313 



QBODB8T. 



QBODKBY. 



844 



circle, an imporUnt survey wu undertaken in Franc* toy Casein' 

 de Thury and Lacaille, for the purpoM of verifying the former measure 

 of the meridian and laying the foundation of an accurate map of the 

 kingdom. Six new bases were measured, each twice ; that near Paris 

 fire time*. The angle* were observed with a 2-fcet quadrant, and 

 were reduced to the horizon and centre of the station. The latitude* 

 were observed at the extremities and three intermediate stations ; and 

 the length of the degree deduced from each of the four arcs. The 

 results are not now important, as the same arc has since been measured 

 with still greater precision by Mechain and Delambre. In the course 

 of the operation the length of a degree of longitude was also deter- 

 mined. The terrestrial arc extended across the mouth of the Rhone 

 from Cette in Languedoc to Mont St. Vietoirc in Provence ; and the 

 difference of longitude was found by exploding gunpowder in the open 

 air at an intermediate station, and noting the difference of the apparent 

 times at which the flash was seen at both extremities. (' La Meri- 

 dienne de 1'Observatoire Koyal de Paris Venfice, Ac.,' 1744.) 



In 1751 Boacorich and Lemaire began a survey of the Papal States, 

 and in the course of the operation determined the meridional distance 

 between the parallels of Rome and Rimini. The sides of the triangles 

 were computed from a base measured on the seashore near the latter 

 place, which consisted of two parts making an angle of 170 52' 15". 

 Another base was measured on the Via Appia, near Rome. The 

 angles were observed with a quadrant of 8 feet, and the latitudes with 

 a sector of 9 feet. The result gave 1 = 56,979 toises ; but it has been 

 shown to be affected with errors of considerable magnitude. (Boscovich, 

 ' De Litteraria Expeditione per Pontificam Ditionem ad dimentiendos 

 duos Meridiani Gradus, Ac.,' Romso, 1755 ; De Zach, ' Correspondance 

 Astronomique,' vol. vi.) 



Lacaille, in 1752, measured an arc of meridian at the Cape of Good 

 Hope. The two extremities were connected by two large triangles, 

 whose common side was deduced by means of two small triangles from 

 a base of 64G7'25 toises (78 miles), situated near the middle of the 

 arc. The amplitude (1 13' 17"'33) was determined with a zenith 

 sector of 6 feet, and the angles were measured with a 3-feet quadrant. 

 The final result gave 1= 57,087 toises, or 364,728 English feet, which 

 is nearly equal to the degrees measured in France, 10 farther from 

 the equator. (Lacaille, ' Mdmoires de 1'Acad. Royale des Sciences ' 

 for 1751 ; ' Fundamenta Astronomic,' 1759.) It will be seen that 

 Mr. Maclear has recently succeeded in satisfactorily accounting for 

 this apparent anomaly. 



Beccaria, between 1762 and 1764, measured an arc of the meridian 

 in Lombardy. The instruments and methods used were similar to 

 those of Boecovich. The amplitude was 1 7' 47 "7, and the length of 

 the degree found equal to 57,468 toises. This result greatly exceeds 

 that which other measurers gave reason to expect ; and the cause has 

 been ascribed to the disturbance of the plumb-line of the sector by 

 the attraction of the mountain masses on which the arc abutted at 

 both extremities. (Beccaria, ' Gradus Taurinensis,' &c., 1774.) This 

 arc was re-measured by Plana and Carlini in 1822, who found the 

 amplitude to be 1 7' 31"-07, and the degree equal to 57,625 toises, a 

 result still more at variance with other determinations. 



Two surveys, executed by Liesganig in Austria and Hungary, 

 between 1762 and 1769, have been usually cited in the history of 

 geodetic measures, but are now known to be deserving of no credit. 

 The Austrian operation comprehended nearly three degrees of the 

 meridian of Vienna, from Brunn in Moravia, to Varasdin in Croatia ; 

 and since the beginning of the present century the triangles have been 

 re-measured in the course of a general trigonometrical survey of the 

 Austrian states. For some distance from Brunn, Liesganig's results 

 agree with the recent ones ; but in the last triangles (in consequence, 

 it is supposed, of mistaking a signal) the errors in the length of the 

 side* are from 1066 to 2509 toises; while that in the length of 

 the meridional arc amounts to 4533 toises. Baron Zach, who examined 

 the manuscripts of Liesganig, affirms that both the astronomical and 

 geodetical observations were not only faulty and ill calculated, but de- 

 signedly altered to produce a better agreement. (Liesganig, ' Dimensio 

 graduum Meridianii Viennensis et Hungnrici,' Viennse, 1770; De Zach, 

 ' Correspondance Astronomique,' vol. vii.) 



The resolution adopted by the French Convention in 1791 to 

 establish a decimal system of weights and measures of which the unit 

 should be an aliquot part of the quadrant of the meridian, gave rise to 

 a remeasurement of the meridian of Paris from Dunkirk to Barcelona. 

 In the conduct of this survey, the most important in reference to the 

 figure of the earth that has yet been executed, the French astronomers 

 introduced numerous important improvements both into the theory 

 and practice of geodesy. The northern part, from Dunkirk to Rhodez, 

 including about two-thirds of the whole, was assigned to Delambre, 

 and the southern, from Rhodez to Barcelona, to Mechain. Two base* 

 were measured near the extremities ; one at Melun, the other near 

 Perpignan, by a method which will be described farther on. All the 

 angles, geodetical and astronomical, were measured with repeating 

 circles, and the observations were examined and compared by special 

 commissioners, who fixed the mean values to be used, and directed the 

 calculations. The azimuths and latitudes were determined at five 

 stations, Dunkirk, Paris, Evaux, Carcassonne, and Montjouy, so that 

 the whole was divided into four partial arcs, the lengths and ampli- 

 tude* of which are given in the tilde at the end of this article. No 



doubt can be entertained of the excellence of the geodetical part of 

 this celebrated operation, but the latitudes have been considered liable 

 to some uncertainty, owing to the feeble power of the telescope and 

 other causes depending on the nature of the instruments with which 

 the observations were made. [REPEATINO CIRCLE.] In fact, when 

 Mechain had occasion to determine the latitude at Barcelona, which is 

 only about a mile distant from Montjouy, he found a discordance 

 between the results at these two place* amounting to 3*, and all his 

 efforts to reconcile or explain the inconsistency wore fruitless. 



From the result* of this operation, compared with the degree 

 measured in Peru, the. dimensions and ellipticity of the earth were 

 deduced, and the mitre determined. The earth was assumed to be a 

 spheroid of revolution; the deduced ellipticity was 1-7-334; ami tin- 

 mitre, or ten-millionth part of the quadrant of the meridian, at the 

 temperature of freezing water, was fixed at 443,296 lines of the toise of 

 Peru, the normal temperature of the iron toise being 13 of Reaumur, 

 or 61 15' of Fahr. (' Base du Systcme Mftrique Decimate ;' 3 vols. 

 4to., Paris, 1805, 1807, 1810.) 



The prolongation of the meridian through Spain, which formed a 

 part of the original project, was interrupted by the death of Mechain, 

 but was subsequently effected (1807-1809) by Biot and Arago. By 

 means of a very large triangle, one side of which exceeded 100 miles, 

 they connected the island of Iviza with the coast of Valentia ; anil 

 another triangle carried the arc to Formentera, a small island still 

 farther to the south. The amplitude was thus increased to upwards 

 of 12J degrees. (Biot and Arago, 'Recueil d'Observations Geode- 

 siques,' &c., 1821.) 



It is a circumstance deserving of notice, that notwithstanding the 

 parade of a commission and the extraordinary precautions token to 

 ensure accuracy in the computations, a serious error was committed 

 with respect to this arc, which was only recently detected by Puissant. 

 It appears that, through inadvertence or the misapprehension of a 

 formula, the distance between the parallels of Montjouy and Mola (the 

 station on Formentera) was 'computed without applying the proper 

 correction for the convergence of meridians. The distance originally 

 given by the commissioners was 15360577 toises ; but the distance 

 when the computation is correctly made is 153673-61 toises (Besael, 

 'Astronomische Nachrichten,' No. 438), the difference being 67'84 toiees. 

 In consequence of this correction, and of the introduction of some 

 other arcs since measured into the data for determining the figure of 

 the earth, the length of the quadrant of the meridian expressed in 

 terms of the legal mitre, according to the best determination which 

 can at present be made of the dimensions of the earth, is 10,000,85576 

 mitre! ; in other words, the legal metre would require to be lengthened 

 by about the '00,000,856th part of itself in order to agree with the 

 ideal mitre, a ten-millionth part of the quadrant of the elliptic 

 meridian. This circumstance may serve to show the futility of any 

 proposal to restore a lost standard from its assigned relation to the 

 magnitude of the earth. The French mitre is in fact nothing more 

 than an arbitrary part of the toise of Peru, in terms of which the bases 

 were measured and the meridian computed. 



The arc which was measured by Maupertuis and his associates in 

 Lapland in 1736, was remeasured by Svonberg in 1801-1803, and 

 extended in both directions so as to increase the amplitude about 40". 

 A new base was measured with iron bars which were compared with a 

 standard milrt in Paris. The terrestrial angles, as well as the hit 

 and azimuths, were measured with; repeating circles, and the methods 

 of observing and computing the results the same generally as those of 

 Delambre. All the details of the operation appear to have been 

 executed with great skill and ability : but by reason of the inadequate- 

 ness of the instrument, the latitudes are not supposed to be very 

 certainly determined ; and there is some doubt with respect to the 

 temperature at which the measuring-rods were compared with the 

 standard inelrr. The result gave 1 = 57,196 toises, which agrees much 

 better than that of Maupertuis with other determinations. (Svan- 

 berg, ' Exposition des Operations faites en Lapponie pour la De'termina- 

 tion d'un Arc du Meridien,' Ac., Stockholm, 1805.) 



A trigonometrical survey of Holland was executed under the 

 direction of General Krayenhoff, from 1801 to 1809, which may be 

 regarded as a continuation of the general survey of France. No base 

 was measured, but the distances were computed from a side of one of 

 Delambre's adjacent triangles. The angles were measured with 

 repeating circles, and Delambre's methods adopted throughout. As a 

 verification, some distances were deduced from two different series of 

 triangles, and the greatest discordances were found to amount only to 

 one mitre in 9123. (' Precis Historique des Operations Gcodcsi* . 

 Astronomiqucs faites en Hollandc pour servir de base a la Topographic 

 de cet 6tat; Executes par le Lieutenant-General Krayenhoff,' Ac., 

 A la Haye, 1815.) 



The first geodetic survey executed in England was undertaken 

 with the immediate object of establishing a trigonometrical connection 

 between the observatories of Paris and Greenwich, in order to determine 

 the difference of longitude. A memoir on the subject, drawn up by 

 Cawrini de Thury, was in 1 783 presented by the French ambassador to 

 the king, who placed funds at the disposal of the Koyal Society for 

 providing the requisite apparatus. In order to accomplish the proposed 

 object, it was necessary to connect the observatory of Oreenwich with 

 the French arc of meridian, by carrying a series of triangles from 



