MECHANICAL EQUIVALENT OF PRESSURE MARGULES 531 



Since the work corresponding to one kilogram-meter is 9.8, expressed 

 in these same units therefore it will require at least 



seconds =7.6 hours 



0.0036 



for an amount of kinetic energy equivalent to one kilogram-meter 

 existent in a square-meter column of this hypothetical atmosphere 

 to be consumed by internal friction. 



Now the kinetic energy of this column of atmosphere, assuming 

 each part of it to have a velocity of 10 meters per second is equal 

 to 



8000 X 1 .293 X 50 kg w 2 see' 2 



or more than 50,000 kilogram-meters. Thus we see that the kinetic 

 energy in the atmosphere would last a very long time if it were to 

 be consumed only by such internal friction or viscosity as is effective 

 in strictly parallel or lamellar motions. 



(il.) -RESISTANCES AT THE SURFACE OF THE EARTH 



Other much greater obstacles to motion must be present. The 

 roughness of the surface of the earth, the irregularity of the motion, 

 hence also the numerous small whirls that originate and disappear 

 in the large currents, and even surfaces of discontinuity must be 

 taken into consideration. Possibly the first of these is sufficient 

 so that the loss of energy may not be caused by exterior friction 

 proper, but by impact and the sudden transmission of the energy 

 of the lowest layer of air to solid and fluid bodies. So long as 

 differences of pressure exist the lowest stratum of air will be con- 

 tinuously accelerated and for this purpose the energy will be fur- 

 nished by the upper strata. If now the whole system receives no 

 energy from without, while on the other hand the wth part of the 

 total supply on hand (E) is consumed per unit of time (either by 

 maintenance of waves, or by carrying up of dust and water vapor 

 by pushing or overturning branches, trees, houses, etc.), therefore, 

 we have 



dE E _ i/ n 



— = - ; E = E e ' 



dt n' ° 



The interval of time required to reduce the kinetic energy to \ 

 of the original supply, or to reduce the velocities to \ of their original 



