18 MAGNITUDE, FIGURE, AND 



different from what they are. The absolute size of our globe, 

 with which we are about to occupy ourselves, becomes im- 

 portant in the general economy of nature, on account of the 

 proportion subsisting between it and the mass and velocity of 

 rotation ; for, speaking generally throughout the universe, if 

 the dimensions of planets, the quantity of substance, or mass, 

 of each, and their respective velocities and distances, were all 

 to be increased or decreased in one and the same proportion, 

 then in this ideal Macro- or Micro-cosmos, all phenomena 

 dependent on relations of gravitation would remain un- 

 changed. ( 2 , 



a. Magnitude, Figure (Ellipticity) , and Density of the 

 Earth. 



(Extension of the " Picture of Nature" in Kosmos, Bd. i. 

 S. 171178 and 420425. In the English, Vol. i. 

 p. 154161 and 400405.) 



The Earth has been measured and weighed to obtain its 

 exact form, density, and mass. The precision which has 

 been constantly aimed at in these terrestrial determinations 

 has at the same time benefitted astronomy by the improve- 

 ments in measuring instruments and in methods of analysis 

 which the pursuit has called forth, no less than by the solu- 

 tion of the problem itself. Indeed, a considerable part of 

 the operation of the measurement of degrees is itself astro- 

 nomical ; altitudes of stars determine the curvature of the arc 

 of which the length is found by geodesical operations. 

 Methods have been discovered, in the higher branches of 

 mathematics, for obtaining from given numerical elements 

 the solution of the difficult problems of the form of the 

 Earth, the figure of equilibrium of a fluid homogeneous 



