341 



GEODESY. 



GEODESY. 



342 



than the equatorial by about l-300th ; but they have served at the 

 same time to demonstrate that the earth i% not a spheroid, that it is 

 not a solid of revolution, and that the figures of the northern and 

 southern hemispheres are dissimilar. Hence if we suppose a solid of 

 revolution having its axis in the same direction as that of the earth, 

 and osculating the surface of the latter, the excentricity of this 

 spheroid varies both with the latitude and the longitude of the 

 place. 



If the materials which compose the solid mass of the earth had equal 

 capacities for heat and became liquid at equal temperatures, the 

 spheroid of revolution would most probably be the figure assumed at 

 the epoch when the cooling of the whole had rendered it solid. Such 

 however is not the case ; a great portion of the surface of the globe is 

 yet liquid, and of the solid parts some must have assumed that state 

 prior to others. It is also possible that the temperature of space is 

 variable within the extent of the solar system, and therefore the 

 conditions for the cooling of the northern and southern hemi- 

 spheres may be different, and a very email difference would suffice 

 to produce, in a long series of ages, a marked difference between 

 the temperatures of the two hemispheres, and therefore a corres- 

 ponding difference would arise relative to their forms. The general 

 sphericity of the earth cannot be otherwise conceived than by its 

 primitive fluidity, and the irregular cooling of its parts accounts suffi- 

 ciently for the observed departures from the spheroidical shape, which 

 would have been otherwise produced by the attraction of its parts and 

 the centrifugal force of rotation. The other bodies of the solar system 

 which have short periods of rotation present the analogous appearance 

 of unequal axes, the equatorial axis being always the longer. 



In the trigonometrical survey of portions of the earth's surface, the 

 extent or area may be computed more and more approximately by the 

 suppositions of such portions being plane, spherical, spheroidical, and 

 lastly of being coincident with the osculating spheroid. 



As the method of conducting ordinary surveys for topographical 

 purp *es will be explained under another head [SURVEYING], we 

 shall here treat of geudetical measurements in reference only to 

 general geography and the figure of the earth. We propose therefore 

 to give a short historical notice of the principal trigonometrical surveys 

 which hive been undertaken in different paits of the world for 

 measuring terrestrial degrees, or accurately delineating considerable 

 portions of the earth's surface ; t<> describe the general nature and 

 objects of the operations to be performed in carrying on such surveys, 

 and the principles upon which the computations are made ; and to 

 state the dimensions of the earth, considered as the spheroid of revo- 

 hition, which have been deduced from the comparison of those 

 measures of meridional arcs which appear to have been executed with 

 the greatest precision. 



The merit of first applying trigonometry to geodetic operations 

 bclons.'S to Willebrord Snell [SXELL, in Bros. Drv.], who in 1617 under- 

 took a survey of Holland, for the double purpose of establishing the 

 geographical positions of the principal cities in that country, and 

 measuring a degree of the terrestrial meridian. The method which he 

 followed was the same in principle as that which would be adopted at the 

 present time. Having formed a series of triangles extending over the 

 country, he observed their angles with a quadrant, and computed their 

 sides from a base which was carefully measured with wooden perches 

 on the ground. He also determined the direction of the meridian at 

 Leyden, ami observed its inclination to a side of one of his triangles, 

 and th.reby obtained the bearings of the different angular points. 

 Lastly, by observing the altitude of the pole-star with a five-feet 

 , mt at Alkmaar, Leyden, and Bergen-op-zoom, he determined the 

 amplitudes of two celestial arcs ; and on comparing the amplitudes 

 with the terrestrial distances computed from the triangles, and reduced 

 to the direction of the meridian, he concluded the length of a degree 

 to be 28,500 Rheinland perches, or 55,100 French toises, equivalent to 

 about 06| English miles. The result is about three miles too small. 

 In 1621 Snell measured a new base, and was preparing to correct some 

 errors which he had detected in the calculations, when his labours 

 were cut short by his early death. Musschenbroek, a century after- 

 wards, re-observed the latitudes, and revised the calculations, and 

 found 1 = 57,003 toises, or 69 miles. (Snellius, ' Eratosthenes Batavus 

 de Terra ambitus vera quantitate.' 4c., Lugduni Bat.^1617 ; Musschen- 

 broek, ' Dissertationes Physicae,' &c., Ib., 1729.) 



About the middle of the same century Riccioli and Grimaldi undertook 

 to measure an arc of a great circle of the earth in Lombardy. They 

 formed a chain of triangles between Bologna and Modena, observed their 

 angles wit'i a quadrant, and computed their sides from a base measured 

 on the road leading out of Bologna. The distance between the two cities 

 was found to be 20,439 paces. Instead of reducing this distance to 

 the merMian, according to the method of Snell, Riccioli sought to 

 determine the arc of the vertical circle in the heavens intercepted 

 between the zeniths of the two stations. This determination, which 

 presumes an accurate knowledge of the latitudes and the declinations 

 of the stars, could not, in the state of astronomy at that time, be made 

 with sufficient precision, and accordingly the result was still more 

 erroneous than that of Snell. He found the amplitude of the celestial 

 arc to be 19' 25", whence 1 = 63,159 paces of Bologna, or nearly 744 

 English miles. (Riccioli, ' Geographic et Hydrographire Reformats 

 Libri XII.,' &c., Bonnoniao, 1661.) 



Picardjln 1669, undertook to measure the meridional arc between 

 Paris and Amiens. This operation was conducted with far greater 

 precision than any previous one of the same kind, and the result had a 

 memorable application, as it furnished Newton with a sufficiently 

 accurate knowledge of the earth's diameter, and consequently of the 

 dimensions of the lunar orbit, to enable him to compute the force of 

 terrestrial attraction at the distance of the moon, and thereby establish 

 the law of gravitation. The angles were measured with a quadrant, 

 furnished with telescopes having cross-wires in their foci (an improve- 

 ment in the art of observing then newly introduced), and the sides 

 computed from a base of 5663 toises. The latitudes were observed 

 with a zenith sector at Malvoisine (near Paris), at Amiens, and at an 

 intermediate point, so that two comparisons of celestial and terrestrial 

 ares were obtained, the mean of which gave 1 = 57,060 toises, equivalent 

 to 364,876 English feet, or about 69'1 miles. This is a very near 

 approximation to the true length of the degree at the same place, as it 

 is given by recent and more exact determinations, but it proceeded, in 

 part, from an accidental compensation of errors. (Picard, ' Mesure da 

 la Terre," folio, 1671 ; ' Degre" du MeYidien entre Paris et Amiens, par 

 M. Picard, avec les Observations de MM. de Maupertuis, Clairaut, 

 Camus, Le Monnier, 8vo.' 1740.) 



Picard's measurement gave rise to a more extensive operation, the 

 prolongation of the meridian through the whole extent of the French 

 territory, and the construction of a geometrical map of France. The 

 triangulation for this purpose was begun in 1683 by Dominic Cassini, 

 but after a few angles had been measured, the work was suspended till 

 1700, when it was resumed, and in the following year the triangles were 

 extended to the Pyrenees. The northern part, from Paris to Dunkirk, 

 was completed by James Cassini, in 1718. Cassini adopted Pieard's 

 base, but two bases of verification were measured near the extremities 

 of the arc. A very unexpected result was deduced from this operation, 

 On comparing the celestial arc with the measured distance between the 

 parallels of Paris and Collioure (the southern extremity), the length of 

 the degree was found to be 57,097 toises, while the arc between Paris 

 and Dunkirk gave 1 = 56, 956 toises. From this it appeared that the 

 degrees of the meridian become shorter as the latitude increases a 

 consequence directly opposed to the theory of attraction. (Casiini, 

 'Traite' de la Grandeur et de la Figure de la Terre,' Paris, 1 720 ; 

 Amsterdam, 1723.) 



The discussions to which this result gave rise in the Academy of 

 Sciences were the immediate cause of the two celebrated expeditions 

 to Peru and Lapland, which a few years, 1 iter were und rtaken under 

 the auspices of the French government for the purpose of definitively 

 settling the question of the compression of the earth. In 1735 

 Bouguer, La Condamine, and Godin, members of the Academy, set sail 

 for Peru, where they were joined by two Spanish officers, Juan and 

 Ulloa. From the unfavourable nature of the country, the defective 

 state of their instruments, and other causes, this party encountered 

 very great difficulties, and several years elapsed before they were 

 enabled to complete their object. An arc was at length measured on 

 the plain of Quito, between the parallels of 2' 31" N. and 3" 4' 32" S. 

 lat. A primary base of 6274 toises was measured by Bouguer and 

 Godin separately ; and a base of verification at the southern extremity 

 of 5259 toises was found to differ less than a toise from the length 

 computed from the first base through the series of triangles. The 

 measuring-rods were of deal, 20 feet in length, and compared daily with 

 nn iron toise, which from this application has been called the toise of 

 Peru, and become celebrated in the history of geodesy, being in fact 

 the standard to which all the degrees measured on the Continent 

 have been ultimately referred, and in terms of which the greater 

 number of them have been expressed. The angles were measured with 

 quadrants of 24 feet radius, and reduced to the horizon by calculation ; 

 in some instances the difference of altitude of two signals observed 

 from the same station exceeded a mile. The latitudes at the 

 extremities were observed simultaneously with zenith sectors. Three 

 different results were computed. Bouguer found the length of the 

 degree, reduced to the sea-level, to be 56,753 toises at the temperature 

 of 13 of Reaumur's scale (61} Fahrenheit); Condamine found 

 56,749 toises, and the Spanish officers 56,768 toises. (Bouguer, ' La 

 Figure de \A Terre,' &c., 1749; Condamine, ' Mesure des Trois Premiers 

 Degre's de Meridien dans 1'Hemisphere Australe,' 1751; Juan and 

 Ulloa, ' Voyage Historique de 1'Amdrique meYidionale,' 1752.) 



While Bouguer and his associates were carrying on their operations 

 in Peru, an arc of the meridian wa^ measured near the polar circle by 

 Maupertuis, Clairaut, Camus, Lemonnier, and Outhier. This party 

 reached Tornea, at the extremity of the Gulf of Bothnia, in 1736, and 

 established a chain of triangles along the line of the river stretching 

 northward to the parallel of 66 48' 22" N. lat. A base was measured 

 on the frozen surface of the river. The latitudes were observed with 

 a /"tilth sector by Graham. The amplitude was found to be 57' 29"'6, 

 and the terrestrial distance between the parallels 55,023 toises ; whence 

 1 = 57,422 toises, exceeding Picard's degree by 362 toises. This 

 result (which however is now supposed to err considerably in excess) 

 put an end to all doubts respecting the decrease of the meridional 

 degrees on going from the equator, and the consequent compression of 

 the earth at the poles. (Maupertuis, ' La Figure de la Terre de'ter- 

 mine'e par les Observations au Cercle Polaire/ 1738.) 



Soon after the return of Maupertuis and his party from the polar 



