VOL. LXXXVI.] PHILOSOPHICAL TRANSACTIONS. 685 



creates a force by which the inclination is augmented. And since various causes 

 concur in preventing the 2 centres from remaining adjusted to the vertical with 

 a precision absolutely mathematical, it follows that the least or evanescent incli- 

 nation here mentioned must necessarily subsist, and being continually augmented 

 by the fluid's pressure, must become a sensible rotation, by which the solid 

 oversets from its upright position. 



In either oase, that is, whether the solid floats permanently, or oversets, if it 

 be placed on the surface of a fluid, so that the centre of gravity of the solid 

 and the centre of gravity of the part immersed shall be in the same vertical line, 

 the solid is said to be in a position of equilibrium : and from the preceding ob- 

 servations it appears, that there are 3 species of equilibrium in which a solid 

 may be situated when the 2 centres of gravity just mentioned are in the same 

 vertical line. 1st. The equilibrium of stability, in which the solid floats per- 

 manently in a given position. 2dly. Tiie equilibrium of instability, in which 

 case the solid, though its centre of gravity and that of the part immersed are in 

 the same vertical line, spontaneously oversets, unless sustained by external 

 force. This kind of equilibrium is similar to that which subsists when a needle, 

 or other sharp-pointed body, is placed vertically on a smooth horizontal surface. 

 3dly. The 3d species, being a limit between the former 2, is called the equili- 

 brium of indifference, or the insensible equilibrium, in which the solid rests on 

 the fluid indifferent to motion, without tendency to right itself when inclined, 

 or to incline itself farther. 



These diflferent kinds of equilibrium may perhaps be more clearly perceived, by 

 referring to the instance in which a cylinder was supposed to be placed on the 

 surface of a fluid with the axis vertical. If the axis be assumed double the dia- 

 meter of the base, the solid floats permanently with the axis vertical. It seems 

 evident therefore, that there must be some intermediate proportion between the 

 cylinder's axis and the diameter of the base, greater than 1 to 2, and less than 

 2 to 1, which will correspond to the case intermediate, where stability ceases, 

 and instability begins: this is the precise proportion when the equilibrium is of 

 the species called the equilibrium of indifference, or the insensible equilibrium. 



When a solid body floats permanently on the surface of a fluid, and external 

 force is applied to incline it from its position, the resistance opposed to this 

 inclination is termed the stability of floating. It is obvious to every one's ex- 

 perience, that some floating bodies are more easily inclined from their quiescent 

 position than others; that, after having been inclined, some will return to their 

 original situation with more force and celerity than others; a difference particu- 

 larly observable in ships at sea, in some of which a given impulse of the wind 

 will cause a much greater inclination from the perpendicular than in others. As 

 this property of opposing resistance to heeling or pitching, when regulated to 



