MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 141 



§8. Forces which act during the motion 



During the motion of the air there are two new forces that come 

 into action, namely, the action of the rotation of the earth and the 

 friction between the molecules of air both between themselves and 

 on the surface* of the earth. The action of the rotation of the earth 

 produces properly speaking two forces, the centrifugal force, which 

 with the attraction of the earth produces the resultant g and the 

 force called the composite centrifugal. This latter force which we 

 shall call the deflecting force is perpendicular to the trajectory of 

 the particle of air, and is directed to the right in the northern hemi- 

 sphere and to the left in the southern hemisphere. 



Expressing by v the velocity of the air, by co the angular velocity 

 of the earth and by 6 the latitude, we have the deflecting force 



= 2 co v sin 6 (1) 



The velocity is expressed in meters per second and 



°>-mk- oom72g2 



The deflecting force of the rotation of the earth is found by con- 

 sidering the movement of a point relative to the earth, which is sup- 

 posed to be at rest. If we do not introduce this force in all the 

 dynamic problems that introduce movements relative to the earth, 

 it is because this deflecting force is very feeble and the trajectories 

 do not extend to considerable distances. On the contrary the 

 currents of air travel over large parts of the surface of the earth, 

 and the forces which produce them are very feeble. We may then 

 anticipate that the deflecting force of the rotation of the earth 

 plays an important part in the problems of meteorology. Let us 

 add that this force being perpendicular to the trajectory has no 

 influence on the velocity of the current, but tends only to change its 

 direction. 



On the contrary, friction is a force that tends to diminish the vel- 

 ocity. The complete theory of the friction between the molecules 

 of air is very complicated and will be developed in the second part 

 of these studies. 



For the present Ave admit that friction is a tangential force and 

 opposed to the motion. As to its magnitude we will suppose that 

 it is proportional to the velocity, and expressing by k the coefficient 

 of the friction, we write 



the force of friction = k v (2) 



