Chessin — On the True Potential of the Force of Gravity. 3 



southward direction perpendicular to 0^; finally, the axis 

 Of) parallel to CY, eastward. Then, denoting by S the dis- 

 tance of O from the center of the earth, X the latitude of the 

 point 0, and 6 the angle of the radius vector CO with the 

 plane of the equator, the formulas of transformation will 

 be: 



(4) 



x = S cos ^ + f sin X — ^ cos X, 

 z =S sin — ^ cos X — ^ sin X. 



. , , . . ^U 9U 9U 

 4. The expressions of the partial derivations ;,— , ;^ — , ^-f 



as obtained from (3), readily yield the derivatives of the 

 same function with regard to |, t;, ^, Namely, 



(5), 



9U 



M 3N^ 15iV32 



K^^ B^ ~ W 



(P sin e + I) 



+ ^5 S sin ^ COS X — -^ I cos2 \ — -^^sm\ cos X, 



B" 



(5), 





[ 



~W 



M 3iV loiV^^-* 



+ ^ — 



ir 



/23 -r 7J5 — 7^7 



v^>» ^ ~[]r^ + :r« ~^r^ (s COS 6-0 



i2» 

 where 



(6) e==X — ^, 



H — pi sin a sin X — —^5 f sin X cos X — -ps ^ sm 'X, 



i2s 



(7) i2 = |/S2 + pa + 2a(|sine — ?cos€), 



(8) p=l/f2 + ,;2 + ^, 



