684 PHILOSOPHICAL TBANSACTIONS. [aNNO IjyO. 



solid will change its position till it settles permanently with the axis perpendi- 

 cular to the horizon. 



The cylinder here instanced is caused either to float permanently with its axis 

 vertical, or to overset, according to the different proportions between the length 

 of the axis and the diameter of the base : though an exact estimate of the effects 

 produced by altering these proportions, can only be obtained by mathematical 

 investigation, yet a general idea of the causes by which so remarkable a dif- 

 ference is occasioned in the floating position of the 1 cylinders, will appear obvious 

 by attending to the changes which take place in the position of the line of sup- 

 port, while the solid is inclined from the upright through a small angle. For 

 whenever the line of support, in the direction of which the force of the fluid's 

 pressure acts, does not pass tliruugh the centre of gravity of the floating body, 

 that force must generate a motion of rotation round an horizontal axis which 

 passes through the centre of gravity of the solid ; and must cause an elevation of 

 those parts of the solid which are on the same side of the axis of motion with 

 the line of support, and consequently must depress those parts which are situated 

 on the contrary side of that axis. Admitting therefore, that the solid is adjusted 

 with its centre of gravity and the centre of the immersed part precisely to the 

 same vertical line, and that a small inclination takes place round the axis of 

 motion ; it will depend on the position of the line of support, whether that 

 inclination shall be counteracted, so as to restore the solid to its upright posi- 

 tion, or shall be augmented ; in which latter case the solid oversets. If the 

 nature of the figure should be such as causes the line of support to be moved 

 toward those parts which are immersed by the inclination, that inclination will 

 be counteracted, because the pressure of the fluid generates angular motion in a 

 direction contrary to that in which the solid is inclined ; but if the figure is such 

 as causes the line of support to be moved toward those parts of the solid which 

 are elevated by the inclination, the force of the fluid's pressure must continually 

 augment the inclination ; or, in other words, will cause the solid to overset, or 

 change its position, till it settles in some other, in which the equilibrium is 

 permanent. 



We observe therefore, that a solid floats permanently in a given position, 

 only because the smallest inclination from that position creates a force by which 

 the inclination is immediately counteracted, and the solid becomes restored to 

 its upright position ; and consequently, since the inclination is counteracted 

 while of evanescent magnitude, no sensible deviation from the upright can take 

 place : in cases of instability the solid oversets, though placed on a fluid with 

 the centre of gravity of the solid and that of the part immersed in the same 

 vertical line, because the smallest deviation or inclination from that position 



