16 G. I. TAYLOR ON EDDY MOTION IN THE ATMOSPHERE. 



gradient wind in such a way that if one stands facing the surface wind the gradient 

 wind will be coining from the right if a be positive. 

 Then 



Solving (15) and (16) for A 3 and A, 



A tan a (l+tan a) ^ 



A-? = 7 - ^!G. 



1 + tan' a 



. tan a (l tan a) ,^ 

 l+tan* a 



The surface wind, which we may denote by Q s is equal to 



QG 



\Xtan 5 ( 1 - tan a) 2 + ( 1 - tan a) 2 , 

 1 + tair a 



or 



Q s = Q (i (cos a sin a) (17) 



It is interesting to compare the value given by (17) for the ratio of Q s to Q u with 

 the value, cos a, given by GULDBEHG and MOHN* for the same ratio, and with the 

 most recent observations of wind velocity at different altitudes above the surface of 

 the earth. 



Mr. G. M. B. DOBSON of the Central Flying School at Upavon has recently 

 published! the results of a number of observations made by means of pilot balloons 

 over Salisbury Plain, which is an excellent place for such observations on account of 

 its open situation. He finds that a is smaller for light winds than for strong winds, 

 and he accordingly divides up his ascents into three classes, those which took place in 

 light winds, when the velocity of the wind at a height of 650 metres is below 4' 5 

 metres per second, those in moderate winds between 4' 5 and 13 metres per second, 

 and those in strong winds above 13 metres per second. 



The comparison is shown in Table II. It will be seen that the observed deviation 

 of the surface wind from the gradient direction agrees well with the theory we have 

 been considering, but not with the theory of GULDBERG and MOHN. 



The agreement between theory and observation is, however, more striking in 

 another respect. The deviation of the direction of the wind at any height from the 



* ' Studies of the Movements of the Atmosphere,' 1883-85. An English translation appears in 

 " The Mechanics of the Earth's Atmosphere," by CLEVELAND ABBE ; ' Smithsonian Miscellaneous Collec- 

 tions,' 1910. 



t 'Quarterly Journal of the Royal Meteorological Society,' April, 1914. 



