56 
20. The cause producing rota- 
tion in the screw propeller is the 
force of the engine which is 
measured by a moment of force 
(M), acting at H, a unit of distance 
from the axis AB of the propeller. 
Or, in other words, the force (M), 
measured either in tons or in lbs. 
avoirdupois, acting at the point 
H in a direction perpendicular to the radius CP, must 
balance exactly the force of the engines which are applied 
to turn the screw round, and thereby to give motion to the 
vessel. 
To a given constant moment of force (M), applied through 
the engines to give motion to the propeller in order to propel 
a given vessel, there belongs necessarily a definite uniform 
angular velocity (u) of the propeller, and, also, a definite 
uniform velocity (y) of the vessel. 
The determination of these velocities, in terms of the 
moment (M), and the data supplied by the geometrical 
form of the propeller, is the chief object of the following 
investigation. 
The case, then, to be considered here is, that in which the 
acceleration, produced by the constant application of the 
moment of force (M), has been entirely absorbed by the 
resistance of the water in which the vessel is moving. 
21. In accordance with the usual and well known theory 
of plane areas striking fiuids with given velocities, it follows 
that the normal pressure on the element {a) will vary in 
proportion to the square of its normal velocity. 
The normal pressure, therefore, on the element (a) is, 
either 
fxf^ruGOHv — vcosctj^a (17) 
or, — (v - V)cosa}^a (18) 
according as the propeller strikes the water when it is at 
rest, or when it is in motion with a velocity V in the 
direction of the vessel’s motion. 
