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

 In (6) the integral becomes 



e = 



where x() represents bhe expression in brackets and f has the same meaning as 

 before. 



The curve (&) in fig. 3 represents the values of x (f) for different values of It 

 will be seen that when = 1 '2 the temperature is about T V of the surface 

 temperature 6 a . In actual cases it is not easy to say whether (a) or (/>) is a better 

 representation of the changes in temperature along the air's path. In most cases 

 probably (a) is the best, but, in one case, that of the ascent of May 3rd, the bend in 

 the temperature-height curve was due to the passage of the air across a sharply 

 defined boundary between the warm waters of the Gulf Stream and the cold arctic 

 water over the great Bank of Newfoundland,* and then one might expect (/>) to be 

 a truer representation of the vertical temperature distribution. In either case we 

 shall not be far wrong if we assume that the height to which the new conditions 

 have reached at time t is given by f = 1 '0 or 



z 2 = 2wdt. . . .......... (2) 



If we can measure z, the height of the bend in the temperature-height curve, and 

 if we know t, the interval which has elapsed between the time at which the rate of 

 change of surface temperature along the air's path suddenly altered its value and the 

 time of the ascent, the equation (2) enables us to calculate KJpv or ^(wd). The error 

 in this result may be as great as 30 per cent., but it does at any rate give a good 

 idea of the magnitude of the coefficient of eddy conductivity and of the amount 

 of eddy motion which is necessary in order to produce the vertical temperature 

 distributions which have been observed. 



In some of the cases the potential temperature before the change which caused the 

 bend in the temperature-height curve was not constant at all heights. In the case of 

 the upper bend in the curve shown in fig. 2, for instance, the potential temperature 

 increased with height before the warming which produced the upper band occurred. 

 This, however, makes no difference to the rate at which the bend is propagated 



upwards. It is evident that if 0, and 6 2 be two solutions of = - ^-j , then B l + 6 2 



cC s-i c% 



is also a solution. If the initial potential temperature before the change were 

 6 = T + az, and if the surface temperature were to change suddenly to T, at time 

 t = 0, the temperature at height z at a subsequent time.i would be 



It is evident that the term T + az does not affect the rate at which the bend in the 

 temperature-height curve is propagated upwards. 



* See ' Reports of the " Scotia" Expedition, 1913.' 

 VOL. CCXV. A. C 



