670 Dr. Gr. Green on some Problems 



change of wind direction with height increases in some cases 

 to nearly 180 degrees. 



Case II. — The next question which arises is this : TYnat 

 is the smallest modification of the conditions o£ motion 

 described in Case I. which will corre.-pond with a uniform 

 motion of 0, the centre of isobars at the earth's surface, 

 relatively to the earth, without alteration of the motion of 

 the fluid relative to O ? Let us suppose first that has a 

 steady velocity U in a due east direction, other conditions 

 of motion being as in Case I. This type of motion is 

 represented by 



u = — (o(y — fiz) ; y=fc)# : w = 0. 



&V= : co y ~Q, cos cjj -f yy : & z — ft sin </>. 



0)2 = ; w y -=0 ; &>, = 0. 



Since U is to be regarded as a small velocity, we may 



/ TT \ 2 T T 



neglect terms of the order ( t7 ) or O.^- in the equations 



of p. 666 which then reduce to 



-(o) 2 + 2o)nsin</>>=-^-logp 



QX 



-> ! 



~(a i + 2a>Cldn<p)(i/-/3:) = -k^ logp )> . (7) 



° y 



The integration of these equations again leads to 



klog p = i(co 2 + 2cofl sm$){^ f- (y-/^) 2 }-^ + C. (9) 

 as in Case I., but the constant /3 has now the value given by 



IP 



2f Hcos(£ + „\ 



It will be seen from this relation that the essential 

 difference between this motion and that considered in Case I. 



