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p, = 9pz, and h the height a body must fall to acquire the velo- 
city v, or let »* = 2gh, then substituting these in the expressions 
for the front and back resistances, we have for the front 
p=p,+50°=gp (2 +h), 
and the pressure on the plane area in front increases with the 
depth z, and with A or v’ directly. For the back we have 
p=P,-5v°=9p (2 —h), 
and the pressure on the back of the plane is nothing for z=h, 
and also for all less values of z. This can be seen in the easy 
experiment of moving a flat rod, or even a walking stick briskly 
through the water, when to a certain depth it will be seen that 
air follows the rear of the rod, and to a certain depth there is no 
pressure of water on the rear of the rod. This experiment, in 
accordance with theory, shows that experiments for the resist- 
ances which bodies such as ships and boats moving at the 
surface of water experience must be tried at the surface, and not 
through the body of the fluid. 
Having investigated the above expressions for the front and 
back resistances of a plane moving in a direction perpendicular 
to its surface, the rest of the investigations for the resistances of 
bodies of different forms are similar to those used in elementary 
analytical treatises on hydrostatics and hydrodynamics. Thus, 
if a small plane area moves obliquely in a fluid, let @ be 
the angle between the direction of motion and the perpen- 
dicular to the plane, then the velocity perpendicular to the 
plane is vcos@, and the perpendicular resistance varies as 
v’ cos’ 6, and this resolved in the direction of the motion is 
vcos’@. When a solid of revolution moves in the direction 
of its axis of revolution, taken for the axis of 2, in a fluid, 
we have the area of an elementary ring equal to 27yds if s 
is the arc of the curve by whose revolution the front part of 
