FIGURE OF THE EARTH. 329 



multitude of other, the most common, astronomical or geodesical operations, 

 would scarcely amount in number to sixty. So scanty a result should, in our 

 opinion, be attributed to two quite distinct causes. In the comparative experi- 

 ments made with the pendulum, there is sought, in the first place, a difference of 

 length or of numbers so small that the least inadvertence in the operation, or a 

 disturbing cause unworthy elsewhere of consideration, Avill materially influence 

 the result and impair its exactness. Andmoreovei% even when the observations 

 are conducted throughout with all the requisite accuracy — a thing, we repeat, 

 of great difficulty — still the theoretic principle of their combination for dedvicing 

 the terrestrial ellipticity supposes that the density of our globe, though variable 

 according to an arbitrary law from the surface to the centre, continuos'identically 

 the same in each layer concentric with the superficial one ; an hypothesis which 

 departs in some degree from the reality of nature, and which on that account 

 cannot lead to results of absolute certainty. After these considerations, it will 

 not be a matter of surprise that the values of the terrestrial ellipticity, deduced from 

 experiments made in the present era by Borda first, and afterwards by Biot, 

 chiefly at different points of the French meridian, by Kater in England, by the 

 navigators Freycinet, Duperry, Sabine, Foster and others, under very different 

 and distant latitudes, should sensibly vary from one another, and likewise to 

 some extent the final number, deduced from the examination of all of them, when 

 compared with that which results from the sum of the principal geodesic labors. 

 But to Avhat at most does the difference amount 1 From the experiments made 

 with the pendulum, there results as the value of the earth's polar compression 

 the number ^q, somewhat greater than the fraction gl^ and less than ^; the 

 difference of these two extreme fractions is equal to -^^qq ; so that the d'ifference 

 of the results obtained by help of the pendulum and by the ordinary processes 

 of geodesy will be found to be represented by a number still less than the last. 

 Admitting, then, that the value of the equatorial radius is in metres 6,377,397, 

 there would remain in the length of the polar radius an uncertainty of 2.362 ; 

 and this, it must not be forgotten, on the supposition, really more unfavorable 

 than is warranted, that the doubt respecting the polar compression of the earth 

 would present to us as equally uncertain the two fractions 3J ^j and -^^-^j. But 

 the relation of the number 2.362 to the value of the equatorial or the polar 

 radius is lower than that of 1 to 1000 : thus in the appreciation of a quantity 

 composed of a thousand equal parts, it would be at last doubted whether we 

 had counted one part more or less than Avas proper ! Instead of being surprised 

 at the existence of such an uncertainty as this, it might well cause astonishment, 

 as Prof. Airy has remarked in reference to this subject, that man should have 

 arrived at a knowledge so precise in a matter so difficult and obscure ; while 

 there is still room for confidence that further advances are in his power, and 

 adequate encouragement to persist in the pursuit of the truth. 



That this confidence and encouragement exist is shown by a simple reference 

 to the projects of new geodesical operations and experiments, suggested by 

 some of the most celebrated of cotemporary astronomers. In 1857, for example, 

 Biot proposed to the Academy of Sciences of Paris that a new determination 

 should be undertaken, by methods and with instruments more delicate than 

 were before known, of the whole extent of the arc of Peru as well as of the 

 various arcs of parallel measured in Europe ; that experiments with the pendu- 

 lum should be multiplied in those localities where considerable anomalies have 

 been noted in the direction of the vertical, or where their existence is suspected, 

 with a view to ascertain their cause or causes ; in a word, that no means should 

 be spared of discovering all the accidents of form and density which distinguish 

 the terraqueous globe from the theoretical ellipsoid deiined by Bcssel and the 

 mathematicians who, with a degree of precision difficult to surpass, have cither 

 preceded or followed him in this enterprise. The ideas of Biot, de'iberately 

 considered and digested eventually into the colossal project of measuring a n(;w 



