THE FIGURE OF THE EARTH. 17 



have devoted themselves to the solution of these problems. 

 It is well that we should bear in mind that all the great re- 

 sults which have been attained by intellectual labor and by 

 mathematical combinations of ideas, derive their importance 

 not only from that which they have discovered, and which 

 has been appropriated by science, but more especially from 

 the influence which they have exerted on the development 

 and improvement of analytical methods. 



" The geometrical figure of the earth, in contradistinction 

 to the physical,* determines the surface which the superficies 

 of water would assume in passing through a net-work of 

 canals connected with the ocean, and covering and intersect- 

 ing the earth in every direction. The geometrical surface 

 intersects the directions of the forces vertically, and these 

 forces are composed of all the attractions emanating from 

 the individual particles of the earth, combined with the cen- 

 trifugal force, which corresponds with its velocity of rota- 

 tion.! This surface must be generally considered as approx- 

 imating very closely to an oblate spheroid, for irregularities 

 in the distribution of the masses in the interior of the earth 

 will also, where the local density is altered, give rise to ir- 

 regularity in the geometrical surface, which is the product 

 of the co-operation of unequally distributed elements. The 

 physical surface is the direct product of the surface of the 

 solid and fluid matter on the outer crust of the earth." Al- 

 though, while it is not improbable, judging from geological 

 data, that the incidental alterations which are readily brought 

 about in the fused portions of the interior of the earth, when 

 they are moved by a change of position of the masses, may 

 even modify the geometrical surface by producing curvature 

 of the meridians and parallels in small spaces, and at very 

 widely separated periods of time ; the physical surface of the 

 oceanic parts of our globe is periodically subjected to a 

 change of place in the masses, occasioned by the ebbing and 

 flowing (or, in other words, the local depression and eleva- 

 tion) of the fluid element. The inconsiderable amount of 



* Gauss, Bestimmung des Breitenunterschiedes zwischen den Stern- 

 warten von Gottingen und Altona, 1828, s. 73. (These two observato- 

 ries, by a singular chance, are situated within a few yards of the same 

 meridian.) 



t Bessel, Ueber den Einfluss der Unregelmassigkdten der Figur der 

 Erde auf geoddtische Arbeiten und ihre Vergkichung mil astronomischen 

 Beslimmungen, in Schumacher's Astron. Nachr., bd. xiv., No. 329, s. 

 270; and Bessel and Baeyer, Gradmessung in Ostpreussen, 1838, B. 

 427-442. 



