relating to Rotating Fluid in the Atmospliere. 



673 



In view of the approximate nature of the solutions con- 

 tained in Cases II. and III. it cannot be said that the motions 

 discussed are possible steady motions in the atmosphere. If 

 a motion of the type indicated were established it would be 

 subject to gradual modification owing to the cumulative 

 influence of the smaller terms which have been omitted in 

 the discussion given above. The chief interest to us lies in 

 the fact that the.^e motions retain all the characteristics of 

 the motion of the air in the stationary cyclone or anticyclone, 

 while indicating the nature of the slight disturbances which 

 would produce motion of the system as a whole. 



Case IV. — It is of interest to find also a steady motion 

 which would correspond with the moving cyclone or anti- 

 cyclone and which would be free from the limitations as to 

 the smallness of U and V which have been imposed in 

 Cases II. and III. This can be done in the case where the 

 centre of isobars at the earth's surface has a uniform motion 

 in a direction due East or due West. Let us consider the 

 conditions of motion represented by 



11= — co^ — jSz) ; v = co'x ; w = 



u 



&>r=0 



G) y = 12 cos (f) f -.jj ; GK = Osin</>. 



These conditions of motion must satisfy the system of 

 equations 



- ((oeo' + 2a)'Q sin 4>)' L '~ Tf ( 2^ cos <f> + p ) * j 







(18) 



= —9— *^ 1o sp I 



(! + «f. + -£>'-° 



(19) 



