PATHS OF MOVING PARTICLES SPRUNG 73 



in fact there are many more curved wind paths that are cyclonal 

 than anticy clonal. 



On the contrary it is of the greatest interest to know that the 

 tendency towards change of direction by the rotation of the earth 

 is far greater ani more general than was formerly supposed. The 

 "deflecting force" acting from left to right, corresponding to equa- 

 tion (12) can by substituting the value of p from (18) be written 



A = 2 vco sin <p (22) 



in which <p is to be taken positive for the northern hemisphere and 

 negative for the southern. Therefore, for horizontal motions on 

 the rotating surface of the earth the dynamical differential equations 

 in a rectangular system of coordinates, for which the positive y- 

 axis extends from the positive direction of the #-axis towards the 

 left, are as follows: 



d 2 x v . dy 



-=A + 2wsinco — 



d? dt 



d 2 y dx 



= y — 2 &> sin cc — 



df dt 



(23) 



In fluid motions the given forces generally consist of pressures, 

 so that X and Y are to be replaced respectively by 



— -I — \ and —-(-—) (where a is the density). 

 o\dx } o\dy I 



With reference to the application of these equations and their 

 necessary extension to motion in any direction, reference may be 

 made to the theoretical investigations in the domain of meteorology 10 

 whose number has lately increased to a most encouraging extent. 

 Since, however, the vertical forces can be readily ascertained a short 

 discussion of these may properly follow here as a conclusion to the 

 preceding presentation. 



For motions parallel to the earth's surface the vertical pressure 

 N directed downwards, evidently has the value 



_V 2 = Q _V 2 cos 2 6 _ V 2 sin 2 6 

 R R t R 2 



10 W. Ferrel: Meteorological researches; Reports of the Superintendent 

 of the U. S. Coast and Geodetic Survey for 1875 and 1878. 



C. M. Guldberg et H. Mohn: Etudes sur les mouvements de 1' atmos- 

 phere; programme de l'Universite - de Christiania pour 1876 et 1880. 



J. Finger: Wien, Sitzungsberichte, Jahrg. 1877, 1880. 



