268 LECTURE XXI. 



Thus, when a little figure, containing a bubble of air, is immersed in a jar of 

 water, which is so covered by a bladder that it may be compressed by the 

 hand, the bulk of the figure with its bubble is diminished by the pressure, it 

 is, therefore, less supported by the water, and it begins to sink : and when 

 the hand is removed, it immediately rises again. (Plate XIX. Fig. 248.) 



While a body is actually rising or sinking in a fluid, with an accelerated 

 motion, the force of gravity being partly employed in generating momentum, 

 either in the fluid or in the solid, the whole pressure on the bottom of the 

 vessel is necessarily somewhat lessened. Hence the apparent weight of a jar 

 of water will suffer a slight diminution, while a bullet is descending in it, or 

 while bubbles of air are rising in it, but the difference can seldom be great 

 enough to be rendered easily discoverable to the senses. 



It sometimes happens that a solid body is partly supported by a fluid, and 

 partly by another solid; of this we have an example in one of Dr. Hooke's 

 ingenious inventions for keeping a vessel always full. A half cylinder, or a he- 

 misphere, being partly supported on an axis, which is in the plane of the sur- 

 face of the fluid, its weight is so adjusted, as to be equal to that of a portion 

 of the fluid of half its magnitude: when the vessel is full, it is half immersed, 

 and exerts no pressure on the axis : it descends as the fluid is exhausted, and 

 its tendency to turn round its axis can only be counteracted, by the pressure 

 of the fluid on its flat side, as long as the surface of the remaining portion 

 of the fluid retains its original level. (Plate XIX. Fig. 249.) 



When a fluid is contained in a vessel of a flexible nature, the sides of the 

 vessel will always become curved, in consequence of the pressure, and the 

 more, in proportion as the pressure is greater; the form of the curved surface 

 will also be such that the common centre of gravity of the fluid^and the ves- 

 sel may descend to the lowest point that the circumstances of the case allow; 

 this form is generally of too intricate a nature to be determined by calcula- 

 tion : no mathematician has hitherto been able to investigate, for example, 

 the curvature which a square or rectangular bag of leather will assume when 

 filled with water or with corn. When, indeed, one dimension only of a ves- 

 sel is considered, for instance, when the bottom of a cistern is supposed to be 

 flexible, and to be fixed at two opposite sides, while the ends are simply ia 



