PHILOSOPHICAL TRANSACTIONS. 
I. Some Measurements of Atmospheric Turbulence. 
By Lewis F. Kichardson. 
Communicated by Sir Napier Shaw, F.R.S. 
Received October 16, 1919,—Read February 26, 1920. 
[Plate 1.] 
Contents. 
Page 
I. Notation. 1 
II. Shearing stress deduced from pilot balloon observations. 3 
III. Eddy-viscosity from the same. It varies with height and with direction (anisotropic). . 5 
IV. Eddy-diffusivity from the dispersal of smoke or of parachutes. 5 
V. General theory of eddy-diffusivity deduced from scattering. 8 
VI. Osborne Reynolds’ eddy-stresses. A measure of gustiness. 10 
VII. Summary of theory of scattering of particles of air. 15 
VIII. Numerical values from scattering of particles. 19 
IX. Cumulus eddies in calm weather.26 
X. Summary.28 
I. Notation. 
The following notation is used throughout. The co-ordinate axes are a right-handed 
rectangular system x, y, h, in which Oh is directed vertically upwards, and Ox lies in 
any azimuth which happens to be convenient. Elements of distance to east and to 
north are denoted by de, dn, so that they are special cases of dx, dy. The 
atmospheric density is p, the pressure is p, acceleration of gravity is g, latitude 0 is 
reckoned negative in the southern hemisphere, and w is the angular velocity of 
the earth. Velocities are denoted hyp with a suffix to indicate the direction towards 
which they blow. Momenta per unit volume are denoted by m x , %, m K . The 
eddy-diffusivity is denoted by a capital K as in G. I. Taylor’s recent papers. 
Another, and in the author’s opinion a better, measure of turbulence is f discussed 
in a previous paper.* The relation K to £ is given by 
cp 
4 
= Sx 
a t 
K o\ 
dh 2 
(!) 
where y is either potential temperature, or else mass of water or smoke per mass of 
atmosphere. If p and £ were independent of height, then from (1) we should have 
i = oV K.(2) 
* L. F. Richardson, ‘Roy. Soc. Proc.,’ A, vol. 96 (1919), pp. 9 to 13. 
yol. ccxxi .—a 582. 
B 
[Published June 9, 1920. 
