64 



THE TIDAL PROBLEM. 



An inspection of the diagram shows that the density increases quite 

 uniformly for a considerable distance as we pass from the surface toward 

 the center. We finally come to a central nucleus of nearly uniform density. 

 The density at the center, required by the Laplacian law, is 10.74. This 

 value would be modified if values different from 2.75 and 5.50 be assumed 

 for the surface density and mean density respectively. 



LIST OF SYMBOLS USED, WITH MEANING. 



a^ = mean radius of surface of spheroid. 



a = mean radius of any homogeneous shell in interior of spheroid. 



& = equatorial radius of any homogeneous internal shell of spheroid 



of revolution. 

 6o = equatorial radius of surface of spheroid. 



c = polar radius of any internal homogeneous shell of spheroid. 

 Cfl = polar radius of surface of spheroid. 



Q = a constant = 4.365 for earth-spheroid. 



5 = a constant = 2.4605 for earth-spheroid. 



p = density of any homogeneous shell of mean radius a. 

 /?o = surface density of spheroid = 2.75. 



a^ = equatorial attraction or value of gravity at equator of any spheroid. 

 0^ = polar attraction or value of gravity at pole of any spheroid. 

 w = ratio of centrifugal force at equator to gravity at equator. 



e = eccentricity of any homogeneous internal shell of spheroid. 



ffl = eccentricity of surface of spheroid. 



