MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 195 



We easily see that all these formulae depend on only two con- 

 stants or parameters, namely the altitude h and the maximum veloc- 

 ity V . We can change the last parameter and consider the depres- 

 sion D as the second parameter. Thus the function of U shows that 

 the horizontal. velocity has a maximum value U for £ = V \\ the 

 distance r from point A to the point where U has its maximum 

 value, is 



r = h V £ and U = V V 27 

 The gradient G has its maximum value G m for 



whence 



G = i o 25 V5 2V 

 m p 216 fc 



We shall now choose Z) , expressed in millimeters of height of mer- 

 cury, and r expressed in degrees of the meridian, as the parameters 

 of the system and are thus able to establish the following formulas, 

 by introducing a mean value of p (0.13 18 at the temperature o° 

 and the pressure of 76o mm and for dry air) : 



The maximum horizontal velocity = U = v/30.6 D 

 The maximum horizontal gradient = G m = 0.715 D a /r 

 The distance from G m to the point A = r m = 0.63 r 

 The height of the absolute center O = h = 1.41 r 

 The absolute maximum velocity = V = 2.6 U 



By the aid of the preceding formulae we have calculated the fol- 

 lowing table, in which D denotes the barometric difference: 



£ 0.5 1 2 3 4 



r :r 0.71 1.41 2.83 4.24 5.66 



U:U 0.93 0.92 0.46 0.25 0.15 



G:G m 0.99 0.48 0.06 0.01 0.003 



D:D 0.36 0.75 0.96 0.99 0.9965 



In fig. 23 we have constructed, from this table, the curve of veloc- 

 ity, the curve of gradient and the curve of pressure that determines 

 the system of isobars. We can compare our system of wind to the 

 lower half of a cyclonic system in nature; probably in nature the 

 maximum gradient occurs at the same point as the maximum veloc- 

 ity. The depression D which depends on the physical state of the 

 air, determines the maximum velocity; the maximum gradient 

 depends on the depression and the distance r which in nature prob- 



