SOME MEASUREMENTS OF ATMOSPHERIC TURBULENCE. 
19 
If we replace the summation by an integration over a large area S in the plane of xy, 
the element of mass crossing per unit time is dx dy pv R , so that the “ Austausch ’ 
becomes 
S 
pv n ( h—h 0 ) dx dy which is p times Taylor’s diffusivity as defined in ‘ Phil. 
Trans.,’ A, vol. 215, p. 3. Thus we must suppose that W. Schmidt’s definition of 
“ Austausch ” requires amplification concerning the interval of time and concerning the 
position in it of the velocity, just as Taylor’s definition of K does. 
VIII. Numerical Values Derived from the Scattering of Particles. 
Fig. 1 is a photograph* of the trail of paraffin vapour from an extinguished blast- 
lamp which projected the vapour in a direction at right angles to the wind. It 
shows a cone, with a blunt point due to the finite size of the source of smoke, passing 
smoothly into a form, which certainly diverges less rapidly than the initial cone, and 
which looks like a paraboloid. Opinion might differ slightly as to where to draw the 
lines corresponding to the standard deviation of smoke. In a “ normal ” distribution 
0'68 of the whole number of particles lie between the two standard deviations. If 
the lines are placed as in the accompanying black and white drawing, then it follows, 
as the mean velocity of the smoke was 17 metres/sec., and the density of the air 
was 1'21 x 10 -3 grm. cm. -3 , that 
stress hh = —073 dyne cm. -2 diffusivity = K = 240 cm. 2 sec. -1 
turbulivity = ^ = 340 grm. 2 cm. -2 sec. -5 . 
This photograph was taken in the evening, when the day-wind was diminishing. 
The source was 190 cm. above ground. Obstructions to windward only subtended 
an angle of 2°'l at the source of smoke. The exposure lasted 60 seconds. 
Fig. 2 was taken five minutes later in the same place, with an exposure of 
85 seconds. 
The velocity of the smoke had decreased to 1'3 metres per sec. The measurements 
yield 
hh = — 1 '2 dynes cm. -2 ; K = 750 cm. 2 sec. -1 ; £ = 1050 grm. 2 cm. -2 sec. -5 . 
In this case the photograph shows a distinct neck between the cone and the paraboloid, 
at a distance from the source roughly 1*3 times its height above ground. This neck 
can also be recognized in some other photographs. Its presence signifies that 
the motion of the air was compounded of (i.) a random eddying, plus (ii.) a wave 
motion in which the particle of air executed a wave having a length, relative 
to a point fixed to the earth, roughly 2‘6 times the height of the particle above 
ground. 
* Taken at Benson. 
D 2 
