SOME MEASUREMENTS OF ATMOSPHERIC TURBULENCE. 
15 
it follows that the corrected stress is given by 
hh =- P v' n v' u =- P {{v n -c)(v n -c)-{v H -c) 2 -c'c'} .... (30) 
which is the actual formula used in working up the observations. Here c'c' is the 
square of the standard deviation of the velocity of the parachutes in still air. 
Next we require the product moments in order to find the shearing stresses xh and 
yh. The raw moment v x (v s —c) is found on expanding to be equal to v x (v H — c) + v' x v' n . 
So that the corrected value for the stress is 
xh = pv hP x = P { v x{ v h (% c )}>.(3l) 
and as c'c' does not appear, the scatter of the velocities of the parachutes in still air 
does not make a correction necessary for the shearing stresses. 
VII. Summary of Theory of Scattering of Particles of Air. 
The conclusion we have reached is the following. For any sort of eddy, whether 
due to “ dynamical instability,” or to the rising of heated air in cumuli, the eddy- 
stresses are best measured by equations (22), (24) and the like, because the theory 
from which they are derived is very general; and the eddy-viscosity is best measured 
as the ratio of the shearing eddy-stress to the rate of mean shearing strain. It is 
conceivable that xh found from (24) might turn out to be zero. In that case it would 
be necessary to investigate effects of higher order. This might possibly be done by 
developing, for the quantity {-kpv 2 + p\Js+p) in equation (12) an analysis similar to 
that of (l) to (ll) for potential temperature. The diffusivity for potential 
temperature, on the other hand, should be measured differently according as the 
eddies are produced by variations of potential temperature or not. Thus for cumulus 
eddies we should take the mean of (3), retain the linear term on its right-hand side 
and neglect the quadratic one. Then t 2 —t 1 must be small, so that 
$0 _ 30 (h^—hx) _ /00V / 
W - Hh ~ \dh) ' 11 
(31a) 
The diffusivity is measured as the right side of. this equation divided by 0 2 0/0/? 2 . 
Thus 
K = 
00 
dh 
h 
0 2 0/0A 2 
(32) 
But for eddies due to dynamical instability, neglect the linear term in (3) and measure 
the diffusivity as n 1 w 
K= fcM. (33) 
2fe—O 
where ( t 2 —t x ) must not be too small. It will be interesting to see whether eddy- 
diffusivity is found to be equal to eddy-viscosity divided by density. 
