All-101 81 



9t az ay ax R R + " J- ^-l" w cos y 



- 2w Q COS = .i 9I> + A <! - cot Q av + a£v ^. a£v V 



P 9y 1 ^ 9y 9y2 3x2 R2sin2G 



2 cot aw L , 1 a ca^ avN /ctn 



R ■H J "^ p a~ ^^3 -^z'^ ^^^ 



aw , , aw ^aw , ,,ew , wu uw cot g , ^ n ^ o n ^ r^ 

 "at -^ ^"a^ - ^ a^ + "'elE -^ "F r~~~ + 2v Q cos 9 - 2u Qsin o 



= 1 9£ + A ^ £2i_§ 9y + a v/ , aw __'W__ 2 j;_p_t _Q aj/ L 

 " p ax [" R ay 9y2 9^2 " R2gin2Q " R " ax J 



+ ^ T^ ^A. 1^) (6) 



P az -J az 



Since R Is very large, we shall ner^lect terms divided 

 by R. VJe can do this provided the region is sufficiently far 

 removed from the poles (9 - 0,71:) where cot 9 becomes infinite. 

 The velocity comijonent u is assumed to be much smaller than the 

 components v and w so that we can neglect u throughout the 

 equations of motion. 



Ordinarily, one uses the velocity components u,v,v; to 

 correspond to the directions x,y,z respectively. In equations 

 (^-)-(6), u,-v,w correspond to z,y,x respectively. The negative 

 sign was carried over from the definition of v \'/hich was defined 

 positive southward. If we revert to the more familiar nota- 

 tions and write u' = w, v' = -v, w' = u, we have for equations 

 (!+)-(6)(with the terms with coefficient 1 and all terms con- 

 taining w' neglected) 



