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SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



ably represents the radius of the vertical current. The radius r 

 depends on the height of the vertical current. Finally, it is neces- 

 sary to remark that in our example the vertical velocity is very great; 

 the velocity V at the point .4 represents the vertical velocity at this 

 point. But on the other hand, in natural systems of wind the motion 

 of the air differs much from this motion in our case, because the sur- 

 face of the earth compels the particles of air to follow trajectories of 

 a different form. 



*""-» ■ " Q 



FIG. 23 



Second example. The trajectories are parallel to a vertical plane 

 and pass through a horizontal line. 



We take the plane X Z (see fig. 22) parallel to the trajectories 

 and the axis Y as the horizontal line. The ordinate y disappears 

 and we write 



u = U, x = r and R 2 = x 2 + z 2 



We write the equations of the trajectories under the form 



-J 



x 



R 

 R n 



2at 



1 + 



Rr 



(8) 



Placing t = o, we have R = R ; consequently the particles of air are 

 found at first at the surface of a cylinder whose radius is R . Differ- 

 entiating with respect to t and eliminating the constants we shall 

 have 



u w V a. 



x z R R 2 



For a < o, the air flows towards the axis and for a> o, the air flows 



