57 
The constant fx can be determined by experiment only ; 
it is the normal pressure when, and wcosv— 1, 
upon the element (a). 
22. The formulse (17) and (18) give therefore the normal 
pressure on the element {a) in the two cases under con- 
sideration. 
This resultant pressure, however, remains to be decom- 
posed, in the usual way, into three directions, viz. in the 
direction of the axis AB, in the direction of the radius CP, 
in the direction of a line at right angles to the plane AGP 
respectively. 
By the application of the principles of the decomposition 
of forces the following equations readily obtain. 
Pressure parallel to AB = Thrust. 
= li[rueo^.v - {v- V)cos.a}^acos.a ...(19) 
Pressure parallel to CP = ^{ri^cos.j/ - (v - V)cos.apacos./3 ...(20) 
Pressure perp. to planeACB = fx^riceo^.v- (v - V)cos.apacos.j/ ...(21) 
23. It may be observed with respect to the above three 
pressures that each of them acts at the point P. 
1st. The amount of pressure indicated by formula (19) 
corresponding to each element of the screw popeller, must 
be added together to balance the resistance to the vessel and 
propeller. 
If, therefore, this resistance, in accordance with the usual 
theory, measured by v^, then it follows that 
juV = /xS|mcos.v - (v- V)cos.a}^<xcos.a (22) 
where jj} is the resistance of vessel and screw when moving 
with a velocity unity; and, S signifies the sum of the quan- 
tities 
{rz^cos.v ~{v- V)cos.a}acos.a 
for each point in the propeller blades. 
2nd. The pressure indicated by formula (20) tends to 
twist the axis of the propeller ; and must be counteracted 
by an equal pressure from another blade placed in an oppo- 
site direction to CP. 
3rd. The pressure indicated by formula (21), correspond- 
ing to each element of the propeller blades, must be added 
together. Besides this force there is the skin resistance of 
O 
