MOVEMENT OF AIR IN ANTICYCLONES POCKELS 605 



that occurs in equation (7') cannot be presented in definite form 

 except as the converging series 



J 



_ x d% 1 x 2 1 X 3 1 X* 



= log ^-^2^-3rT3 + 4 L2X4 GtC - 



which series is, however, for large values of x rather inconvenient 

 for computing*. In such cases and when great accuracy is not 

 important we compute only the gradients G and G for R and r 

 and G v G 2 . . G n for a series of intermediate values r v . . r n and 

 then from these compute the pressure in millimeters of mercury 

 for the given r according to the formula 



G,. + G. 

 b = B - ° 2 - 1 (r t -R)- 



G t + G, G„ 4- G 



- — — 1 (r, - r t ) ... - -V-(' - O ... (8) 



where 5 represents the barometric reading at the distance r = R 

 and the values of r are expressed in units of 111/ km [or degrees of a 

 great circle]. 



The objection might be urged that according to equation (7) 

 the difference (P — p) becomes infinite for an infinitely large value 

 of r (logarithm of r). But it must be noted that for very large 

 distances the assumptions made by us become in part inapplicable 

 (for example the geographic latitude can no longer be considered 

 as constant) and this too quite independent of the fact that in the 

 actual atmosphere the neighboring cyclones or other anticyclones 

 affect the distribution of wind and barometric pressure. There- 

 fore we need only expect that our results will apply up to moderate 

 distances from the center of the anticyclone, which may perhaps be 

 slightly larger than the radius of the inner region. 



In order to show that within these limits the theoretical results 

 as concerns wind-force and pressure-difference correspond to 

 those actually occuring, I have computed in detail the following 

 example : 



The constants X and k are considered as given previously for that 

 portion of the earth's surface over which the anticyclonal system 

 of winds prevail; on the other hand the parameters y and R which 

 also occur in our final formulas remain adjustable in order to repre- 



*Smithsonian Mathematical Tables. Washington, 1909. Table IV, pp. 

 225-262.— -C. A. 



