674 Problems relating to Rotating Fluid in the Atmosphere. 



The equation derivable from these to represent the distri- 

 bution of pressure or density throughout the fluid consistent 

 with the above motion is 



* iog/> = i(<W + 2co'n sin <£ + 2-^. O cos <f> + ~^j x 2 



H4(o>g>' + 2o>X2 sin fl (y^M* + l^fan cos + 5A ,2 



~^ + C, (20) 



where C is the value of klogp at point 0, the centre of 

 isobars drawn at the earth's surface. 



It is easy to show that the required conditions are fulfilled 

 provided 



«' 2 W« + ^2ficos£+E)., . . . (21) 



and /3 = 



2(ncos^+^ 



(22) 



w 1 -\-2Q sin <fi 



From these equations we learn that the relative path of 

 each fluid particle about the centre of rotation in its own 

 plane is not a circle but an ellipse whose axes are due east 

 and due north respectively, these axes being proportional 

 to VvV and ll^co respectively. We fall back again 

 upon our former ease of a circular path if 



5 = _20 C os£; ( 23) 



that is, if the centre of isobars moves relative to the earth 

 uniformly west at a speed equal to twice the speed of a 

 point on the earth's surface coinciding with it at any instant. 

 It can readily be verified from equation (20) above that the 

 isobars are ellipses concentric and coaxal with the ellipses 

 representing the paths of the fluid. Hence isobars are also 

 lines of flow in all the cases considered. 



If the motion of the air in cyclones and anticyclones is, 

 as we have assumed, mainly horizontal, it may be possible 

 to obtain from actual observations some confirmation of the 

 conditions of motion and corresponding pressure distributions 

 indicated by theory in the above cases. As we have already 

 indicated for the case of a stationary cyclone or anticyclone, 

 the inclination of the axis, or line of centres of rotation in 

 the upper layers of the atmosphere, could be determined by 

 observations of the wind velocity at various heights above 

 the ground taken at one or two points within the area 



