VOL. LXXXVI.] PHILOSOPHICAL TRANSACTIONS. 687 



timber, the specific gravity of which is to that of water as 1 to 2, should be 

 placed on the surface of that fluid with one of the flat surfaces parallel to the 

 horizon, the length being assumed considerably greater than the breadth, no 

 motion of rotation can take place round the transverse axis, by which the extre- 

 mities of the beam would be elevated or depressed ; but the solid will sponta- 

 neously revolve in this instance round the longer axis, changing its position till 

 it settles with an angle upward. 



In like manner, if the same solid should be placed horizontally on the surface 

 of the water with an angle upward, it will not spontaneously change its posi- 

 tion ; but if one extremity of the beam should be forcibly elevated, and the 

 other depressed, so as to incline the longer axis to the horizon, as soon as all 

 external force is removed, the beam will revolve on a transverse horizontal axis, 

 passing through the centre of gravity, and perpendicular to the longer axis, till 

 it settles in such a position as to leave the longer axis horizontal. These are 

 instances in which the figure of the body, and the particular nature of the case, 

 determine the axis round which the solid revolves, while it changes its situation 

 on a fluid's surface : this axis is called, for the sake of distinction, the axis 

 of motion. 



The axis of motion, round which the solid revolves, having been determined, 

 and the specific gravity being known, it appears from the preceding observations, 

 that the positions of permanent floating will be obtained, first by finding the 

 several positions of equilibrium through which the solid may be conceived to 

 pass, while it revolves round the axis of motion ; and 2dly, by determining in 

 which of those positions the equilibrium is permanent, and in which of them it 

 is momentary and unstable. Mr. A. then gives analytical calculations, and geo- 

 metrical illustrations, of the difl^erent stabilities of several forms of bodies ; but 

 by calculations and processes much too long and uninteresting to be here 

 reprinted. 



Having computed analytically the equilibrium for a parabolic conoid, it is in- 

 ferred, from this determination it appears, that if the axis should be to the 

 parameter in a proportion less than that of 3 to 4, no specific gravity can be 

 given to the solid which will make it float in the equilibrium, which is the limit 

 between the stability and instability of floating; 2dly, if the specific gravity of 

 the solid bear a greater proportion to that of the fluid than the proportion which 

 the square of the difference between the axis and f of the parameter bears to 

 the square of the axis, when the axis is placed vertical, the solid will float with 

 stability in that position : and 3dly, if the specific gravity of the solid bears a 

 less proportion to the specific gravity of the fluid than that which the square of 

 the aforesaid difference bears to the square of the axis, the solid will overset 

 when placed on the fluid with the axis vertical, and will. settle permanently with 



