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Between Villejuif and Juvisi, Picard measured a base of 5,663 toises, and by means of five triangles, resting on that line, deduced a distance from Mareil to Malvoisin equal, in the units just cited, to 32897. This line, much greater than the first, served him now for a base to connect Malvoisin with Sourdon, near Amiens, by a chain of triangles in the direction of the meridian. The arc comprised between the two last points was 1° 11'57", and the distance deduced from the triangulation and projected on the meridian was 68.430 toises; whence there resulted for the value of a terrestrial degree the number 57064. Still later, Picard extended the operations to Amiens, and the degree then stood reduced to 57.057 toises; or, taking a middle term, to 57.060; a result which, assuming the sphericity of the globe, implied as the length of the earth's radius 3,269,300 units of the above name.*
Although in this memorable operation, on which we have dwelt somewhat, as being the first among those really worthy of confidence, Picard displayed great talent and activity, the result obtained was closely approximate to the truth only through a singular combination of errors; since, as appeared in the sequel, there was a very considerable one in the value of the first base, nor was that which existed in the quantity of the arc insignificant; two circumstances which, as they affected the result in opposite directions, were neutralized as regarded the operation itself, but were afterwards the source of much extraneons confusion and of long and warm discussions: a sad proof that imperfection, under some disguise or other, lurks in all the works of man; and that, without doing injustice to the memory or merits of the learned, we should never blindly surrender our belief to their authority.
The rotation of the earth being by this time a fact received without contradiction in the scientific world, of necessity soon drew with it its natural conse. |. thus, the ideas of the less weight of bodies at the equator than in the neighborhood of the poles from the effect of the centrifugal force opposed to gravitation, and of the compression of the globe in the direction of the axis of movement, had begun to take root in all reflecting and unprejudiced minds, when an observation, in some degree unexpected, gave confirmation to this view of the question. The academician Richer, having been sent to Guiana, in 1672, for scientific purposes of different kinds, returned to his country the following year, and among other results of his expedition presented to the Academy an observation which, though incidentally made, proved to be the most important of all: the astronomical pendulum which, at Paris, gave an oscillation of one second, was found to move more slowly in Guiana, to the extent of making in a day 88 oscillations fewer than at the former point. This indicated an energy of gravitation at the equator inferior to that in high northern latitudes, the existence of the centrifugal force due to the rotary movement of
* The toise spoken of is that of France, containing 6.39459 feet, which dates from the time of Charlemagne, and is said to have originated with the Arabs. For many centuries the standard of this unit of measure was little known, and from time to time underwent modifications, the results of ignorance or carelessness more than of fraud, until in 1663 a new one was prepared and deposited in a secure place, in order to serve as a type for all of its kind; it was to this standard that Picard and the geometers who succeeded him referred their desic operations. A century afterwards the iron rule which was adopted for the jof measurement of trigonometrical bases in Peru, also a toise in length, but better constructed than the toise of Picard's time and in a better state of preservation than the latter, was, at the suggestion of Condamine, declared to be the legal unit, at a temperature of 132 Reaumur, or 16° centigrade, that having been its medium temperature during the operations near the equator. The subsequent labors of Delambre and Mechain served to fix the length of the new lineal unit, or, in other words, of the metre, which, at the temperature of 0° is, in lines, 443,296, thus establishing between the metre and the toise the ratio of 1 to 1.94903631. This last number has been employed as factor in the remainder of this article, while it has been thought proper to convert the ancient units into the modern, or more usual of the decimal metric system.
the earth, and the great probability of the ellipticity of the globe. But as the ideas of attraction and of central and centrifugal forces had not as yet become familiarized, and as the phenomenon discovered by Richer might proceed from an unknown cause, the Academy suspended its judgment upon the consequences deducible from that phenomenon, until new and repeated observations should confirm or disprove them. The confirmation was not long deferred, for Halley, repeating four years after in St. Helena the same experiments which Richer had made, obtained an identical result, and the fact has subsequently been realized in all the regions of the earth as well as upon the high seas. We may take this occasion to remark that in the study of nature there are problems whose solution, after resisting for ages all the forces of man, seems at some determinate epoch to become practicable in a hundred different ways; such a problem, undoubtedly, was that which now occupies us. In the sixteenth century Copernicus, Galileo, and whosoever thought as they did respecting the movement of the earth, were regarded with scorn or aversion; in the middle of the seventeenth, the roundness and rotation of the globe are admitted without difficulty; in 1670 Picard determines by a satisfactory process the value of the earth's radius; two years later, the observations of Richer show that the form of the globe differs sensibly from the spherical; about the same time, Cassini, by means of the telescope, perceives and measures the remarkable oblateness of Jupiter, thus supplying from analogy a weighty reason for admitting without other proof that of the earth; while Huyghens and Newton, preceding and directing, as it were, the methods of observation, deduce the same result by process of reasoning, establish the extreme limits within which its numerical expression must be comprised, and ascend to the cause from which it proceeds. Honorable epoch for the human intellect in which such capital discoveries rapidly succeed one another! With the songs of triumph, however, soon mingle the notes of discord, and for some years the problem of the figure of the earth remains stationary and proves to be beset with unexpected difficulties. The Academy of Paris, stimulated by the prompt and apparently satisfactory termination of the measurement of the terrestrial degree by Picard, conceived the idea of prolonging the operations instituted by that savant from one extremity of France to the other, or, more precisely, from Amiens to Perpigman; a bold enterprise for that epoch, which the intelligent activity of Dominico Cassini realized in the latter part of the century. But when Cassini, the operations and calculations being concluded, compared with one another the values of the 7° of the meridian measured, he observed with surprise that their length continually diminished from south to north, as if the curvature of the earth increased towards the poles, or its radius diminished; or, in other terms, as if the compression of the globe corresponded to the equatorial region, contrary to all that was then conjectured or deduced from theory; a consequence which the same astronomer still arrived at after having prolonged the French meridian north from Amiens to Dunkirk, at the end of the year 1713. A conflict thus became unavoidable and imminent. On the one hand, the authority of Newton interposed itself; on the other, that, scarcely less weighty, of the French geometers, as well as the national pride of the latter; and as between the extremes in discussion there could be no possible compromise, the scientific world was divided into two parties; all that had been done or deduced to determine the true figure of the earth was brought before the tribunal of opinion, from the principle of the universal attraction of matter to the ability of the observers who had officiated in the measurement of the arc of the meridian. After much time had been lost in barren and heated discussions, the French Academy of Sciences, at the suggestion of Maupertuis and Bouguer, two of the most distinguished savants of their age, adopted the only feasible plan for setting the question finally at rest. With this view, two delegations, composed chiefly of members of the Academy, and provided with the most delicate instruments for observing then known, were despatched, one towards the equator, the other to a high northern latitude, for the purpose of measuring one or more degrees of the meridian, from the comparison of which measurements, if effected with accuracy, might readily be deduced the direction of the terrestrial compression and its value, or the amount of divergence from a spherical form. Maupertuis himself, assisted by Clairaut, Le Monnier, Camus, Outhier, and the Swedish astronomer Celsius, undertook the second of the operations referred to, proceeding to Lapland in 1736, as far as the 76° of latitude; and although it might have seemed that the rigors of the climate would present obstacles little less than insuperable, he had the good fortune to terminate his undertaking in scarcely more than two months. The triangulation extended from the mountain of Kittis at the north to the church of Tornea at the south; the base, of 7.407 toises, was measured upon the frozen river bearing the lattername, under conditions of exactness scarcely to be attained in any other climate; the quantity of the arc measured was 57'29", and the resulting value of the degree of the meridian equal to 57.438 toises, or 378 more than the degree of Picard, as would be naturally the case on the supposition of the earth's being flattened towards the poles. The other commission destined for the equator, and composed of Godin, La Condamine and Bouguer, had sailed a year earlier, or in 1735, and by order of the Spanish government was joined at Quito by D. Jorge Juan and D. Antonio de Ulloa, both worthy, from their zeal and intelligence, to co-operate with the French delegation. To recite the hardships to which these distinguished men were subjected during the eight years occupied in their prescribed task, the disappointments which they encountered, the deficiencies to be remedied, the precautions to be taken, and the sagacity and skill of which they made proof, would be beside our present purpose. Suffice it to say, that their measurement of the arc in Peru, notwithstanding the recent progress of practical astronomy, is still considered as a masterly operation in its kind. The degree of Peru, of 56.753 toises, compared with that which Picard had measured in the north of France, pointed substantially to the same result with that already obtained by the collation of this last with the degree of Lapland; that is to say, to the polar compression of the terrestrial globe. To what, then, was it attributable that from the examination of the different degrees of the French meridian there resulted a diametrically opposite consequence to the above? From the fact before hinted at, that the first base measured by Picard labored under a considerable error, compensated, indeed, as regarded the final result by other errors of quite a distinct kind which were committed in the course of the operations, and which by a rare concurrence of circumstances operated in an opposite direction to the preceding. Without distrusting its exactness, Cassini also took that first line for the base of a triangulation much more extensive and important than that of Picard, and hence arose those incidental anomalies which involved the learned in so much confusion, until the illustrious La Caille divined from what source that incomprehensible difficulty emanated. The base in question having been rectified by successive admeasurements in 1740–1754, and the calculations corrected, the capital discrepancy, which till that date had interfered with the various geodesic results, disappeared. In stating that the contradiction disappeared, we would only be understood to say that, after the epoch just referred to, there was a unanimous concurrence in the fact of the defective sphericity of the earth and the flattening of its poles; as regards the definite value of this, and the geometric figure to which our globe most nearly approaches, neither did such unanimity then, nor, to our regret, does it still prevail; perhaps, indeed, the conditions of the problem forbid that it should ever do so. From the values of the degree measured in Lapland and of the mean degree of France, there was deduced, as the expression of the terrestrial oblateness the fraction TH; which means that, representing the equatorial radius by a length of 132 units of any kind, the polar radius would be 131 of the same. A comparison of the degree of Peru with the French gave for the value of this inequality the number sor; that of the extreme degrees of Peru and Lapland #g; while, according to Newton, theory assigned to this quantity the value Thus it was that, in a point so delicate and interesting, it still seemed ifficult to know upon what to rely, notwithstanding the diligence and solicitude applied to the solution of the question in all its bearings. It might have seemed that here were contradictions enough; but in proportion as other values of a degree of the meridian were determined, as by Boscovich between Rome and Rimini in 1754, by Beccaria in Piedmont in 1762, by Liesganig in Hungary and Austria in 1768, by Mason and Dixon in America, about the same period, and by La Caille near the Cape of Good Hope, new irregularities or anomalies were constantly encountered, incomprehensible upon any one principle, or inexplicable by the adoption of any regular and unique type, however complicated, as the figure of the earth. The confusion grew to such an extent that every one felt impelled to investigate its origin; and while some ascribed it to the physical conditions of the globe, admitting no assimilation of its form to any geometrical type, others imputed it to a defect of the instruments, others to the occasional oscitancy of the observers, and others again to errors of calculation. There was a little of all these. The calculations were revised and considerable errors detected, in the degree of Lapland among others; the observations were discussed, and were found not to be worthy of unrestricted confidence; the condition of the instruments was examined and was not found to be unimpeachable; in fine, since Bouguer first suspected it in his expedition to Peru until now, there have been encountered, in the local attractions of mountains and in the difference of thickness and of material in the crust of the earth, numerous causes of perturbation in the direction of the vertical—that is to say, of the first line of reference; which causes must necessarily exert an injurious influence on the final results of the observations. To whatever attributable, the fact remains, that till near the end of the last century the uncertainty respecting the value of the terrestrial flattening was complete. When we shall have finished the recital of geodesic operations conducted subsequently to those already mentioned, we shall see whether or not the same doubt exists at this advanced stage of the present century. The idea of establishing a system of weights and measures whose fundamental unit, instead of being arbitrary, should present a simple relation to some important element of the same kind derived from the physical world, induced the republican government of France to order in 1792 a new measurement of the terrestrial globe. The operations instituted by Picard and continued by the Cassinis, Maraldi and La Caille, on account of the imperfection of the instruments employed and the errors and doubts involved, were deemed insufficient for the purpose; and Delambre and Mechain assumed the colossal task of renewing them from the beginning and completing them according to various criterions. Delambre exhibited his science and talent in the measurement of the French meridian from Dunkirk to Perpignan, and Mechain in the prolongation of this line through Catalonia to the coasts of Valencia. The labors of these two celebrated geometers having been concluded in 1799, the value of the earth's polar compression was, with the concurrence of an assemblage of savants of different countries, computed at #1, and upon this computation the length of the metre, the base of the new system of weights and measures, was taken as the ten millionth part of one quarter of the meridian just measured.* In 1803 Mechain passed anew into Spain with the intention of prolonging the arc of the meridian to the Balearic islands; but being placed in detention in the fortress of Montjuich, in consequence of the ill understanding then subsisting between his own government and ours, he took the occasion to rectify his former calculations and observations, and from the mortification which he experienced at observing certain discrepancies, fell into a state of dejection, and after having been previously set at liberty, died at Castellon de la Plana in the year 1805. During the two following years, Biot and Arago, assisted by the Spaniards Chaix and Rodriguez, not less worthy of participating in this work than Don Jorge Juan and Ulloa in that of Peru, carried the operation to the issue contemplated by the too scrupulous Mechain. The British triangulation was initiated in 1784 under the direction of General Roy, with the twofold object of perfecting the geographical chart of the United Kingdom, and at the same time prolonging towards the north the measurement of a terrestrial meridian. After being suspended in 1788, these labors were resumed in 1793 under the supervision of W. Mudge, who extended the geodesic system to the extreme confines of Scotland, and deduced, as the value of the earth's compression, the fraction soi, being identical with that obtained in France; yet the Spaniard Rodriguez soon after demonstrated that in the course of the British operations frequent and, to a certain extent, inexplicable anomalies were distinguishable. After the preceding measurements the following are the principal ones in the order of their dates: That of the arc of Lapland in 1801, undertaken with a view of verifying and extending the work of Maupertius. That effected in India, in 1802, 1803, by Colonel Lambton, from which there resulted at first a flattening of go, which Rodriguez, in repeating the calculations, reduced to go. The same Lambton inaugurated another vast operation which, continued by Captain Everest, embraced an actual arc of more than 21°, from Cape Comorin to Kaliana, north of Delhi. That of Piedmont, 1821 to 1823, conducted by the Italian astronomers Carlini and Plana. That of the meridian of Dorpat, begun in 1817 and 1821 by Tenner and W. Struve, and which up to this time prolonged north and south from the frozen coast of Norway to the mouths of the Danube, comprises an arc of more than 25°. Those of Hanover and Denmark, accomplished by Gauss and Schumacher, at the same date with the Piedmontese triangulation. The Prussian, corresponding to the meridian of Köningsberg, which, under the superintendence of Bessel and Bāyer, exhibits a model in labors of this nature, and which it will be difficult for any future ones to excel. Besides these important triangulations, still another deserves notice, which was effected by Maclear in the extreme south of Africa, with the object of
* The calculations required to fix the length of the metre were executed by Swinden on the part of Holland, Tralles of Switzerland. Laplace and Legendre of France, and Ciscar of Spain. Delambre showed, not long afterwards, that, as well in the selection and analysis of the elements of the calculation as in the calculation itself, not all the circumspection desirable had been observed; a judgment which analogous works, effected in the course of the present century, have fully confirmed. The difference between the legal and the theoretic metre—a difference which will never be perfectly known—is, however, very small, and abates but little or not at all the merit of the decimal metric system, which possesses, in other respects, the most unquestionable advantages over other systems now in use. Still it is well to know that between the metre and the quarter of the meridian there does not exist the simple relation which was at first supposed, that unit having been reduced to a conventional type, as is also the case with all others of its kind. s On this subject may be consulted the Tratado de Meteorologia Antiqua y Moderna, per M.