Oblateness of a Rotating Planet. 705 



zero. As the first equation a x b v — 1 = determines b l} all the 

 other 6's are determined seriatim. 

 In this manner we find 



^=^? + g|? 2 + 2-48^appros. . . (10) 



e=-^ q+4:'27q 2 + ll'96q 3 approx. 

 o 



11. The ratio (p of the centrifugal force to gravity at the 

 equator is 



2wpaq 



/i 2 o /sin -1 ? VI— A o 



Vl-*-. 2tt^~— ? j-2wpaq 



substituting for 7 and <? their values in 77 or e we get 

 •4 2 



4 142 ., , 

 = - e — r^r- e ~ ® c «j 

 1/,) 



or reversing, for the condition of homogeneity, 

 »?=4*+ 924 ^ 2 ^ ( '- 



12. For the Earth 



2=-00230. 



For any other planet its q, or 7,, can be found from the 

 equation 



ft-^rf. < 12 ) 



in which the unaccented quantities refer to the Earth, the 

 accented to the planet. 



Phil. Mag. S. 6. Vol. 19. Mo. 113. May 1910. 2 Z 



