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Excerpt from The Marine Engineer and Naval Architect, Vol. 46: March, 1923 When a ship is a oat, the mean draught can be deter mined only approximately. Considering only the external and physical sources of in accuracy, Admiral Taylor pointed out that these can amount to 'as much as one-half-oi one per cent. Of the displacement. In the choice, therefore, of any approximate method of integra tion, such a method should yield no more than this percentage inaccuracy and, preferably, should be even correct to within i per cent. Of the true displacement. It is further desirable that the-rule adopted should slightly underestimate the dis placement in order that the inaccuracy may be treated as a margin against possible contingencies. From these considera tions Admiral Taylor was lead to adopt the ordinary trapezoidal rule with 21 ordinates for purposes of displacement calculation. Moreover, as an error of per cent. Is permissible, a vessel whose mean beam is 40 it. Need only have the ordinates of the waterplane measured to the nearest 0 1 of a foot, and hence the half-ordinates to the nearest0'05 of a foot. Thus, it is suffi ciently accurate in vessels of this size to measure the ordinates to the first decimal place. This fact was very clearly brought out in an example given by Admiral Taylor in the paper previously referred to, for a greater accuracy was actually obtained in the calculation of a mathematically lined vessel whose correct displacement was '5 tons, by using ordinates correct to one decimal place than by using ordinates correct to two and three decimal places. To obtain the same accuracy as the ordinary trapezoidal, naturally fewer ordinates may be used-with the Simpson's, the corrected trapezoidal and the mean trapezoidal rule. The sine curve used in the example on page 8 was integrated by the ordinary, the corrected and the mean trapezoidal rules, over a range of number of ordinates and the percentage errors obtained. These are plotted in Fig. 3 to a base of number of ordinates, and only refer to such curvilinear figures as have their least ordinate at one end and greatest at the other. For figures such as waterplanes, whose least ordinates are at each end and their greatest amidships, the number of ordinates should be halved and then increased by one, in order to obtain the relative accuracy from Fig. 3. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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