93 
the vessel which it propels, leads to the conclusion that this 
assumption is by no means a correct one. A slight correc- 
tion in the formula 2 will therefore be necessary to meet 
the case when the element (a) strikes the water which has 
a velocity (V) in the direction of the axis A.B. By resol- 
ving Y in the direction of the normal line the result will be 
Ycosa. This resolved velocity must be added to N in 
equation (2), then it follows that the element (a) striking 
the water at rest with a normal velocity N 1 where 
N 1 = rucosy - (v - V)cosa (4) 
will be exactly the same as the element (a) striking the 
water, having a velocity Y in the direction of the axis, with 
a velocity N — rucosy — vcosa. 
In this case the surface of vanishing pressure is deduced 
from (4) by the relation 
rwcosy 
v= — - + V 5 
COSa 
Equation (5) will do good service in explaining the perplex- 
ing phenomenon of negative slip which has been one of the 
experiences of screw propulsion by means of the common 
Archimedean screw. 
It will be observed that the element (a) of the screw pro- 
peller blade can be made to assume any position in space by 
assigning suitable values to the angles a, (3 , y which fix 
absolutely the direction of the radius of curvature of the 
propeller blade at the given point P. Now the question 
naturally arises, from what has been said in the foregoing 
articles, viz., what values must be given to the angles a, j3 , 
y at the point P, and how must they vary from point to 
point on the propeller blade, so that the resistance in the 
direction of the axis shall be a maximum when the resist- 
ance to angular motion is a given quantity ? 
It is hardly necessary to add that the solution of the 
above problem is not easily accomplished. It is to be hoped, 
however, that practical experience in union with mechanics 
