SHIP BUILDING. 33 



should lie in the same transverse plane for the ship to sail well. If it 

 appears from calculation that this is not the case, the necessary changes 

 must be introduced. 



4. Stability. The stability of the vessel may be regarded in two points 

 of view : first, the hydrostatic, when the floating body is at rest ; secondly, 

 the hydrodynamic, when it is in motion. A parallelopipedon whose specific 

 gravity is not more than 0.211 will always float with one surface out of 

 water, but as the specific gravity increases the surface inclines, so that with 

 the specific gravity of 0.75 the diagonal of the body lies in the water-line, 

 and it then always turns in the water. This proposition is of great import- 

 ance to the ship-builder, as it affects the form of the ship's body. 



It is evident that the resultant of the force exercised by the water in order 

 to sustain a ship, and to counteract its tendency to fall on the side, operates 

 through the centre of gravity of the immersed part, and that the direction of 

 this force is perpendicular to the surface of the water. Hence, when the 

 ship tends to fall over, the force of the water strives to restore it to its place, 

 and the amount of this force measures the degree of stability. Whenever 

 a ship assumes the direction represented in pi. 7, fig. 5, a prismatic body, 

 E, emerges from the water, while another, I, must be immersed. Both 

 these portions, dissimilar as they may be in the form of the ship, are neces- 

 sarily of equal weight, since the effect of their pressure is the same, and 

 their line of intersection, S, must be straight, and at the same time parallel to 

 the axis of rotation which passes through the centre of gravity G. Let ab be 

 the line which separates the immersed portion from the portion not immersed, 

 G the centre of gravity of the whole ship, F the centre of gravity of the 

 immersed part when the ship stands upright, and Q the same point 

 when the ship inclines to the side. Now suppose QTVM drawn perpendi- 

 cularly through Q, the lines FT and GV through F and G, perpendicular to 

 QM, and through G the line GO parallel to QM, intersecting FT in O. 

 Now, since in the inclination of the ship the volume E is taken away and 

 the volume I added, and since the contents of every volume are supposed to 

 be combined at its centre of gravity, it follows that the volume E will 

 appear transferred to I ; and calling the horizontal distance of the centre of 

 gravity y, we have the momentum ?/E or yG proceeding from the transference 

 of E. Now, when the ship inclines at the angle ASa, or the equal angle 

 FGO, the water must act upwards in the direction of the line QM, and in pro- 

 portion to the weight of the ship or its pressure, which we will call D ; and 

 the force which is to restore the ship to an upright position, or rather turn 

 it around the axis passing through the point G, is, according to Attwood, 

 D X GV = D X FT — D X FO, and since D x FT, the horizontal momentum 

 produced by the transference of E to I, is equal to the momentum of E, 

 that is, equal to yl, we have D x GV = yl — D X FO = yl — D x FG x 

 sin. FGO. Now putting i for FG, and s for sin. FGO, the angle of inclina- 

 tion, we have the formula for determining the stability of the vessel, D X GV 

 = yl — Dis. The simple inspection of figs. 6 and 7, where A and B repre- 

 sent two ships with equal water lines and equal centres of gravity both of 

 the whole and of the immersed parts will show, that if the side lines of one ship 



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