26 
MR. LEWIS F. RICHARDSON ON 
justification for this procedure is that Taylor has given reasons* for supposing that 
the viscosity, and therefore also the conductivity, is proportional to the velocity. 
For comparison with the present observations, the diagram shows Taylor’s mean 
value of the diffusivity at the Eiffel Tower, t and also some general means} deduced 
from precipitation by the writer. 
In order to compare them it has been necessary to assume some corresponding 
velocities; for which purpose I have taken 540 cm. sec. -1 at the mean height of the 
Eiffel Tower, 700 cm. sec. -1 as a world-mean at 500 metres and 1000 cm. sec. -1 for 
the same at 8500 metres. These are based on information given in Hann’s 
‘ Meteorology.’ The conversion formulae between eddy-conductivity, diffusivity and £ 
have been given in Section I. In order to compress into a diagram the large ranges 
of height and conductivity, logarithms have been plotted. A smooth curve is drawn 
through the clustered observations over land. It shows a maximum between the 
heights of 100 and 1000 metres, and a marked falling off above and below. Not 
only c/v but also c the conductivity has a maximum here. Taylor’s first 
observations related to heights near this maximum and so he naturally came to the 
conclusion that there was no marked variation with height. 
IX. Cumulus Eddies in Calm Weather. 
The familiar sequence, which can be observed in many places, is here illustrated by 
the mean of some selected days in latitude 49° in France, on the bare grass moors to 
the west of the forest of Argonne, in the month of May. The sun rose at 4h. 20m. 
local apparent time, hut could not be seen for mist. By 6h. the disk of the sun 
became visible. At 7|-h. the mist was rising in large pieces, leaving a brilliant blue 
sky. At 9h. the first cumuli appeared over the forest. About half-an-hour later 
they appeared over the grass land also. By noon the cumuli covered of the sky. 
By 16h. the cumuli had begun to spread out horizontally, and by 19h. they had 
vanished, leaving the sky clear again. 
Now here we have a collection of eddies in which the rising parts, represented by 
the cumuli, visibly move to a level where they remain by mixing with their 
surroundings. So we should be able to calculate the diffusivity K by the direct 
application of the formula given by G. I. Taylor (‘ Phil. Trans.,’ A, vol. 215, p. 3) 
K = i Jj A v H (h-h')dxdy, .(1) 
where h—h! is the height through which the air has moved before mixing, d h is its 
vertical velocity, and A is a large horizontal area. Only, as Taylor’s formula assumes 
* G. I. Taylor, ‘Roy. Soc. Proc.,’ A, vol. 92, pp. 196-199. 
t G. I. Taylor, ‘Roy. Soc. Proc.,’ A, vol. 94 (1917), p. 141. 
1 L. F. Richardson, ‘Roy. Soc. Proc.,’ A, vol. 96 (1919), p. 18. 
