MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 17 1 



at a point so distant that we can neglect the velocity, we have ap- 

 proximately for the equation of the living force or energy, assum- 

 ing the density of the air to be constant, 



J^ = tl«-F (1) 



P 



in which F expresses the energy consumed in overcoming friction 

 or the work of the friction along the surface of the earth. We shall 

 find 



Po ~ Po = p(i V + F) (2) 



The work of friction [or done in overcoming friction] depends on 

 the path traversed by the particles of air and on the variation of the 

 velocity. There are whirlwinds where the work F is very small 

 and others where it is very great. It is especially the dimension 

 of the whirlwind that determines the work of friction. In every 

 case we see that the horizontal velocity depends principally on the 

 barometric depression p Q ' — p , which we can consider as the meas- 

 ure of the force of the current. Let us denote by D the barometric 

 depression at the surface of the earth. For ascending currents by 

 introducing f(z) we shall have 



D = p '-p = pA\ --rj^r) (3) 



V p' f (2) / 



The depression cannot exceed the value given by this equation 

 after substituting p = p' . 



Let us assume the pressure in the calm atmosphere equal to 76o mm 

 and designate by D m the maximum value of the depression expressed 

 in millimeters, we have 



ZP„ = 760(l- f -A_) (4) 



For descending currents, we find in the same way, 



p - p' = p'( p p \ m - 1) (5) 



D m = 760 (/(*)- 1) (6) 



Here D denotes the excess of pressure in the center of the whirl- 

 wind over the pressure of the calm atmosphere and D m its maxi- 

 mum value. 



