XXX 



THE PROGRESS OF 



published the first investigation of Ihem in tli 

 Memoirs of the Academy of Sciences for 1737 

 Simpson also gave a demonstration of them in 

 his Is*ays, published in 1740. 



2. Figure of the earth, Newton, from the 

 theory of universal gravitation, had shown tha 

 the figure of the earth uas an oblate spheroid 

 flattened at the poles. Mm the trigonometrica 

 measurement of France, begun by Picard in 

 1675, and finished by Cassini in 1716, led to a 

 different conclusion. For the degrees on thi 

 north of Paris, instead of lengthening, as ough 

 to have been the case, according to Newton 1 ! 

 theory, uere -shorter by about jith part than 

 those to the south of that capital. This indicate* 

 the diameter of the earth through the poles longer 

 than the equatorial diameter, in the proportion 

 of 96 to 95. This was laid hold of by the Carte- 

 sians in their reasonings against the Newtonian 

 philosophy. 



A clock, made by Graham, having been car- 

 ried out to Jamaica in 1732, by Colin Campbell 

 was ascertained by astronomical observations at 

 the Black River, in latitude 18, (allowing for the 

 influence of heat on the pendulum) to go 1' 58" 

 every day slower than in London. Bradley 

 found that this variation exceeded what would 

 suit the figure calculated by Newton. He, there- 

 fore, suspected some diminution of gravity in the 

 equatorial regions. But the subsequent investiga 

 tions of Maclaurin demonstrated the accuracy of 

 the Newtonian conclusions. The French trian- 

 gulation being resumed in 1740, an error was 

 detected in the measurement of the base, and 

 another not less considerable in the observation 

 of the meridional arc. But the work was not 

 terminated till the year 1754. In the extent of 

 above eight degrees, their lengths appeared 

 regularly to increase from Perpignan to Dunkirk 

 by about -Lth part, marking obviously the 

 oblateness of the spheroid. 



Condamine, in the year 1733, urged the 

 Academy of Sciences to send a party to measure 

 a degree under the equator. The academy 

 adopted the project with zeal, and were lucky 

 enough to obtain the concurrence and support of 

 government In May, 1735, the academicians, 

 Condamine, Bouguer, and Godin sailed from 

 Hochelle to Peru, where they were joined by 

 Juan and Ulloa, two naval officers, deputed by 

 the king of Spain. In the month of July, 1736, 

 they met at Quito, under the line. They chose 

 a valley of the Cordilleras, running about 200 

 miles southwards from that city, and enclosed on 

 both sides by the loftiest ranges of the Andes. 

 Divided into two sets, they carried a series of 

 triangles along the flanks and summits of those 

 mountains, and connected them with the base 

 measured below. The task was peculiarly ardu- 



ous, owing to the severity of the climate, and the 

 total want of accommodation. But eight years 

 of indefatigable industry enabled them to finish 

 the measurement assigned to them. Bouguer, 

 the most eminent of them nil, gave a complete 

 narrative of all their various operations in his 

 Treatise on the Figure of the Earth, not publish- 

 ed till 1749 ; and one of the most scientific works 

 that has ever appeared. He concluded that the 

 earth is not only an oblate spheroid, but so con- 

 siderably flattened as to have its equatorial dia- 

 meter to its axis as 179 to 178. 



3Ieanwhile Maupertuis prevailed on the 

 French minister, Maurepas, to despatch another 

 company, which he reluctantly consented to lead, 

 for a similar purpose, to the arctic circle. The 

 associates of Maupertuis were Monnier, Camus, 

 Orthier, and Clairaut, by far the most eminent 

 of them all. They arrived in Stockholm in 

 June, 1736, and were joined by Celsius, the pro- 

 fessor of astronomy at Upsala, who had brought 

 from London Graham's zenith sector and transit 

 instruments. They proceeded to the bottom of 

 the Gulf of Bothnia, and selected Torneo as their 

 principal station. Their triangles extended from 

 this town to Kittis, a distance of about sixty 

 miles. The whole was finished in little more 

 than a year; and the length of a degree of lati- 

 tude at the Arctic circle was found to be 57,419 

 toises, or 349 toises longer than the correspond- 

 ing measurement at Paris. This gave the ratio 

 of 178 to 179 to the polar and equatorial dia- 

 meters very nearly agreeing with the more 

 extensive operations afterwards performed in 

 Peru. 



But this arctic triangulation, bearing evident 

 marks of haste, became suspected of inaccuracy ; 

 and at the suggestion of Melanderhielm, the Swe- 

 dish academy, about the beginning of the present 

 century, sent Svanberg, with proper assistants, to 

 resume the operations. They not only reclined 

 he former observations, but carried the measure- 

 ment about forty miles farther north. It was de- 

 ermined that the length of a degree in Lapland 

 s only 57,209 toises. This, compared with 

 ^assini's measurement in France, reduces the 

 blateness to ^th of the axis. Comparing the 

 measurements in Lapland and Peru, we obtain 

 he ratio of 302 to 301 for the equatorial and 

 olar diameters. 



Other measurements were made at the Cape of 

 iood Hope, in the papal territories, in England, 

 n the East Indies, but as they have not served to 

 iminish, but rather to increase the anomalies, 

 e need not notice them here. The convertible 

 emliilum of captain Kater, which he was very 

 anguine would furnish an invariable standard of 

 ineal measure, has been also employed as a 

 means of deducing the figure of the earth. But 



