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It may be further alleged against the choice of the French commissioners, that there is in the unit which they have fixed on, something that is even worse than an arbitrary element-one which is hypothetical, and accompanied with some degree of uncertainty. The quadrant of the meridian itself is not the immediate object of mensuration, at least in its whole length. That length is concluded from the mensuration of a part, on the supposition that the meridian is an ellipsis, and that the ratio of its axes to one another is known. It is supposed, too, that the meridians are similar and equal curves ; so that in whatever place of the world an arch of the meridian is measured, the quadrant deduced from it will be of the same magnitude. It is well known that these suppositions are not rigorously true, and, what is most material of all, that a very large arch, or several different arches of the meridian, must be measured before the length of the whole can be determined with tolerable exactness. In all these respects, the pendulum, in the latitude of 45°, seems to us to have the decided preference above all others. The determination of it involves no theory—at least none about the conclusions of which the slightest doubt is entertained : it is at all times easily examined; and nature constantly holds out the prototype with which our standard may be compared, and from which, if lost, the knowledge of it may easily be recovered.
For these reasons, notwithstanding our profound respect for the genius and talents of the five academicians above named, we acknowledge that we are unable to acquiesce in the arguments by which they appear to have been determined.
But however this be, it cannot be questioned that after the French academicians had laid down their plan, their method of carrying it into execution was most expeditious and accurate.
Six different commissions for carrying all the parts of the plan into execution, that is, for ascertaining the unit of weight, the length of the pendulum, &c. &c. were appointed ; and the principal part, to wit, the measurement of the arch just mentioned, was committed to Mechain and Delambre, who began their operations in summer, 1792. The instruments which these mathematicians were to employ, both in their astronomical and geodetical observations, were the repeating circles of Borda. Four new instruments of that kind, and of somewhat larger dimensions, were executed by Lenoir, a very skilful artist, and put into the hands of Mechain and Delambre.
Two bases were measured, one at Melun, by Delambre, of 6075.9 toises, another at Perpignan, by Mechain, of 6006.248 toises. It appears from Delambre's account, that when the second of these bases was inferred from the first, it was found only about ten or eleven inches shorter than it turned out to be by actual measurement. When it is considered that the distance be
tween them is about 360330 toises, or something more than 436 English miles, it will be admitted that this coincidence is a proof of extreme accuracy.
The observations, when finished, were laid before a commission formed of members of the National Institute, and a great number of learned and scientific men from Germany, Denmark, Holland, Italy, &c. who had accepted the invitation given them to assist in the solution of this great problem. The manner of proceeding before this commission was such as to give the utmost degree of authenticity and correctness to all the parts of the work. The three angles of every triangle were separately examined ; and after comparing the different observations of each angle, with all the circumstances entered into the original notebooks and registers, and attending to all the explanations furnished by the two observers themselves, the commissioners drew up the table of triangles, such as it is given at the end of this volume, and such as was to be used in all the subsequent calculations. These calculations were all separately carried on by four different persons—Tralles, Van Swinden, Legendre, and Delambre himself. Each gave in his own calculations; and their differences, if there were any, being again examined, the result was finally agreed on. The observations for the azimuth were subjected to the like examination ; and, from all these combined, the length of the arch of the meridian was inferred. The observations for the latitude made at Dunkirk, Paris, Evaux, Carcasonne, and Montjouy, were also produced : so that the celestial arch became known. The comparison of the two gave, for the compression of the earth, adi; for the quadrant of the meridian, 5130740 toises; and, consequently, for the metre, 443.295986 lines.
During this interval, Mechain and Delambre had each fixed the latitude of his observatory by no less than 1800 observations, in order to determine from thence the latitude of the Pantheon, which was a little to the westward of the meridian, and the vertex of four of the triangles. These observations agreed with one another to the sixth part of a second.
The special commission for determining the length of the metre, consisted, at this time, of Van Swinden, Tralles, Laplace, Legendre, Siscar, Mechain, and Delambre. Their report, drawn up by Van Swinden, is dated in 1799.
In the course of their survey, the French astronomers determined the latitudes of five different points of the meridional arch with great exactness, viz. Dunkirk, 51° 2' 10"; Paris, at the Pantheon, 48° 50' 49"}; Steeple of Evaux, 46° 10' 42" ; Tower of St. Vincent, at Carcasonne, 43° 12' 54"; Tower of Montjouy, at Barcelona, 41° 21' 45". The amplitudes of the arches thus found, being compared with the terrestrial measurements, led to some results that were unexpected, and that are certainly highly
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 Evaux 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 not 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