1910. | The Wave-muking Resistance of Shaps. 199 
properties of a ship in terms of the coefficients of a simple equivalent pressure 
distribution of the type specified. Another point which must be noted is that 
the previous expression is obtained by considering two-dimensional motion 
only; but the bow and stern of a ship act more like point disturbances than 
as transverse line systems, hence there are diverging, as well as transverse, 
waves. In default of a fuller analysis, I have suggested for certain reasons 
the addition to R of a term ae~%9/®*; it is retained for the present, because it 
indicates the necessity for some expression of the diverging waves and it 
agrees with certain general properties of them, and also in several cases it 
allows us to obtain better numerical agreement at lower speeds. 
We suppose that R is expressed in pounds per ton displacement of the ship, 
also V is the speed in knots, L the length of the ship on the water line in 
feet, and ¢ is equal to V/,/L; then we have 
1 = ae-37 + B (1 — cos ne) e-® Ibs. per ton, (2) 
where m = 11°30/L and n = 11°31/L. 
In the following examples attention is directed chiefly to the variations of 
8 and m, and incidentally to those of y and ». The length d cannot be taken 
directly as the length of the entrance or run of the ship, for it will depend also 
on the lines of the model; but one may expect the ratio b/L to decrease as 
the slope of the model at the bow is increased, and conversely; similarly the 
number x will vary in a direction which may be predicted. In the previous 
paper sufficient agreement was found when m and m were assigned fixed 
values; in many cases the mean curve of residuary resistance appeared to 
havea point of infiection near c = 1°3, and for this we had m = 2:53; further, 
the humps and hollows agreed with n = 10:2 for the angle n/c? in radians, or 
n = 584 for the angle in degrees. With none of the coefficients fixed before- 
hand, it is necessary to adopt some method of approximation. Drawing the 
experimental curve of residuary resistance on a suitable scale, a fair mean 
curve was sketched in and an equation R = Ae~”/” was found, generally by 
graphical methods, to fit this as closely as possible ; in fact it was the original 
intention to limit the study to the two leading coefficients A and m so deter- 
mined. The value of m is now fixed, and from the intersections of the mean 
curve with the actual oscillating curve one could assign a value to m with 
sufficient accuracy. Finally the three remaining quantities were found from 
three points on the actual curve, for example, at c = 0°6, 1:2, 18, if the curve 
extended so far. In practice the lowest point determines «, for the term in 8 
is negligible there ; for the same reason the values of 8 and y are more satis- 
factory when fairly high values of ¢ are available. In all cases the 
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