456 



JOSEPH BARRELL 



whole in the directions of the three principal axes are R and 2R. 

 Let it be required to find the value of the equatorial radius 2P 

 and semipolar axis P of the oblate spheroid of equal volume in 

 _^ which the axes have these proportions. Then 



P=i.oSR 



It is seen that the five spheres of density o . 020 

 have the same mass as a sphere whose radius is 

 i.jiR and density 0.020; the same mass also as 

 the unit sphere of density o. 100 and radius R and 

 the oblate spheroid of density 0.020 and semipolar 

 axis I . oSR, equatorial radius 2 . 16R. The vertical 

 section of this spheriod is shown in dotted outline 

 in Fig. 9. The distribution of mass and gravita- 

 tive effect of the five spheres will be 

 nearly the same as for such a spheroid. 

 The nature of the differences, as in cases 

 A and B , will be 

 discussed later. 

 The effect of 

 the distribution 

 of mass along a 

 horizontal hne 

 and in a plane 

 has been con- 

 sidered in cases 

 A, B,C. There 

 remains to be 

 considered the 

 effect of the dis- 

 tribution along 



a vertical line and in a vertical plane. Case D, Fig. 10, is given to 

 show the effect of the distribution along a vertical line. The 

 unbroken-line curves show the values of Fv and Fh for a sphere 

 with density and depth corresponding to the unit sphere previously 



Scale ofdisfances 

 100 aooKm. 



Cased 



Pephh of 12 8 Km. 



Fig. 10. — Horizontal and vertical components of the gravi- 

 tative force due, first, to a sphere of 32 km. radius, density 

 o. 100, depth to center 64 km., and second, to the same mass 

 expanded into three such spheres with centers on a vertical 

 line at depths of 32, 64, and 96 km. 



