16 COSMOS. 



tation would be quite different from what they now are. 

 The absolute size of our planet, which we are here consider- 

 ing, maintains its importance in the collective economy of 

 nature merely by the relations which it bears to mass and 

 rotation ; for even in the universe, if the dimensions of the 

 planets, the quantitative admixture of the bodies which com- 

 pose them, their velocities and distances from one another, 

 Avere all to increase or diminish in one and the same propor- 

 tion, all the phenomena depending upon relations of gravita- 

 tion would remain unchanged in this ideal macrocosmos, or 

 microcosmos.* 



a. Size, Figure, Ellipticity, and Density of tlie EartJu 

 (Expansion of the Picture of Nature, Cosmos, vol. i., p. 163-171.) 



The earth has been measured and weighed in order to de- 

 termine its form, density, and mass. The accuracy which 

 lias been incessantly aimed at in these terrestrial determina- 

 tions has contributed, simultaneously with the solution of 

 the problems of astronomy, to improve instruments of meas- 

 urement and methods of analysis. A very important part 

 of the process involved in the measurement of a degree is 

 strictly astronomical, since the altitudes of stars determine 

 the curvature of the arc, whose length is found by the solu- 

 tion of a series of triangles. The higher departments of 

 mathematics have succeeded, from given numerical data, in 

 solving the difficult problems of the figure of the earth, and 

 the surface of equilibrium of a fluid homogeneous, or dense 

 shell-like heterogeneous mass, which rotates uniformly round 

 a solid axis. Since the time of Newton and Huygens, the 

 most distinguished geometricians of the eighteenth century 



* "The law of reciprocal attraction which acts inversely as the 

 square of the distance is that of emanations, proceeding from a cen- 

 tre. It appears to be the law of all those forces whose action is per- 

 ceptible at sensible distances, as in the case of electrical and magnet- 

 ic forces. One of the remarkable properties of this law is that, if the 

 dimensions of all the bodies in the universe, together with their mu- 

 tual distances and their velocities, were proportionally increased or 

 diminished, they would still describe curves precisely similar to those 

 which they now describe ; so that the universe, after being thus suc- 

 cessively reduced to the smallest conceivable limits, would still always 

 present the same appearance to the observer. These appearances are 

 consequently independent of the dimensions of the universe, as. in vir- 

 tue of the law of the ratio which exists between force and velocity, 

 they are independent of absolute movement in space." Lnplace, 7:'a- 

 jtrts'.tion dn Syst. tin JAw/? (femc ed.), p. 3S/>. 



