BOOK give the results of those measures, with the names of the astronomers to whom we are indebted for them: II. These measures Picard and Cassini. De Thury and G. Cassini. Note. One toise is equal to 1.06575 English fathoms. Frisi endeavoured to calculate a regular curve according to Newton's theory, which might correspond to those twelve degrees, but he found them either too great or too small; the errors which should be supposed in the measurement in order to reduce them to a regular ellipse, whose minor axis would be to the major in the ratio of 250 to 231, amounted to more than 100 toises, or 1064 fathoms the degree, and for the degree of Hungary to more than 200 toises, or 213 fathoms. Frisi also endeavoured to find, by binary and decimal combinations, a mean term between the different depressions by Frisi. pointed out by the measures; but as a severe criticism of the compared accuracy of each measure did not precede his combinations, we shall not here cite any of the results; we shall only observe that, by choosing, among his binary combinations, the six in which we can have confidence, we find for the mean term a depression almost identical with that furnished by the observations of the pendulum and the late French measures. Here is the comparison: The difference of the axes, or the absolute value of the depression, being taken for unity, the first degree combined with the third, gives for the major axis of the earth 505 si II. milar parts; with the fourth, $53; with the seventh, 292,5; BOOK with the ninth, 290,4; with the tenth, 307,4; and with the eleventh, 270. Therefore the mean term of the depression is equal to 1 rors. The acknowledged impossibility of finding one regular Errors in curve which would correspond with the different degrees those ermeasured, produced different opinions among philosophers. The operation of M. Maupertuis in Lapland was first condemned as uncertain, either on account of the negligence with which it was conducted, or because the arc measured was not of sufficient extent, or, lastly, on account of the doubts which this mathematician himself had entertained with respect to the result of his measurement.* The same judgment should be passed on the measure of Father Liesganig, executed with very inaccurate instruments, and wherein it is now demonstrated that there is a confusion of two stars nine degrees distant from each other, and other constant errors from 10 to 12 seconds, which correspond to 150 toises, or 160 fathoms; consequently this measurement does not deserve to be taken into consideration. Not being aware of this error in the operation of Licsganig, some very excellent mathematicians have given themselves the useless trouble of attempting to reconcile the irregularity of the degrees of Austria and Hungary with the general theory. The measures which might be safely relied on, took in but a small portion of the globe. Neither Frisi nor the other philosophers who have written on this subject, were acquainted with the degree measured in the year 1702, in China, in the 40th degree of latitude, by the Jesuit Thomas, the value of which degree was found to be 56,987.899 toises, or 60735 fathoms of six feet each; which, by supposing a depression of 331, would differ on He makes the degree in his Figure of the Earth, 57,405, and in the Elements of Geography, 57,438. + Zach. Astron. Correspond. viii. 507, et seq. Dubourguet, Traité de Navig. p. 283, 308. &c. II. BOOK ly 25,983 toises, or 26 fathoms, in excess from the value presumed. But this measurement being susceptible of several interpretations, there can be no great harm in neglecting it.* Errors caused by Some persons have been tempted to doubt of the possiattraction, bility of measuring a degree of the meridian with perfect accuracy. The errors inseparable from the nature of the instruments then employed, might amount to 3 or 4 seconds for the celestial arc, or 60 toises for the terrestrial degree. The attraction of mountains, which deranged the plumb line by which the vertical is determined, excited the most restless doubts. This effect of gravitation, a striking proof of Newton's general theory, might affect measurements in other respects executed with the greatest care, since a deviation of the vertical line, of 15 seconds only, at both extremities of the arc measured, would cause an error of 500 toises, or 533 fathoms, which quantity is greater than the presumed difference of the two extreme degrees under the equator and the pole. But Newton had estimated this attraction at two minutes, for a mountain three English miles in height and six broad. This estimate, it is true, has appeared excessive. By the observations which Bouguer and La Condamine carefully made in 1737, in Peru, near the mountain of Chimborazo, the plumb-line deviated 7 seconds in consequence of the attractive force of that mountain, which, according to Newton's theory, should have produced an effect 13 times greater; but the nature of the volcanic rocks of that mountain renders the experiment dubious. Similar effects have been observed in the Pyrenees, the Alps, the Appennine mountains, and in Scotland, where Maskelyne repeated those observations with the utmost precision, Hallerstein, Obser. Astr. Pekini Sinarum factæ, p. 366. Vindob. 1768. Comp. Zach. Ast. Corresp. i. 248, 251, 589, 594. + D'Alembert, Encyclopedie, Fig. de la Terre. Bouguer, Fig. de la Terre, Sect. 1. 4. &c. Bouguer, Fig. de la Terre. II. 53 and obtained a result which approaches nearer to Newton's BOOK theory.* It is very possible that this attraction may have affected the measures taken by Lacaille, since that astronomer performed no experiment to determine the effect of the mountains of the southern part of Africa, on the plumb-line of the instrument which he made use of. the irregu the meri. At length, a simple and decisive idea presented itself to Opinion the mind of some superior geniuses, who were fatigued with concerning the interminable dispute of the earth's depression. It was larity of supposed that the curvature of the terrestrial spheroid might dians. be subject to some slight irregularities. Why should nature, which is not fond of geometrical figures, have made the earth a perfect and regular ellipsoid? Buffon was one of the first who proposed this opinion;† Condamine seems to have favoured it, and Maupertuis, who at first had loudly rejected it, at last only doubted of it: Lacaille, whose measures did not agree with any other, naturally inclined to an explication which justified his operations. However, natural philosophers in general still objected to this opinion, which was feebly supported by those who had advanced it. thesis. A more serious attempt to maintain the regular ellipsoid, M. Klüwas made by M. Klügel, a German mathematician. To de- gel's hypomonstrate that all the degrees accurately measured, even that of Lacaille, might be applied to a regular ellipse, he supposed a small difference existed between the minor primitive axis of the terrestrial ellipsoid, Pp Fig. 16, and the actual axis of rotation п; whence would result for example, that the Cape of Good Hope, might have been originally nearer to the south pole, or, more accurately speaking, that the southern extremity of the axis of rotation. has changed its position with respect to the equator Eq. Therefore the southern degree a b, although more distant from the pole of rotation than the northern degree from Philosophical Transactions, 1775, p. 500. + Nat. Hist. tom. i. p. 165. Rapport sur les Mésures du Pérou, p. 262. II. BOOK the pole п, might nevertheless be in the same situation with respect to the true minor axis of the ellipsoid Pp; and would consequently have the same absolute value, notwithstanding the difference of latitude.* It is obvious what revolutions would take place on the earth, if this hypothesis had any foundation. It is evident that the major axis of the globe would no more coincide with the plane of the equator; and is it possible, according to the laws of hydrostatics, that the terrestrial ellipsoid could perform its revolution round any other axis than its real minor axis? But, whatever objections may be made to M. Klügel, his hypothesis appears so ingenious, and would be so fruitful in interesting results for physical geography, that we thought proper to give an idea of it here. Biot, &c. Such were the doubts of astronomers and mathematicians respecting the figure of the earth, when a political project afforded an opportunity for undertaking a new measure of the arc of the meridian, which, passing through Measure the capital, traverses France. The National Convention ment con- ordered that a uniform and permanent system of weights ducted by Delambre, and measures should be established. The philosophers proMechai, posed to found the basis of this system upon nature, and to take as the primitive unity of measure, or metre, the ten millionth part of a quadrant of the terrestrial meridian, that is, the space between the equator and the pole. It was said that a metrology founded on such a basis would belong to every age and nation. But how were they to find precisely the length of the fourth part of the meridian? They could not deduce it from the ancient measures, for these contradicted each other; it was therefore determined that the new metrological system should be rendered more authentic by founding upon new operations, conducted with a precision till then unknown, and directed by the most able astronomers. Delambre and Mechain were appointed to measure the arc of the meridian intercepted between the Klügel, Dimensions de la Terre, &c. in the Astronomical Collections of Berlin, iii, 164, 169. |