220 
James Small. 
is limited only by the presence of obstacles such as trees and 
mountains, and by the relative humidity of the atmosphere. 
V 
A ^ 
: / 
-~>H 
'*S 
Fig. 28. For explanation see text. 
Considering Fig. 28, let 
W=pressure of the minimum wind for dispersal, 
w=velocity equivalent to W, 
M=pressure of the effective part of W, 
m=velocity equivalent to M, i.e., the rate at which the wind 
overtakes the fruit moving with the velocity of h.' 
R=normal component of M, 
S=tangential component of M (i.e., surface slip), 
H=horizontal component of R, 
H'=pressure exerted on the pappus by H, 
h'=velocity equivalent to H', 
V=vertical component of R, 
#=angle of axis of fruit with horizontal. 
Since the value of V is M cos# sin#, the minimum wind 
required for dispersal will depend on the value of cos# x sin# and 
thus on the angle at which the fruit is tilted. The product of 
cos# x sin# varies from + ’5 to—-5 and reaches its maximum value 
of-f'5 when #=45°. The position of the fruit in which M cos# 
sin# reaches its maximum value for any given wind is, therefore, 
with the axis of the fruit at 45° to the horizontal. Since any wind 
which is able to lift the fruit will carry it along, the minimum 
wind which will disperse the fruit will be the one with which the 
fruit assumes an angle of 45°. The value of # in this particular 
case is, therefore, 45°. An angle of 45° for the pappus (with the 
• 
fruit in the normal position) is the usual one for the pappus in the 
