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by a normal pressure outwards py, which is constant for all 
points at the instant under consideration. 
Thus if 4PQ be a portion of the curvilinear margin of a 
leaf exposed to the resistance of the current which is moving 
with velocity » in the direction CB, o the density of the 
water, t the tension at the point P, 7+ dr the tension at the 
contiguous point Q, the are AP=s, dQ =s+ 4s, ¢ the angle 
-made by the tangent at P with BO, 6+6¢ that at @; then, 
assuming the usual law of resistance due to the current, the 
element PQ when the power of growth is just balanced, will be 
in equilibrium under the following mechanical forces: 
Tension + at P along tangent at P in a direction remote 
from Q, 
tension t+5r7 at Q along tangent at Q im a direction remote 
from P, 
‘ 1 ; ‘ 
resistance 5 ov" sin® @. ds normally inwards, 
pressure p.ds normally outwards. 
By resolving these forces first tangentially with respect to 
P and then normally, the following equations are obtained : 
—T+(r+6r) cos 6+ (p — 5 ov" sintg ) be. sin = 0, 
(r + dr) sin dg — (p-5 avt sin’ ¢ ) 8s.cos 2 =0; 
and passing to the limit when 67, 6¢, ds are indefinitely di- 
minished, it is readily seen that 
dt 
a 
dp _ 1 2 ae fn 
de P59 oU mn $; 
