( 49 ) 



In general ir is tlierefore not possible lo derive any conclusions 

 concerning the gradient from the diurnal variation of barometric 

 pressure as observed at a given place, and neither would it be 

 possible to increase liic number of stations and the acciiracN' of the 

 observations to sucli a degree, that the gradient variation coidd be 

 experimentally deduced. 



The inverse way is therefore indicated and from the knoiim 

 variation of the wind we must try to derive the imknoiim\'i\\\\Qnm\ 

 variation of the gradient, whicli of course is possible only with the 

 help of a suitable mechanical theory of the air motion. 



'2. If, neglecting jjossible and probable vertical motions, the 

 rotation of the earth is taken into account, and the influence of 

 friction is assumed to be proportional to tlie velocity, the relation 

 between gradient and air motion may be represented by the following 

 expressions, the same as used e.g. by Obkrbeck ^} in his well known 

 paper on cyclonic motion : 



ÖU 1 Ö/7 



^ -f- ncm -(- /u ^ — — v~ 



^ ] (1) 



du 1 dp 



■r 7mv -\- he z=: — — v" 



Ot (^, OX 



In these formulae // and v are considered to be directed tow^ards 

 North, ,i] and u towards East. 



a = 2 cos <f 



<p = polar distance. 



)i z= angular velocity of the earth. 



If we put : 



/ :=^ kn 

 then, after division by ii and for the case of a i)criodically varying 

 gradient, (1) becomes 



1 ÖU \ èp ' 



— - — (- au -\^ kü =^ — - = II, cos {out — Aj)i 



n Ot (,n oy I 



1 du 1 dp \ 



— — — ai' -\- kn = — — -— = 11.^ cos{qnt — X^)] 

 n ot Q?i Ox 



The amplitudes H^ and //^ are proportionate to the gradient 

 directed towards Koi'lh and East, (/ is the order of the |)erio(l under 

 consideration. 



Representing the conijionents of the velocity of the airparticles by : 



v = Acos{qnt--C,)\ 



(^) 



71 ^ B cos {qnt — C,) ' 



^) Ann. d. Phys. u. Ch. 1882, 17, (128—148). 

 Proceedings Royal Acad. Amsterdam. Vol. XIV. 



