregularity, and to give information of it. The force with which Schehalien disturbed the plumb-line was about of gravity, or nearly four parts in 134959. We think that, without any exaggerated suppositions, by the presence of an extensive stratum of gneiss, or of hornblende schistus, or of any great body of granite imme

1

34376

diately under the surface at one place, and of chalk, common sandstone or limestone at another, a difference in the intensity of gravity, even greater than the preceding, may be readily produced. The extreme sensibility to which the apparatus of the pendulum has been brought by Captain KATER, though it adds infinitely to the value of the instrument, will not, probably, add to the consistency of its reports. On that very

account, however, those reports will afford more important information concerning the constitution of the Globe; and the manner of extracting from them the most probable average result is also sufficiently understood.

We venture to throw out these conjectures before the new results have been communicated, (except those of Paris and London); and if we are wrong, we have the satisfaction to know, that our error will be soon corrected.

As the Academy of Sciences was already engaged in experiments of the same kind with those which were to be undertaken under the direction of the Royal Society of London, it was resolved by the latter, on the motion, we believe, of the PRESIDENT, to invite the former to authorize some of its members to join in the experimental and astronomical researches of which England was about to become the theatre. The invitation was accepted; the Governments of both countries signified their acquiescence, and offered their support; and the friends of science everywhere rejoiced in this mark of cordiality exchanged between two societies which the misfortunes of Europe had so long placed at a distance from one another. In the beginning of the summer 1817, M. BioT arrived in England, furnished with an apparatus for determining the length of the pendulum, the same, we believe nearly, that was used by BORDA and CASSINI. It was agreed that observations on the length of the pendulum should be made at London, at Edinburgh, and at the northern extremity of the greatest arc of the meridian that was to be determined by the trigonometrical survey of Britain, which, as was already known, must terminate in Shetland, between the small islands of Unst and Balta. M. BIOT, accompanied by Col. MUDGE, his son Captain MUDGE, and Dr OLYNTHUS GREGORY, repaired to Edinburgh, and, having made observations at Leith Fort, embarked for Shetland. They were joined by Captain COLBY, who conducted the trigonometrical survey, and who, with the zenith sector, was about to observe the highest latitude to which his system of triangles would extend. Col. MUDGE was forced, by bad health, to return; M. BIOT and Dr GREGORY made their observations separately, but in the same small island; and the former continued till late in the season on the barren rock,

where he was almost left alone, surrounded by a stormy sea and a dusky and inclement sky. The spirits of a man accustomed to the finer climates of the south, must have sunk in such a situation, had they not been supported by his love of science, and his zeal for promoting its interests. He has written an account of his visit to Great Britain, and particularly of his reception in Scotland and the Isles, drawn up in an excellent spirit, full of good temper, cheerfulness, and a disposition to be pleased; and abounding also in judicious remarks, The Shetland Isles seem particularly to have interested him; and the contrast between the aspects which the moral and physical world presented in that remote region, to have struck him forcibly. He was pleased with the kindness, hospitality, and intelligence of his hosts; and they, no doubt, were filled with respect for an illustrious stranger, who, from the centre of civilization, had penetrated into their distant isle, and was connecting, with the researches and the renown of Science, the obscure and sequestered corner in which Providence had fixed their habitation. He must have experienced feelings of high gratification, on considering that he had now assisted in defining both extremities of a line, extending from the most southerly of the Balearic to the most northerly of the Shetland Isles, the longest that the finger of Geometry had yet attempted to trace, or her rod to measure, on the surface of the earth;a work that, in all ages, it will be the boast of the 19th century to have accomplished. The different aspects of nature, at the remote stations which he had successively occupied, would not fail to present themselves with all the force that contrast can bestow; -the bright sun, the cloudless skies of the south, the glowing tints and the fine colouring of the Mediterranean, compared with the misty isle on which he now stood, and the tempestuous ocean which was raging at his feet. If he turned to the moral world, the contrast was also great, but it was reversed; and he would, perhaps, think of the fierce barbarians before whom he or his companions had been forced to fly, when the lonely islander was opening his cottage to receive him, and defend him from the storm. He would not then fail to reflect, how much more powerful moral causes are, than physical, in determining the good or evil of the human character.

M. Bror, on his return to London in the autumn, was joined by MM. ARAGO and HUMBOLDT, and, in conjunction with these illustrious associates, completed his experiments. The results have not yet, we believe, been given to the public; neither have those of Dr GREGORY. The scientific world waits impatiently for both.

During the present summer Capt. KATER has visited the same stations, as well as some others particularly connected with the trigonometrical survey, employing the apparatus above described for ascertaining the length of the pendulum. The result of observations made at six different points, from Unst in Shetland to Dunnose in the Isle of Wight, may be expected in the course of the ensuing winter. A great advantage that results from the manner in which his experiments are made, is the comparative shortness of the time that they take up. After the rate of the clock has been ascertained, the observations of the pendulum may be finished in three or four days, and the number of its vibrations in twenty-four hours, determined within a fraction of a second. Thence the length of the seconds pendulum is easily deduced, being, to that of the invariable pendulum used in the experiment, and of which the length is already accurately known, as the square of the number of vibrations performed by this last in twenty-four hours, to the square of 86400, the number of seconds in the same time. When the experiments are conducted in the way followed by the French astronomers, the length of the pendulum must be measured anew at every station. We cannot help thinking, that the frequent repetition of an operation, which it is always difficult to perform with accuracy, ought as much as possible to be avoided.

While we are concluding this article, we learn, with great satisfaction, the further progress of other operations connected with those of which we have been giving an account. Captain COLBY, after finishing his campaign among the Scottish mountains, is at this moment on his way to Dunkirk, for the purpose, as we suppose, of joining the French mathematicians, in order to examine, over again, the junction of the English and French triangles, and to determine the latitude of the extreme point of the meridian of Paris with the zenith sector-the same excellent instrument that has been used for all the celestial observations in the British survey. As this will involve a comparison between that sector and RAMSDEN'S great theodolite on the one hand, and the repeating circle on the other, it will be an experiment of great interest to astronomers; and, we believe, the conduct of it could not be in better hands than those into which it is about to be committed. Orders, we understand, have been given by LORD LIVERPOOL for preparing every thing that may be required along the coast of Britain. The liberality and steadiness with which Administration has supported the trigonometrical survey from its com-mencement, is deserving of the greatest praise, and is a strong claim to the gratitude of the Scientific World.