SOME MEASUREMENTS OF ATMOSPHERIC TURBULENCE. 
13 
Then the normal eddy-stresses, xx and hh, are found thus 
XX pP xP x P {.Px Px){Px P-x) 
= -^2(X-X)(X-X). (20) 
So 
•Xic = —p<t x 2 It\ .(21) 
where <r x is the “standard deviation” of the dots in the .x-direction. If rr H is the 
corresponding quantity vertically 
hh = —p<Tn 2 T~ 2 .(22) 
So the direct eddy-stress in the direction of the wind is intimately related to the 
gustiness shown by a tube-anemometer. 
The shearing eddy-stress 
xh = = -4 - 2 (X-X) (H-H).(23) 
t n 
So 
Xh — — pT (24) 
where r XH is the correlation between the co-ordinates X and H of the dots. 
By projecting the puffs on the other two co-ordinate planes we should be able to 
measure similarly the remaining components of eddy-stress. 
To find the eddy-viscosity we must compare the sheering eddy-stress xh with 
(+ which is the rate of shearing strain in the mean motion. Usually dv H /dx 
is negligible, so that the rate of shearing is dv x /dli, a quantity which can easily 
be observed. At first sight one might think that dv x /dh was simply related to the 
slope of the regression line in the scatter diagram ; but on examination this proves 
not to be the case. The slope of the regression line is independent of r, because (18) 
is satisfied for all permissible intervals of time. 
It should be noted that no shearing stress such as —pp'x v 'ii can exceed, in absolute 
value, the geometric mean of the corresponding pair of direct stresses —pp'xP'x, 
—pp'np ' H f° r the same reason that a correlation coefficient cannot exceed unity. 
The probable errors of eddy-stresses, determined from the scattering of particles 
moving with the air, may be taken to be as follows 
Probable error of xx = 0'674 . xx / V I .(25) 
Probable error of xh = 0‘674 ., + .y : ' ~ .(26) 
