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deserving of attention. It appears that the length of the degree of the meridian, though it decrease constantly on going from the north to the south, as it ought to do, does in fact decrease very irregularly. Towards the northern extremity of the arch, the decrease is slow, and at the rate of not more than four toises in the degrees that lie between Dunkirk and Evaux. From Evanx to Carcasonne, the degrees diminish rapidly, at the rate of 30 or 31 toises; and from Carcasonne to Barcelona, the diminution becomes again much slower, and is about 14 toises to a degree.
This irregularity in the differences of degrees, does pot arise from a cause that is apparent on the surface. It very much resembles that which was experienced by Colonel Mudge as he went northward from the coast of the channel, when he found that the degrees, instead of increasing, came to diminish about the middle of the arch. In both cases, we may suspect the effect to have arisen, partly from the vicinity of the sea, partly perhaps from inequalities of density under the surface, or other irregularities in the superficial part of the globe. From whatever causes they arise, the repetition of operations, such as those we are now treating of, is what alone can be expected to throw new light upon the subject. Additional experiments on the attraction of mountains would probably tend to the same object, and might lead to other valuable conclusions.
We cannot finish our account of these scientific operations, without expressing our wishes that the uniformity of measures and of weights were introduced into our own, and into every other civilized country. The difficulty is not so great as we are apt to think, when we consider the matter at a distance; and to effect it requires, in reality, nothing but for the legislature to say, it shall be done. As to the standard to be adopted, though we think the pendulum would have afforded the most convenient; yet when one has been actually fixed on and determined, that circumstance must greatly outweigh every other consideration. The system adopted by the French, if not absolutely the best, is so very near it, that the difference is of no account. In one point it is very unexceptionable; it involves nothing that savours of the peculiarities of any country; insomuch, as the commissioners observe, that if all the history which we have been considering were forgotten, and the results of the operations only preserved, it would be impossible to tell with what nation this system had originated. The wisest measure, therefore, for the other nations of Europe, is certainly to adopt the metrical system of the French, with the exception perhaps of the division of the circle, where the number 600, as mentioned above, might be conveniently substituted for 400. It would not be necessary to adopt their names, which might not assort very well with the sounds that compose the languages of other nations. But the
metre, by whatever name it may be called, ought to be adopted as the unit of length, and all the other measures of linear extension derived from it by decimal multiplication and division. It is true, that this cannot be done, especially in our own case, without a certain sacrifice of national vanity; and the times do not give much encouragement to hope that such a sacrifice will be made. The calamities which the power and ambition of the French government have brought on Europe, induce us to look with jealousy and suspicion on their most innocent and laudable exertions. We ought not, however, to yield to such prejudices, where good sense and argument are so obviously against them. In a matter that concerns the arts and sciences only, the maxim may be safely admitted, Fas est et ab hoste doceri.
Art. II. An Account of Experiments for Determining the Length of
the Pendulum Vibrating Seconds in the Latitude of London. Ву Captain Henry Kater, F. R. S. From the Philosophical Transactions. London, 1818.
[Review—Sept. 1818.] The end of the last century, and the beginning of the present, have been distinguished by a series of Geographical and Astronomical measurements, more accurate and extensive than any yet recorded in the history of science. A proposal made by CASSINI in 1783, for connecting the Observatories of Paris and Greenwich by a series of triangles, and for ascertaining the relative position of these two great centres of Astronomical knowledge by actual measurement, gave a beginning to the new operations. The junction of the two Observatories was executed with great skill and accuracy by the geometers of England and France; the new resources displayed, and the improvements introduced, will cause this survey to be remembered as an era in the practical application of Mathematical science.
The want of system in the Weights and Measures of every country ; the perplexity which that occasions; the ambiguous language it forces us to speak; the useless labour to which it subjects us, and the endless frauds which it conceals, have been long the disgrace of civilized nations. Add to this, the perishable character thus impressed on all our knowledge concerning the magnitude and weight of bodies, and the impossibility, by a description in words, of giving to posterity any precise information on these subjects, without reference to some natural object that continues always of the same dimensions. The provision which the art of printing has so happily made for conveying the knowledge of one age entire and perfect to another, suffers in the case of magnitude a great and very pernicious exception, for which there is no remedy but such reference as has just been mentioned. Philosophers had often complained of these evils, and had point
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, Mecủain, 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, ils 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, NewTON demonstrated, that the same fraction, viz. at 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, zio, or is. Hence the oblatenesss appearing from the measurement of degrees to be ziz, the increase of gravity from the equator to the poles, or, which is the same, the shortening of the pendulum, must be its 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 cbservations 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 bad 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
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 con sisted 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 com. pared 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