230 Intelligence and Miscellaneous Articles. 



of inertia can be expressed by 



a,y + bW=a 2 b\ 



Differentiating this equation, we have 



dy _ ocb 2 1 



dec 



V<* 



and observing that the first member represents the cotangent of 

 the latitude <p of a point M 

 whose coordinates are oc and 



y (figure), and that - repre- 

 sents the cotangent of the 

 latitude of the same point 

 referred to the centre of the 

 ellipsoid, we have 



Vl- gn*0 ___ & 2 cos 

 sin^> a 2 sin 0' 



and 



sin0 



am *= Vl-cosW(2-, 2 )' 



where 



.„ « 2 -5 2 



y 









a? 







S"^""\ 



,'I\ J \ x 







jb-_ 



/ 1 



1 | 



\ V 



\ 



\ 



2V \ 





p 



C 



o p\ 



\ 











^ £ 





On the other hand, let ME represent the direction and the 

 intensity of the attraction of the whole ellipsoid upon the point M, 

 which attraction we designate by g ; and put MO = /o ; angle MEE 

 = d l ; angular velocity =io. Then the resultant of the attraction 

 g and the centrifugal force at M must coincide with the normal 

 MN, for centrifugal force is parallel to EE ; and since this latter 

 force is expressed by w 2 p cos V we have for the resultant itself, 



f : sin B^g :j^/T^|(^?) ; 



and therefore 



sin 



sin0. 



\A— !9 .?( 2 -y0 



