6q2 philosophical transactions. [anno 1796. 



city continually retarded, till it arrives at the greatest inclination on the other 

 side. This rolling of the ship, with alternate acceleration and retardation of the 

 angular velocity, will evidently depend on the force by which the angular motion 

 is generated ; that is, on the force of stability, and its variation corresponding 

 to the several angular distances of the vessel from its upright position ; from this 

 cause arises one of the principal difficulties in the practice of naval architecture ; 

 i. e. to give a vessel a sufficient degree of stability, and at the saine time to avoid 

 the inconveniences which proceed from an angular velocity of rolling, increasing 

 and decreasing too rapidly. It is certain that the variation of the force of sta- 

 bility depends principally on the shape given to the sides of the vessel, which 

 admit of being so constructed, all other circumstances permitting, that the 

 force shall increase either slowly or rapidly to its limit. 



From the preceding investigations we observe that some floating bodies 

 during their inclination from O" to 90°, pass through a position of equilibrium, 

 in which the force of stability becomes evanescent: in other bodies, no limit of 

 this kind takes place ; a dit!erence which depends partly on their forms, and 

 partly on the disposition of the centres of gravity of the solids and of the im- 

 mersed volumes. It may be satisfactory to consider, in a general view, the 

 effects produced on the motion of ships by the different proportions of their 

 stability while they are inclined round the longer axes. If a vessel should be of 

 a cylindrical form, floating with its axis horizontal, the vertical sections must 

 necessarily be equal circles : supposing the centre of gravity of such a cylinder 

 to be situated out of the axis, the vessel will float permanently with its centre of 

 gravity, and the centre of the section passing through it, in the same vertical 

 line : if such a vessel should be inclined from the upright by external force, it 

 will be impelled in a contrary direction by the force of stability, which increases 

 exactly in the proportion of the sine of the angle of inclination : it is plain 

 therefore, that a vessel of this description, during its inclination by heeling, 

 cannot arrive at any limit where the force of stability is evanescent; on the 

 contrary, it must continually increase till the inclination is augmented to 90° 

 where it will have become greater than at any other angle. 



Let another case be assumed : suppose the form of the vessel to be a square 

 parallelopiped, floating permanently with one of the flat surfaces upward ; when 

 this solid has been inclined round the longer axis through J 3 degrees, the sta- 

 bility will be evanescent, and the least inclination greater than that angle will 

 cause the vessel to overset : in this case, as the vessel is gradually inclined from 

 the upright, the stability will tirst increase to a maximum, and afterward de- 

 crease ; differing altogether from the variation of the stability in the preceding 

 case, when the vessel was supposed to be of a cylindrical form. Though vessels 

 are usually so constructed that during any inclination Irom 0'^ to 90° they do not 



