DENSITY OF THE EARTH. 19 



mass, or that of a solid sli ell-like non-homogeneous mass, 

 rotating round a fixed axis. Erom Newton and Huygens, 

 the most celebrated geometricians of the eighteenth century 

 were occupied with this solution. Here, as always, it is 

 well to remember, that whatever is achieved by intellectual 

 effort and mathematical research, derives its value, not alone 

 from that which is actually discovered and added to the 

 domain of human knowledge ; but also, and more especially, 

 from the higher perfection and power to which the analytical 

 instrument has been wrought in the course of the investi- 

 gation. 



" The geometrical, as distinguished from the actual phy- 

 sical, figure of the Earth, ( 3 ) is determined by what would be 

 the surface of water in a network of canals everywhere 

 covering the earth in connection with the ocean. This 

 ideal geometric surface (the extension and completion 

 of the oceanic surface) is everywhere perpendicular to the 

 direction of the forces compounded of all the attractions 

 proceeding from the several particles of which the earth is 

 composed, combined with the centrifugal force corresponding 

 to its velocity of rotation. ( 4 ) This figure can only be 

 regarded as approximating, on the whole, very nearly to 

 that of an elliptic spheroid of revolution ; for irregularities 

 in the distribution of the mass in the interior of the earth 

 produce, not only local variations of density, but also 

 irregularity in the geometric surface, which is the product 

 of the concurrent action of unequally distributed elements. 

 The physical surface of the earth is that of the actually 

 existing land and water." Geological reasons render it not 

 improbable that accidental alterations which may take place 

 in the molten materials in tip intrrior of the earth, easily 



