MECHANICAL EQUIVALENT OF PRESSURE MARGULES 



5 2 9 



PART III. FRICTION 

 (io.) INTERNAL FRICTION OR VISCOSITY 



There are many obstacles to the analytical treatment of great 

 currents of air; one of these is the difficulty of introducing the 

 influence of friction in a proper manner into the equations of 

 motion. This influence certainly is very large: the unequal warm- 

 ings of the air are continually giving rise to new differences of pres- 

 sure and new motions, but there is no corresponding steady increase 

 in the mechanical energy. Hence for large intervals of time the 

 whole increase of energy is consumed by friction. An argument 

 for this conclusion can also be based on the motions of individual 

 masses of air. Thus, near the ground and in by far the most 

 numerous cases we find a component of the wind in the direction 

 of the pressure gradient; hence the motion of the wind is thereby 

 accelerated. The same peculiarity or a motion perpendicular to 

 the resultant force also occurs in the upper layer, or at least the 

 study of the winds during balloon voyages has as yet established 

 nothing as to winds contrary to the barometric gradient. It is 

 scarcely to be doubted that such cases do occur, but they appear 

 not to be very frequent. There is no other reason for the diminu- 

 tion of velocity except movement against the active forces and 

 friction. If the first of these very rarely occurs then in general it 

 must be true that the friction prevents the steady acceleration of 

 the moving mass of air. 



And yet the influence of the internal friction or viscosity of the 

 air on movements that occupy a large volume is certainly very 

 slight. This nas been demonstrated many times and in various 

 ways by Helmholtz. Perhaps it will not be superfluous to estimate 

 the consumption of energy by viscosity by using the following 

 equation deduced by Stokes: 



du v - 



+ — 

 dz 



}dk. 



