200 Dr. T. H. Havelock. [June 7, 
approximation was not carried further than the circumstances seemed to 
warrant ; the values of the coefficients are given generally in round numbers, 
and the theoretical curves were calculated throughout their range from 
the formule so obtained. 
3. The first series is taken from a paper by D. W. Taylor* on the influence 
of the shape of midship-section upon the resistance of ships; from the 
curves in that paper I have taken four, which form a series having the same 
midship-section coefficient, but with different displacements. The data and 
the results are given in the following table :— 
Table I.—Models I to IV. 
Displace- | Displace- 
No. ment |ment-length | Beam. Draft. a. B. Y- m. N. 
in lbs. coefficient. 
i 500 26 6 1°365 0°467 16 81 O14 | 2°7 584 
II 1000 53 °2 1-930 0 660 2°0 160 0:18 | 3°0 540 
Til 1500 “79:8 2 °364 0-809 2-0 240 0-18 | 3:2 540 
IV 2000 119°7 2 895 0-991 2°5 360 0-18 | 3°5 540 
Cylindrical coefficient = 0°68 ; midship-section coefficient = 0°90; 
water-line length = 20°51 feet; beam/draft = 2-923. 
The curves in fig. 1 indicate the results of the analysis; in each case the 
continuous curve is the experimental curve of residuary resistance; the 
points marked by circles have been calculated from the formula (2), while 
the broken curve is a mean curve graphed from the expression 
ae m9 + Be-mlc’ The calculated curves have been extended as far as ¢ = 3, 
in order to include the highest theoretical point of intersection of the mean 
and oscillating curves. 
The third column in Table I refers to a coefficient of fineness used by 
Taylor in the paper referred to; it is defined as D/(L/100)*, where D is the 
displacement of the model in salt water in tons, and L is the water-line 
length in feet. It is a method of estimating the proportions of a model by 
the displacement of a ship of the same lines and of 100-feet length. 
From the numbers in Table I, 8 appears practically proportional to the 
displacement. The resistance R has been calculated in pounds per ton 
displacement, so that dimensionally 8 is a pure number. In this series 
certain quantities are constant, namely, with the ordinary notaticn, L, B/H, 
(Bx Hx L)/D, and (area of midship-section)/(B x H). As far as this series 
is concerned we might regard £ as proportional, for instance, to (B x H)/L? 
or to the displacement-length coefficient. 
*D.W. Taylor, ‘Trans. Amer. Soc. Nav. Arch.,’ vol. 16, p. 13 (1908). 
72 
