

relating to Rotating Fluid in the Atmosphere. 671 



is that the axis of the cyclone or anticyclone is now inclined 

 to the vertical line through at a greater angle than before, 

 for the same value of co (positive) in each case. The axis 

 still remains in a meridian plane through at each instant. 

 When the inclination of the axis to the vertical line OZ 

 exceeds the value given in equation (5), the centre of 

 isobars moves towards the East ; when the inclination falls 

 short of the value given in equation (5), the centre of 

 isobars moves towards the West. A westward velocity equal 

 to the velocity of a point on the earth's surface brings the 

 centre of isobars to rest in space, and the axis of rotation is 

 then vertical. (See also Case IV.) 



Case III. — We proceed now to consider what modification 

 of the conditions of motion described in Case I. would 

 correspond with a motion of the centre of isobars towards 

 the North as well as towards the East. If we take U, V as 

 the velocity components of east and north respectively, 

 and if we assume that the motion of the fluid relative to the 

 point is of the same type as that of the previous cases of 

 motion, we can represent the conditions of motion by 



u=—(o(y — j3s) ; v — co(x — otz) ; iv = 0. 



v u 



w x =- ^ — — <j) ; oy== O cos <£ + =p- ; co z = fl smcp. 



0)^ = 0= — cp : &) y = ; co z = Q, cos <j) . <p. 



Owing to the existence of the component of velocity V 

 towards the north the angular velocity of the axes OX and 

 OY about OZ is continually undergoing change. If we 

 regard the total angular velocity of a particle of fluid about 

 OZ as constant, while the relative angular velocity co changes, 

 this gives the conditions 



a) + O sin = constant .... (11) 



and w + H cos </>.$ = (12) 



As the immediate intention is to determine the effect of a 

 small modification of the conditions of stationary cyclonic 



motion, we may treat terms of the order, H 2 , — p-. flp 3 



ip V 2 



P2 J IT2 as negligible. To the order of approximation stated, 



