FIGURE O^ THE EARTH. 319 



to our regret, does it Htill prevail ; perhaps, indeed, the conditions of the prob- 

 lem forbid that it should ever do so. 



From the values of the degree measured in Lapland and of the mean degree 

 of France, there was deduced, as the expression of the terrestrial oblatenoss the 

 fraction ^^2 5 which means that, representing the equatorial radius by a length 

 of lo2 units of any kind, the polar radius would be 131 of the same. A com- 

 parison of the degree of Peru with the French gave for the value of this ine- 

 quality the number ^L . that of the extreme degrees of Peru and Lapland 

 ^\q ; while, according to Newton, theory assigned to this quantity the value 

 2^0- Thus it was that, in a point so delicate and interesting, it still seemed 

 ditiicult to know upon what to rely, notwithstanding the diligerice and solicitude 

 applied to the solution of the question in all its bearings. 



It might have seemed that here were contradictions enough ; but in propor- 

 tion as other values of a degree of the meridian were determined, as by liosco- 

 vich between Rome and Rimini in 1754. by Beccaria in Piedmont in i7G2, by 

 Liesgauig in Hungary and Austria in 1768, by l^Lison and Dixon in xVmerica, 

 about the same period, and by La Caille near the Cape of Good Hope, new ir- 

 regularities or anomalies were constantly encountered, incomprehensible upon 

 any one principle, or inexplicable by the adoption of any regular and unique 

 type, however complicated, as the figure of the earth. The confusion grew to 

 such an extent that every one felt impelled to investigate its origin ; and while 

 some ascribed it to the physical conditions of the globe, admitting no assimilation 

 of its form to any geometrical type, others imputed it to a defect of the instru- 

 ments, others to the occasional oscitancy of the observers, and others again to 

 errors of calculation. There was a little of all these. The calculations were 

 revised and considerable errors detected, in the degree of Lapland among 

 others; the observations were discussed, and were found not to be worthy of 

 unrestricted confidence ; the condition of the instruments was examined and 

 was not found to be unimpeachable ; in fine, since Bouguer first suspected it 

 in his expedition to Peru until now, there have been encountered, in the local 

 attractions of mountains and in the diftercnce of thickness and of material in the 

 crust of the earth, numerous causes of perturbation in the direction of the ver- 

 tical — that is to say, of the first line of reference ; which causes must necessa- 

 rily exert an injui-ious influence on the final results of the observations. To 

 whatever attributable, the fact remains, that till near the end of the last cen- 

 tury the uncertainty respecting the value of the terrestrial flattening was com- 

 plete. When we shall have finished the recital of geodesic operations conducted 

 subsequently to those already mentioned, Ave shall see whether or not the same 

 doubt exists at this advanced stage of the present century. 



The idea of establishing a system of weights and measures whose fundamen- 

 tal unit, instead of being arbitrary, should present a simple relation to some im- 

 portant element of the same kind derived from the physical world, induced the 

 republican government of France to order in 1792 a new measurement of the 

 terrestrial globe. The operations instituted by Picard and continued by the 

 Cassinis, Maraldi and La Caille, on account of the imperfection of the instru- 

 ments employed and the errors and doubts involved, were deemed insufficient 

 for the purpose ; and Delambre and Mechain assumed the colossal task of re- 

 newing them from the beginning and completing them according to various cri- 

 terions. Delambre exhibited his science and talent in the measurement of the 

 French meridian from Dunkirk to Perpignan, and Mechain in the prolongation 

 of this 'line through Catalonia to the coasts of Valencia. The labors of these 

 two celebrated geometers having been concluded in 1799, the value of the 

 earth's polar compression was, with the concurrence of an assemblage of 

 savants of different countries, computed at g-i^, and upon this computation the 

 length of the metre, the base of the new system of weights and measures, was 



