Intelligence and Miscellaneous Articles. 231 



Comparing this value of sin with the preceding one, we find 



e\2-e*)= tanflcotanfl ^2- gJ?U sin20 i~ sin20 . 



When and X become equal to each other, that is when the 

 point M is considered very near to the equator of the ellipsoid, 

 then 



sin 2 0, — sin 2 Q 



sin 2 d x cos 2 d 



= 0; tan0cotan0 x = l ; |0=a; 



and 



,*(2-* 2 )=^Y2-— ); 



9 \ 9 J 



Since the ellipticity is expressed by e= - , we have 



2o It) CI r -i 



e-e 2 = — ; [a] 



and neglecting e 8 , we have, approximately, 



Now, in the case of our planet, 

 2tt 



; a = 6,377,278 metres; #=9 metres 81,462; 



86184 

 (including centrifugal force). 



Hence _ 1 



e 578* 



This value is entirely too small compared with yuu as deduced 

 from geodetical measurement of arcs of meridians and parallels. 

 What can be concluded from this ? Are we to believe that the 

 theory is false ? No, it seems to be in perfect accordance with the 

 conditions of our globe. In fact, if the Earth is at present almost 

 wholly rigid, as Sir W. Thomson has shown it to be, and we admit 

 that, from the time when its mass was wholly liquid, its diurnal 

 rotation has been progressively slowed by the resistance of tides, 

 it follows that, as soon as the liquidity of the mass began to be 

 impaired by the effect of cooling, the flattening could no more 



