MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 203 



of observations the coefficient of friction remains unknown for the 

 upper strata. Neglecting the vertical depression E, the sum of the 

 two horizontal depressions, D Q at* the surface of the earth and D 

 in the upper stratum, is equal to the difference of the weights of the 

 columns of air [see §20, eq. (12)]. We can approximately calculate 

 this difference by equation (4) of § 17. To fix our ideas we assume 

 that the air at the point A has the virtual temperature T = 298°, 

 and the coefficient m = 6, if there is an ascending current. At the 

 point B the calm air has the virtual temperature T Q ' = 294 and the 

 coefficient m' = 7. If we assume that the air moves from B to 

 A and there ascends, we shall find by the formula (6) of §16, that 

 the ascending current extends up to a height of 4918 111 and that the 

 difference of weight of the columns of air is 3.i mm . Assume D = 

 2 mm anc [ £} = II mm_ jf ^he extent of the system of wind B A is 

 20 we shall find by the formula (10), U = io m . The time the 

 current requires to move from B to A is expressed in hours. 



10 6 20 1 1QQ ., 



— . . — - = 123 . 3 hours 



9 \ U 3600 



If now the air from B can in 123 hours attain the physical state 

 belonging to the air at A, then this system of wind is realized and, 

 as we see, the parameters of the system are determined by the physi- 

 cal state of the air and of the surface of the earth. If we assume the 

 distance B A = 16 , we shall have U = 12.5™ and the time equals 

 103 hours, but in this case the air from B will arrive at A with tem- 

 perature lower than the temperature at A, and consequently the 

 depression will diminish and the system of wind cannot be perma- 

 nent. 



§26. Cyclonic system of the second order 



We have already in § 12 and § 13 studied the cyclones of the sec- 

 ond order in respect to the motion along the surface of the earth. 

 We have assumed that the horizontal current has a constant height 

 h in the exterior portions and that the horizontal velocity increases 

 in this part toward the center and attains its maximum value U 

 at the distance r from the center of the isobars. Then the current 

 enters into the interior portion, where its velocity decreases at the 

 same time that the motion is changed little by little into a vertical 

 motion. Let the mean vertical velocity be w and the angle between 

 the gradient and the maximum velocity be </> ; the condition that 



