All-101 



82 



|^'.u.||Vv.|M' .2Qv' sln(Z) 



P 9^ lax2 ay2 P az ^^^gz ^ ^^^ 



ir'"^ '''li'-^ '''ly' + 2Qu' sin (I) - Q^r sin G cos 



= - 1 .8J2 + a|^^'+ -£^'1+ i 4- (A. 9XL) (8) 



P 9y [9^ ay2 1^ p az ' 3 az ' 



(9) 



1 9£ = _ H 

 p az ^ 



If the above procedure be carried out for the con- 

 tinuity equation, the latter becomes 



9u' + av' + aw' ^ (10) 



ax ay az 



In making the transformation from spherical to 

 rectangular coordinates, we must consider the distortion of 

 the spherical surface as a result of the mapping process. 

 Specifically, a rectangle in the rectangular system maps into 

 a region on the suhere in such a manner that the east-west 

 distance remains constant and the right angles between the 

 lines X = const, and y = const, map into obtuse angles be- 

 tween the lines on the sphere corresponding to x = const, and 

 y = const. Thus, the mapping is not conformal. 



V/ith the above transform.atlon we have mapped a 

 spherical surface onto the plane. Our real aim, however, is 

 to map the equilibrium surface which establishes itself as a 



