[6] The principle which underlies the experiment is this:—If any one body forming part of a system of heavy bodies be moved from one position in the system to another, the weight of the body moved multiplied into the distance through which it is moved, is precisely equal to the weight of the whole system of bodies multiplied into the distance through which the common centre of gravity of the whole has moved. If in a ship, therefore, a movable weight of known amount is moved across the deck through a given known distance, the centre of gravity of the ship itself, with all on board, has been moved in a line parallel to that through which the small weight has been transferred, and through a distance inversely proportioned to the weight of the whole ship to the weight moved. If, for instance, a weight of five tons should be moved through a distance of twenty feet, then multiplying this weight into this distance and dividing by the total weight of the ship, the distance through which the ship’s centre of gravity has travelled parallel to the deck is obtained. If, at the same time, an exact measure of the angle through which the ship has been inclined by moving the five tons through the distance named has been taken, and the position of the ship’s metacentre has been obtained, then the elements of a triangle are known—namely, the degrees in each of its angles, and the length of one of the sides—and from these the length of the remaining sides of the triangle is easily deduced. One of these sides will be the distance between the metacentre of the ship and its centre of gravity, and, consequently, the metacentre being known from calculation, the position of the centre of gravity becomes known also.
[7] The classification of strains here given is as contained in White’s “Manual of Naval Architecture.” To this authoritative source readers must turn who wish a full exposition of the several problems go shortly dealt with in these pages.
[8] This will be more fully referred to further on, but it may be stated here that the need for independent calculation is largely obviated, owing to the existence of “co-efficients,” deduced from investigations made by experts. Further, the existence and influence of the Registration Societies are such that the codes of scantling and the structural supervision instituted by them together constitute the only guarantee of structural strength generally desiderated.
[9] Suppose the dimensions of a proposed vessel to be 320 × 36 × 26½ feet, then, according to a method of approximation largely in use, the sum of these dimensions divided by 100 gives what is known as the “cubic number”—(320 × 36 × 26½ ÷ 100) = 3052 cubic number. Suppose that for a vessel already built, similar in type and dimensions, or of similar proportions, to the one proposed, the cubic number, when divided into the ship’s actual weight (i.e., the displacement minus the weight of machinery and the dead-weight carried), gives say ·53, then this figure represents the “co-efficient” of ship’s weight, and applying it in the case supposed gives:—3052 × ·53 = 1620, the weight of hull for proposed vessel. This example illustrates the manner in which the weight of machinery is estimated, and indicates the nature and use of the general term “co-efficient:” frequently employed in this chapter.
[10] One such method, devised and followed by Mr C. Zimmermann in his daily practice as chief draughtsman to the Barrow Shipbuilding Company, and described by him before the Institution of Naval Architects in 1883, gives with very little preliminary calculation, and at once, a close approximation to the correct displacement. Another system, originated and used in practice by Mr Chas. H. Johnson, chief designer to Messrs Wm. Denny & Brothers, consists of an analysis of the lines of vessels of various degrees of fineness and fulness previously built, formulated for daily use in a series of curves of areas, giving, for sections at certain fixed distances from midships—in terms of percentage to the midship area—the particular area specially suited to afford the required displacement; and at the same time to maintain the general form of hull which in actual practice has proved satisfactory with respect to speed. In his later practice, Mr Johnson has found it preferable to use the block form of analysis of Mr A. C. Kirk (considered further on in matters relating to speed), using the three sides of that form as a basis upon which to group the water-lines.
[11] For illustrated descriptions of this and other improved calculating instruments referred to in this chapter, see [Appendix].
[12] This experimental method, it may be explained, has long been practised in connection with ships built for the Royal Navy, and for a considerable number of years it has been systematically followed in some leading merchant shipyards. Messrs A. & J. Inglis, Pointhouse, Glasgow, and Messrs Wm. Denny & Bros., Dumbarton, were amongst the earliest firms to systematically adopt the practice. With the former it has been customary to incline every vessel of distinctive type built by them since 1871, and with the latter the practice has been constantly followed from a date somewhat subsequent. For some years past other firms on the Clyde and elsewhere have adopted the method, the data so accumulated being found an admirable basis from which to estimate the height of the centre of gravity in proposed vessels. Tables giving the results of inclining experiments made on various types of merchant steamships and sailing vessels will be found in “White’s Manual of Naval Architecture,” pages 82-87.
[13] From the first volume (1860) of the Transactions of the Institution of Naval Architects, it is seen that Dr Inman, Samuel Read, and Dr Woolley had each already found different methods of simplifying Atwood’s calculations.
[14] Various other methods of simplifying the calculations based on Atwood’s theorem were subsequently proposed, and one or two different methods also brought forward—notably one in 1876 by the late Mr Charles W. Merrifield, afterwards improved by the late Professor Rankine, and one by Mr J. Macfarlane Gray, of the Board of Trade, described by that gentleman in 1875, but since considerably improved. Most of them were laid before the Institution of Naval Architects in papers which will be found enumerated in the list at end of chapter. While such propositions did not contribute directly to bring the problem of stability to its presently accepted form, they deserve to be remembered as tokens of the great labour and skill which have been expended in founding and developing this branch of scientific naval architecture.
[15] “On Cross-Curves of Stability; their Uses, and a Method of Constructing Them, Obviating the Necessity for the Usual Correction for the Differences of the Wedges of Immersion and Emersion.”