MOVEMENTS OF ATMOSPHERE OULDBERG AND MOHN 235 



at the same time that the equation of continuity 



du dv 

 dx dy 

 is fulfilled. 



The absolute horizontal velocity U is determined by 



IP = u 2 + v 2 — - - • (5) 



Writing 



dF dF 



u = — , v = — 



dx dy 



we shall have 



x — £ 

 Fj =M log. nat. r + N arc ( tang = 



7 - ij 



Writing 



x — £ 



F t = N log. nat. r — M arc ( tang = 



y - tj 



Equations (i) and (2) assume the form 



1 dp n . n dF t u dF d 2 F 1 dU 2 



- JL = 2 co sin S — - 1 - k — _ \ . 



p dx dx dx dx dt dx 



1 dp . dF x h dF d?F dU 2 



— = 2 co sin 6 — - — k — _ — ^ . 



p dy dy dy dy dt dy 



consequently we have 



P 



- = 2 co sn 



p dt 



P = 2 co sin 6F X - kF - — - * W + C . . . (6) 



Writing 



x — £ = r sin <p 

 y — rj =■ r cos <p 



