FIGURE OF THE EARTH, 323 



their poles, or the extremities of the axis of rotation, and an induction founded 

 on well-proved facts, showing that the terraqueous globe existed, at some very- 

 remote period, in a state of perfect fluidity, furnished suificient grounds for con- 

 cluding that the earth, instead of being spherical, would naturally present an 

 elliptical figure, or one slightly depressed in the direction of the polar axis. 

 This being conceived, it remained simply to deduce from geodesical operations 

 the value of the depression, or, Avhat amounts to the same thing, the relation of 

 the two axes of the generating ellipsoid, as well as the definite dimensions of 

 those axes, for all which it had, in strictness, sufficed to measure two small 

 arcs of meridian in widely separated latitudes — one, for instance, near the equa- 

 tor, the other in some inhabitable region nearest to either pole ; nor, on the 

 above supposition, would it have been of consequence whether those arcs cor- 

 responded to the same or to difi"erent meridians, while any intermediate arc, 

 which might be measured, would serve for the verification of the former, as well 

 as of the law of ellipticity, assumed as a point of departure. When the results 

 of the scientific expeditious to Peru and Lapland were known, and were com- 

 pared in the proposed view with those obtained in France, and for the first time 

 the values of the oblateness of the earth and of the equatorial and polar axes 

 were deduced, it was observed, not without surprise, that between the final de- 

 ductions drawn, with the aid of so much experience, and with the theoretical 

 ideas generated by those laborious investigations, there did not exist all the 

 conformity which had been hoped for. The discordance, however, was at once 

 attributed, not so much to the defect of the theory, as to the errors, to a certain 

 extent inevitable, which had been committed in the course of the operations, or 

 to local irregularities in the surface of the earth ; but, as time advanced, and 

 instruments were improved, while the obstacles already overcome served as 

 useful indications to succeeding observers, the conviction was acquired, cither 

 that the form of the earth was not so simple and regular as was at first sup- 

 posed, or, more probably, that the heterogeneity of its mass, and the inequality 

 of the thickness of its crust, acting as disturbing causes, embarrassed the labors 

 of geodesy, and opposed their indefinite advancement. Certain it is, at any rate, 

 that at the close of the last century, as has been already intimated, great inde- 

 cision prevailed as to the real value of the earth's ellipticity, and that, but for 

 the resort to an ingenious mode of eluding the difficulty, the same doubt would 

 have prevailed on this point to the present day. A single citation will prove 

 the truth of what has been just said. The "Russian general, Schubert, a dis- 

 tinguished mathematician and astronomer, collated, in a memoir published at 

 St. Petersburg in 1859,* the elements of the eight principal arcs of meridian 

 yet known, being the Russian arc, measured by Hansteen, Sclander, Struve, 

 and Tenner ; the Prussian, the English, and the French arcs ; the arc measured 

 in Pennsylvania by Mason and Dixon ; that in Peru, by the Franco-Spanish 

 commission ; that in India, by Lambton and Everest ; and that measured at 

 the Cape of Good Hope by Maclear. By combining these eight arcs, two hy^ 

 two, in all possible manners, the Russian savant deduced, for the elements 

 of the terrestrial ellipsoid, twenty-eight difTerent results, between limits much 

 wider, doubtless, than the reader would imagine. Limiting ourselves, for 

 example, to the polar compression, the twenty-eight valuations just cited 

 group themselves in this manner : Three are higher than the fraction 3^17 ; fo"!' 

 are higher than ^iij, and lower than the preceding fraction ; nine are comprised 

 between the last and ^i^ ; seven between that and -^^ ; three between -r^^o and 

 5I0 ; and two, finally, being those corresponding to the combinations of the 

 Russian with the Prussian arc, and of the arc of the Cape with that of Pennsyl- 

 vania, are lower than the fraction y^W- Supposing even that there weregood 

 and sufficient reasons for subtracting from the extreme values, it will still be 



* EsMi d'une Determination dc la Veritable Figure de la Tcrre. 



