710 Prof. P. Lowell on the Limits of the" 



condensation, the following amounts which are set opposite 

 their values of rj for homogeneity and their actual observed 

 flattening^ 171. 



Earth . 

 Mars . 

 Jupiter . 



Saturn . 



21. To see how this value of tj 2 compares with Olairaut's 

 approximation to it to terms of the first order in the ellipticity, 

 we shall express t) 2 in terms of (j>. 



V- 



Va- 



Vi- 



»■ 



1 



1 



1 



1 



231-7 



579-7 



297 5 



579-2 



1 



1 



1 



1 



174 



436 



190 



435 



1 



1 



1 



1 



9-13 



23*4 



15-8 



22-8 



1 



1 



1 



1 



4-97 



13'1 



9-5 



12-5 



Since 



15 675 2 , 

 I* 8 7*+ 896 ^ + 



5 , 4 , 

 V= ^V-2+ g% 8 , very approx.; 



whence, combining this with equation (11), we get 



209 

 $ = 2r}2 + 2lu^ 2 + =2t; 2 + % 2 ? very approx.; 



and reversing, 



9 ?2= <j 0- ijfiijt* &c. = - <^>- -</> 2 , very approx. . (1 6) 



We thus find accordance between the two results to the 

 first order of approximation, and also how to evaluate the 

 neglected terms in his result. 



The two limiting values of the oblateness corresponding, 

 the one to homogeneity, the other to central concentration, 

 in the matter constituting the planet, give us an insight into 

 the present distribution of that matter. The upper limit is 



very closely j <£, and therefore depends upon the ratio <f> borne 



by the centrifugal force to gravity at the equator in the homo- 

 geneous state. The lower limit, on the other hand, depends 

 directly on q, that is on the rotation spin and the mean density 



