SOME MEASUREMENTS OF ATMOSPHERIC TURBULENCE. 
5 
III. Eddy-viscosity from Pilot Balloon Observations. 
( Abridged , January 22, 1920.) The method of the last section will give the 
difference of the shearing stresses on two surfaces of any horizontal slab of air. If we 
choose one of the surfaces so that dv/dh = 0 and consequently also the stress 
vanishes, we obtain the stress on the other surface. This has been done for some 
very smooth means for Lindenberg (E. Gold, Met. Office, ‘ Geophys. Mem.,’ V., p. 143). 
The results are set out in the following table :— 
Table II.—Lindenberg. 
The x axis is directed with the surface wind. The stress is that exerted by the 
upper on the lower layer. 
Height above 
mean sea, 
kilometres. 
Eddy-shearing-stresses. 
Rates of mean shearing. 
Eddy viscosities. 
xh 
dynes cm. -2 . 
yh 
dynes cm. -2 . 
3 j'x 
dh 
sec. -1 10 3 x 
0 '\, 
dh 
sec. -1 10 3 x 
Parallel 
to wind. 
xh 
Perpendicular 
to wind. 
yh 
3 v x \dh 
dyne cm. -2 sec. 
dvy/dh 
dyne cm. -2 sec. 
1-0 
+ 0-05 
-0-09 
- 1*0 
- 0-2 
50 
450 
0-8 
+ 0*01 
-0-37 
- 1*2 
- 1*6 
10 
250 
0-7 
zero 
0-6 
+ 0-02 
-0*71 
1 
- 3*2 
20 
220 
0-4 
+ 0-09 
-0*99 
60 
- 9-0 
15 
110 
0-3 
+ 0-39 
- 1-06 
12-5 
- 12-2 
31 
87 
0-2 
+ 0-69 
-0-90 
0*12 ground 
+ 1-10 
-0*64 
21-5? 
-17-5? 
51 
37 
To obtain a quantity comparable with f we must multiply the eddy-viscosity by 
g 2 p which is approximately 1100 c.g.s. units. 
The mean of the viscosities in the two directions increases with height as we 
might expect from other observations ( vide Part VIII., below, also ‘ Roy. Soc. Proc.,’ 
A, vol. 96 (1919), p. 18). But the most interesting thing about this table is the 
marked lack of isotropy in viscosity. The air appears to he more viscous, for large 
motions, across the wind than parallel to it, except just near the ground. 
IV. Eddy-diffusivity from Smoke or Floating Bodies. 
Some direct measurements have been made by observing the gradually increasing 
scatter of smoke or other visible material carried along by the air. The changes in 
height of a large number of small portions of air are observed during a fixed interval 
of time. These changes are found to be distributed about their mean value 
