x 



THE RELATION BETWEEN WIND VELOCITY AT ONE 

 THOUSAND METERS ALTITUDE AND THE SURFACE 

 PRESSURE DISTRIBUTION 



BY E. GOLD, M.A. 

 Fellow of St. John's College, Cambridge 



[Communicated to the Royal Society, London, by Dr. W. N. Shaw, F.R.S. 



February 25, and Read March 5, igo8. Printed in Proc. Roy. 



Soc. Vol., 80, May 25, igo8] 



For the steady horizontal motion of air along a path whose radius 

 of curvature is r, we may write directly the equation 



(tor sin X ± v) 2 _ 1 dp (cor sin X ) 2 

 r p dr r 



expressing the fact that the part of the centrifugal force arising from 

 the motion of the wind is balanced by the effective gradient of pres- 

 sure. 



In the equation p is atmospheric pressure, p density, v velocity 

 of moving air, X is latitude, and co is the angular velocity of the 

 earth about its axis. 



If dp/dr be negative, it is clear that v and co r sin X must have 

 opposite signs: or, for motion in a path concave towards the higher 

 pressure, the air must rotate in a clockwise direction, the well- 

 known result for anticyclonic motion. Further, the maximum nu- 

 merical value of 



1 dp (co r sin X) 2 

 pdr 1S ~2~ 



and the corresponding maximum value for v is co r sin X. Therefore, 

 in anticyclonic regions there are limiting values which the gradient 

 and the velocity cannot exceed. This limiting value of v for lati- 

 tude 50 and r = 100 miles is approximately 20 miles per hour. 



At the surface of the earth, owing to friction and eddies, the mean 

 direction of the motion of the air is nearly always inclined to the 

 isobars; but over the sea the inclination is very much less, and it 

 seemed probable that in the upper regions of the atmosphere, if 



113 



