672 Dr. G. Green on some Problems 



the equations to be fulfilled then take the form 



\ 



— (&r + 2coD. sin <f>) (x—az) — —h~ log p 



-(a 2 + 2&Qsm<l>){y-Pz)=--k^- Aogp \- (13) 



(| + ^ + 4) l0g ^°- ' * ' ' (U) 



An equation similar to 3 and 9 can readily be obtained by 



integration, namely : — 



Ho g/ Q = i(ar + 2a)n sin (/>){(> -*c) 2 + Q/-/3c) 2 }-^-+ C\ (15) 



where is again the value of Jc log p at each instant at 0, 

 the centre of isobars at the surface of the earth. In order 

 that the third equation (13) above may be fulfilled, a. and ft 

 must be chosen so that 



9 A 



/3= 



cd + 212 sin cb 



2 (a cos + g) 



co + 20. sin 



(16) 

 (17) 



The values of « and /3 so chosen are not constants but 

 functions of the time. Their variations with respect to time, 

 however, are of the order of magnitude of the terms which 

 we have agreed to neglect. The continuity equation is also 

 in this case not exactly fulfilled, though its fulfilment is 

 secured to the desired order of approximation. 



From the equations which we have obtained for this case 

 it appears that the axis or rotation does not remain in the 

 meridian plane when the centre of isobars has a motion 

 towards the Xorth or South. The inclination of the axis to 

 the meridian plane through is towards the west side when 

 the motion of is towards the north, and towards the east 

 side when the motion of is towards the south, in the 

 Xorthern hemisphere. According to equations (16) and 

 (17) above, a knowledge of the angle of inclination of the 

 axis of the rotating fluid is all that is necessarv to enable us 

 to determine the rate at which the system moves to the Xorth 

 or East. 



