SOME MEASUREMENTS OF ATMOSPHERIC TURBULENCE. 
7 
evaporating. The cold NH 4 CL smoke proved more satisfactory in these ways. 
Lycopodium dust might be better still, as isolated grains would fall at a definite 
rate relative to the air. But I have not succeeded in making the lumps break up 
into grains. The downy parachute which carries the seed of the dandelion, Taraxacum 
officinale , has been found to be convenient. When the seed is broken off, the 
parachute falls at a rate of 10 to 15 cm. sec. -1 in still air. The standard deviation of 
this rate must be allowed for. The formulas for correction are given below. A brown 
parachute, twice as large each way as that of tarax.acum, grows near Benson. I am 
indebted to the Botanical Department of the British Museum for a search among 
their dried specimens for a large white parachute. A splendid one came from an 
African plant called strophanthus. The parachute is about 6 cm. in diameter and has 
a long stalk by which it can be held conveniently. When the seeds were broken off 
the parachutes fell, in still air, at an average rate of 20 cm. sec. -1 . 
Other artificial clouds, which have been used with success, are paraffin-oil vapour 
from an extinguished blast lamp, and smoke of phosphorus pentoxide made by 
dropping calcium phosphide into dilute hydrochloric acid. In strong winds the smoke 
from a firework known as “ Vesuvius ”* is convenient. 
If one could mark and follow individual molecules equation (5) would give the 
molecular diffusivity in still air, 0'2 cm. 2 sec. -1 . Actually what we observe is the 
centre of a small puff of smoke, and this is not constantly the position of the same 
molecules, so that in still air we find K = 0. To be perfectly exact all observations 
of K by this method should be increased by 0'2 cm. 2 sec. -1 , an entirely negligible 
correction. In any theory the diffusivity depends on the motions which the theory 
does not follow in detail. In laboratory experiments, in which the molecular motion 
only is ignored, K is taken as 0'2 cm. 2 sec. -1 . In meteorological telegraphy variations 
of wind of less than 10 minutes’ duration are ordinarily ignored, and there is an 
appropriate, much larger, value of the diffusivity. In a certain scheme for numerical 
prediction it is proposed to average the wind over periods of 6 hours, and the 
further variations thus omitted must be taken into account by further increase in K. 
It follows that the puffs of smoke should be so small as to allow the smallest eddies 
to be observed, and, for the last-named purpose, that the observations should be 
spread over a period of 6 hours. In obtaining the data in the following table 
I believe the former condition has been fulfilled, but the latter has not. When only 
the order of K or f is required, it is enough to assume that the standard deviation 
is it of the distance between the extremes of height observed, when the number of 
observations is about 40. 
Observations very near the earth's surface have peculiarities. It is obvious that 
bxl^h = 0 at an impermeable horizontal surface. This condition can be satisfied in 
the integral by taking the portion of the distribution which would be cut off by the 
surface, reflecting it in the surface, and adding it to the rest of the distribution. 
* Made by Messrs. C. T. Brock & Co, 
