668 Dr. Gr. Green on some Problems 



with uniform angular velocity co about a centre in its own 

 plane. This type of motion is represented by 



u=—-cc(y—.ftz); v — cox; w — 0. 



co x = ; cOy = D. coscf) ; co z = D, sin <j>. 



The equations (A) and (B) of page 666 then take the form 



(co 2 + 2o>0 sin &)x =-k b !° g P 



^ 



-(a) 2 + 2a)0 sin fify—fa) = -A'^Iog p (1) 



+ 2coCl cos <l>(y— ftz) — — <?— &^log p 



(i + ^ + #°^=° w 



The integration of the first three equations gives 



Ichg p = i(co 2 + 2con sin (j>){,T 2 +( !/ -/3zy}-gz + C, (3) 



as the general equation determining the density and pressure 

 at any point in the neighbourhood of 0. The constant C 

 represents the value of klogp at point itself. In order 

 that the above integral may satisfy the third equation of 

 motion, ft must be chosen according to the equation 



8= 2Qcos ^ . (4) 



p a) + 211 sin w 



The continuity equation is then fulfilled also ; and the 

 equation (3) corresponds to conditions of pressure and of 

 motion which are possible in the atmosphere. 



When co is taken positive in the same direction as the 

 earth's rotation, the atmospheric motion described above 

 corresponds with that obtaining in the stationary cyclone. 

 When co is taken negative the motion corresponds with that 

 obtaining in the stationary anticyclone. In each plane 

 parallel to the surface of the earth the air is in motion about 

 a definite centre determined by the height of the plane above 

 the earth's surface at 0. Referred to the point 0, the 

 centre of isobars drawn on the earth's surface, the line of 

 centres of rotation lies in the meridian plane ZOY and is 

 inclined to the vertical line drawn through towards the 

 North in the Northern hemisphere at an angle i given by 



. 2ncos<£ 

 tnm = ft= — , t>n . , (5) 



co + 212 sin <p v 7 



