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for any assumed angular velocity (u) the greater the velo- 
city of the element is in its normal direction the greater is 
the force with which the element of the screw propeller 
blade will strike the water. 
In consequence of this it is absolutely necessary to com- 
pute geometrically the normal velocity of the element (a) 
by means of the data supplied by the dimensions of the 
propeller, its angular velocity (u) and its velocity (y) in the 
direction of the axis AB, in order to determine the amount 
of resistance to angular motion and motion parallel to AB. 
This is the preliminary proposition the solution of which 
can be found without any reference to the theory of the 
resistance of fluids. 
3. Suppose, then, that the element ( a ) placed at P is sub- 
ject to the influences of two causes, viz. the velocity (rw) 
perpendicular to the plane ABP. and the velocity (v) paral- 
lel to the axis AB. The object now is to find an expression 
for the normal velocity arising from these two causes. 
To do this it is only necessary to resolve (ru) the angular 
velocity and the velocity (y) parallel to AB into two direc- 
tions, viz. : perpendicular and parallel to the normal line. 
Thus is obtained, 
rwcosv — velocity parallel to normal, 
rwsinv = velocity perpendicular to normal. 
The latter velocity produces no effect upon the water, as 
friction in this case is entirely disregarded. 
The former, however, is the velocity with which the 
element (a) of the propeller blade strikes the water in the 
case when there is no motion parallel to AB. 
The effect of (v) the velocity parallel to AB, in the direc- 
tion of the normal to the element ( a ) must be deducted 
from ('mcosy) in order to obtain the full normal velocity 
with which the element ( a ) strikes the water. The resolu- 
tion of (y) in the direction of the normal will be vcosa, 
