THE PROBLEM OF THE HULL AND ITS SCREW PROPELLER. 187 
Turn now to Fig. 7. The abscissas of this figure are values of load fraction 
= a P. -y while the ordinates are values of speed fraction = - The point whose ab- 
scissa value and ordinate value are both unity is the point of basic condition, while 
diagonals passing through the origin and crossing the ordinate = 
of a = L are diagonals of effective thrust ratios, the ratio being equal to the load 
p. 
at which the diagonal intersects the ordinate = = I, and is ex- 
pressed by ae in which e. t. is the actual effective thrust while E. T. is the basic 
= I, at any value 
thrust of the propeller. 
Lay down the curve where Z; = Z,, one of the points of which must be the 
point of basic condition, and it will be found that the curve, marked A, will follow 
the law— 
I. H. P., or S. H. P., varies as 3.09 Log ‘S) or Z, varies as 3.09 Log ‘-)) 
which is the same as that for Z; when s = S. 
Boe the new basic a of the second order, S,, the ordinate of any point 
on A, — V, ” . the value of Zs; for z taken from curve 1, Fig. 6, Zs,; the original basic 
slip, S, the corresponding value of the ordinate = and the value of Z; for a taken 
from curve 2, Fig. 6, Zs, 
Log S + Zs = Log Si ate Z 5x5 
from which for any assumed values of S,, = with its corresponding value of Zs,, 
can be found a curve of values of S for a series of assumed values of = p (each less 
than a with the corresponding values of Zs. Taking a series of values of S, for 
any value of ~ , and it will be found that as S, increases S will increase and ~ di- 
V,; ‘ V 
minish until S, equals approximately 21 per cent, when the value of S will become 
constant for any further decrease of a 
The values of = and the values of S at which the latter becomes constant are 
the limits at which the change from basic slips of the first order to those of the 
second order occurs, and this statement is borne out by all the data available. The 
curve of these slips is shown at the lower part of Fig. 7, while the limiting curve of 
a is shown, marked B. For type 1 and type 3 vessels, this shift of Z; values does not 
occur, so far as can be ascertained, but Zs is taken always from curve 1, Fig. 6. 
