To apply this investigation to the actual circumstan ces of a ship, let Fig. 4 be referred to, and which is sup posed to represent the vertical plane of the body.
The equally distant sections are represented by 7r, 0, Z, X, u, cc. afore the section ep, and by 32, 30, 28, &c. abaft the same plane. The line 1, 1, also, denotes the load water section, and below which arc drawn the pa rallel and equally distant planes, 2, 2; 3, 3; 4, 4, eec. By this construction, the whole surface of the body be comes divided into trapeziums, like 1:32r0E, each of which, by means of one of its diagonals as wE, may again be divided into triangles.
From A, in the same figure, draw AC perpendicular to Btr ; and from a- and E, the lines =I and EF, perpen dicular to Ep and PT. Again from C, draw CD per pendicular to the water line; and from and I, the lines FII and 1G also perpendicular to the same line; and in this manner proceed for all the triangular spaces.
This being accomplished, draw, as in Fig. I, Plate CCCCXCII, two parallel lines IK, LM, at the same distance from each other, as the sections, and draw NO at right angles to them. Set off AC, Fig. 4, Plate CCCCXCI, from N to P in Fig. 1, Plate CCCCXCII, and make NQ equal to the distance of the section it from the stem, and draw PQ. But as the interval be tween the first section a- and the stem is less than that between the sections, and as this latter distance is taken for the perpendicular effect on the forces un every space, draw from the point 0, the line OR parallel to PQ.
Set nil also DC, Fig 4, from U to \V in Fig. I, Plate CCCCXCII, perpendicular to NR; and from N, draw through the point \V, the line NX. Also from N, let fall the perpendicular NS on OR, and from S, the per pendicular ST upon NO. Then it will follow from the preceding investigation, that NT will be the relative direct force acting on the sut face of the triangle A B7r.
Again, draw RT, and from X, the right line XY per pendicular to LM. Then will XY be the vertical force which acts against the same triangle; and in this man lier are found the direct and vertical forces acting on the triangle 25, Fig. 4.
To find the direct and vertical forces which act on the triangle 24, we make ab, Fig. I, Plate CCCCXCI I,
perpendicular to L:41, and set off the distances EF, Fig. 4, Plate CCCCXCI, from a to c, Fig. I, Plate CCCCXCII. From a di aw also ad perpendicular to be, and from d, the line de perpendicular to ab. Then will ae be the direct force. Draw again cc, and set off the distance FH, Fig. 4, Plate CCCCXCI, from the line be, Fig. I, Plate CCCCXCII, to the line LM per pendicular to the latter. Then will fg represent the vertical force acting on the triangle 24, Fig. 4, Plate CCCCXCI.
These various forces, multiplyed by the areas of the respective triangles, will produce the effect of the fluid on each of them.
In the same manner may the forces on the afterpart of the vessel he found, the construction for which is re presented in Fig. 2, Plate CCCCXCII.
The distance between the sections is 4.95 feet ; and between the water lines 2.25 feet. The computations for the direct forces, are entered in the following Tables: 6 X 105 '2'2. + 7 X 76.39 =-. 18.12.
13 x 4.95 Consequently, the vessel whose resistance we have en deavoured to estimate, will experience a resistance equi valent to that of a plane whose surface is 36.24 square feet; or, in other words, of a square whose linear edge is 6 feet, the velocity of the plane being the same as that of the vessel.
Such, however, are the difficulties attendant on this subject, that Dr. Inman, in a note to his Translation of Chapman's Treatise on Shipbuilding, observes that it is difficult to draw from the theory of resistances, "any particular conclusions applicable to shipbuilding," but that, " generally, the resistance to ships moving with the same velocity, seems to depend on the following cir C111115talICCS : First, on the area of the midship section, as causing a greater or less displacement of dun{ by the motion of the ship.
Secondly, on the form of the fore body, as causing more or less additional resistance from the motion of the ship, considering only the inertia of the particles displaced ;—that is, supposing the void space left astern in consequence of the displacement to be instantly tilled by the fluid.