190 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



As the resultant force of the internal friction does not necessarily 

 act in the direction opposite to the motion therefore the direction of 

 the motion of the air in the stratum of maximum velocity remains 

 uncertain. Probably it does not sensibly deviate from a direction 

 perpendicular to the gradient. 



How are the velocity and the direction of the motion related in 

 the different strata of a current ? This is a problem hardly solvable 

 in the present state of our knowledge of the laws of friction and in 

 the absence of precise observations of the gradients and the motions 

 of the upper strata of the atmosphere. 



§23. A rotary current of air 



We shall now consider a mass of air revolving about a vertical 

 axis in consequence of the motion of the surrounding air. The 

 exterior air moves in circular trajectories and with constant veloc- 

 ity and by internal friction produces a rotation of the interior mass 

 of air. We have therefore a mass of air within a cylindrical bound- 

 ary whose velocity is given and which turns about a vertical axis 

 by reason of internal friction. The tangential velocity U is a 

 function of the distance r from the axis; the isobars are concentric 

 circles; the gradient is directed along the radius. The acting 

 forces are the force of the gradient, the centrifugal force and the 

 deflecting force of the rotation of the earth, all of which act in the 

 direction of the radius, and finally the force of the internal friction 

 which acts in the direction of the tangent. We neglect the friction 

 at the surface of the earth, so that the velocity is independent of the 

 altitude. The resultant of the internal frictions acts tangentially 

 on each element and should be equal to zero, because there exists 

 no tangential force with which to establish equilibrium; the result 

 is, that the internal friction along a cylindrical surface must be con- 

 stant. Let the mass of rotating air be divided into cylindrical por- 

 tions which rotate with different velocities. The internal friction 

 is due to the differences of the velocities U, but the radius r varies 

 at the same time and Avith it the frictional surface; it is necessary 

 therefore, to make the friction proportional to the variation of the 

 product of the velocity and the frictional surface, divided by the 

 increase of the volume. We shall find then 



d(rU) 



— = — = a — constant ( 1 ) 



r a r 



