merchant steamer of about 5000 tons displacement, and the case would stand something as under: No less a quantity than 320 tons would be transferred from the hull to the cargo-carrying power; and this increase would tell greatly in favour of the steel ship during a service of twenty or thirty years. It is only necessary to add that steel loses nothing as compared with iron in the variety of the forms in which it is produced, the efficiency of its connections, and its adaptability to the combinations required in the structure of a ship. Reduced thicknesses of plates and bars of course render necessary greater precautions against local failure, and particularly against buckling in the plating on decks, sides, or bottoms. Hence, if steel comes into general use, some longitudinal system of framing is likely to secure general adoption. Reduced thicknesses also necessitate greater care to prevent corrosion; and it is to be noted—although experience on this point is not sufficiently extensive to enable a definite opinion to be formed-that steel appears to corrode in sea-water rather more rapidly than iron. As to fouling, steel ships appear but little, if anything, better off than iron ships; in this particular further experience is requisite before a sound judgment can be formed. Mild steel of the character described may ultimately be displaced by some stronger material having equally good qualities as regards ductility and workability. If the manufacturers can succeed in producing such steel at moderate cost, the shipbuilder will be happy to avail himself of the opportunity to advance still further the combination of strength with lightness. CHAPTER XI. THE RESISTANCE OF SHIPS. No branch of the theory of naval architecture has a richer literature than that which forms the subject of this chapter. It would be a formidable task merely to enumerate the names of eminent mathematicians and experimentalists who have endeavoured to discover the laws of the resistance which water offers to the progress of ships; and still more formidable would be any attempt to describe the very various theories that have been devised. Again and again has the discovery been announced of the "form of least resistance," but none of these has largely influenced the practical work of designing ships, nor can any be regarded as resting on a thoroughly scientific basis. In fact, a century and a half of almost continuous inquiry has firmly established the conviction that the problem is one which pure theory can never be expected to solve. Although earlier theories of resistance are now discarded, and the present state of knowledge on the subject is confessedly imperfect, great advances have been made within the last half-century, and most valuable experimental data have been collected. The modern or "stream-line" theory of resistance may now be regarded as firmly established. Many eminent English mathematicians have been concerned in the introduction and development of this theory, as well as in the conduct of the experiments by which it has been put to the test. Of these, however, two only need be named. The late Professor Rankine did much * to practically apply the theory to calculations for the resistances and speeds of ships; and the broad generalisations which we owe to him have served ever since as guides to later investigators. Mr. W. Froude is the second worker in this field of inquiry, whose labours deserve especial mention. The experiments which for some years past he has been conducting for the Admiralty are beyond all comparison with any that have gone before them; the greatest value attaches to the small portions of his results which have yet been published; and when the inquiry is completed, and the results are fully discussed, naval architects will be in possession of a mass of facts which cannot but prove highly advantageous to the designs of future ships. These experiments of Mr. Froude have been carried on upon the basis of the stream-line theory of resistance, and have fully confirmed its soundness. In addition, however, to this service, Mr. Froude has done more than any one else to elucidate and popularise the theory. His clear and masterly sketches of its main features are well worthy of careful study; and they have the advantage of being almost entirely free from mathematics, so that the general reader can readily follow the reasoning and the experiments by which it is supported. In attempting, as we now propose to do, a brief outline of this modern theory, we gladly acknowledge our indebtedness to both Professor Rankine and Mr. Froude. A few prefatory remarks are necessary in explanation of terms that will be frequently employed. Water is not, what is termed, a perfect fluid; its particles do not move past one another with absolute freedom, but exercise a certain amount of rubbing or friction upon one another, and upon any solid body past which they move. Suppose a thin board with a plane surface to be immersed in water and moved end-on, or edgewise, it will experience what is termed * See div. i. chap. v. of Shipbuilding, Theoretical and Practical, edited by Professor Rankine. + See British Association Reports for 1875. frictional resistance from the water with which its surface comes into contact. The amount of this frictional resistance will depend upon the area and the length of the plane, as well as the degree of roughness of its surface and the speed of its motion. If this plane is moved in a direction at right angles to its surface, it encounters quite a different kind of resistance, termed direct or sometimes head resistance; this depends upon the area of the plane and the speed of its motion. Should the plane be moved obliquely, instead of at right angles to its surface, the resistance may be regarded as a compound of direct and frictional resistance. Supposing either direct or oblique motion to take place, the plane would leave an eddying "wake" behind it, as indicated somewhat roughly in Fig. 117, and the motion thus created FIG. 117 amongst the particles constitutes a very important element in their resistance to the passage of the plane. If the plane is not wholly immersed, or if its upper edge is near the surface, and it is moved directly or obliquely, it will heap up water in front as it advances, and create waves which will move away into the surrounding water as they are formed, and will be succeeded by others. Such wave-making requires the expenditure of power, and constitutes a virtual increase to the resistance. If the plane were immersed very deeply, it would create little or no surface disturbance, and, therefore, require less force to propel it at a certain speed than would a plane of equal immersed area moving at the surface with a portion situated above that surface. This statement is directly opposed to the opinion frequently entertained; which confuses the greater hydrostatical pressure on the plane, due to its deeper immersion, with the dynamical conditions incidental to motion. Were the deeply immersed plane at rest at any depth, the pressures on its front and back surfaces would clearly balance one another. When it is moved ahead at a uniform speed, it has at each instant to impart a certain amount of motion to the water disturbed by its passage; but the momentum thus produced is not influenced by the hydrostatical pressures on the plane, corresponding to the depth of its immersion. Water is practically incompressible; apart from surface disturbance, the quantity of water, and therefore the weight, set in motion by the plane, will be nearly constant for all depths, at any assigned speed. In other words, if there were no surface disturbance, the resistance at any speed would be independent of the depth. The earlier theories of resistance dealt almost exclusively with direct or oblique resistance, said little respecting frictional resistance, and nothing as to the other kinds. Commonly, the immersed surface of the ship was assumed to be subdivided into a great number of pieces, each of very small area, and approximately plane. The angle of obliquity of each of these elementary planes with the line of advance of the ship her keel-line-was ascertained; and its resistance was calculated exactly as if it were a detached plane moving alone at the assumed speed. For quantitative purposes, experiments were to be made with small planes of known area moved at known speeds, and set at different angles of obliquity; the resistances being observed. It was generally accepted that the resistance varied with the area of the plane, the square of the speed, and the square of the sine of the angle of obliquity. But obviously there was a radical error in applying unit-forces of resistance, obtained from the movements of detached planes, to the case of a ship where all the hypothetical elementary planes were associated in the formation of a fair curved surface, and none of them could have that eddying wake (like that in Fig. 117) which necessarily accompanied each experimental plane and formed so important an element of its resistance. This objection does not apply to the experiments made under the auspices. of the French Academy of Sciences, during the last century, by Bossut, Condorcet, D'Alembert, Romme, and others; these |