Chap. xix.] HYDROSTATIC PARADOX. 191 



worked by a lever. Of course the upward movement 

 of the press is correspondingly slow. 



It arises further from the principle of Pascal 

 that the pressure exerted on the bottom of a vessel 

 depends upon the extent of surface of the bottom of 

 the vessel, and the height of the liquid column which 

 it supports. Thus, let AB'C' (Fig. 94) be a glass 

 vessel with the tube-shaped portion 

 AA', and let it be filled with some 

 liquid. Consider the area be of the 

 bottom of the vessel. It is manifest 

 that it sustains not only the pressure 

 of the column of liquid A'6c, but of 

 the column AA' as well, so that its 

 pressure is conditioned by its area Fig. 94. 



7 ,i i 1 , r? ,1 i drostatic Para- 



6c, and the height ot the column 



of liquid it supports, viz. Ac. But 

 by Pascal's law, the column AA' transmits its 

 pressure equally in all directions, and not only, 

 therefore, on the small section of the bottom 

 be, but on the whole bottom B'C'. So that every 

 portion of the surface B'C' of area equal to be bears 

 not only the pressure of the liquid column up to the 

 level of A', but also the pressure of the column 

 AA'. Thus the pressure on the bottom B'C' is equal 

 to the pressure of a column of liquid whose base is 

 equal to B'C', and whose height is equal to AC ; and so 

 the pressure on B'C' is as great as it would be if the 

 vessel had had the shape BB'C'C, the shape indicated 

 by the dotted lines. Thus the pressure on the bottom 

 of a vessel is independent of the shape of the vessel, 

 but is determined by the area of the bottom, and the 

 height of the column of liquid it supports. 



This must not be misunderstood. If two vessels, 

 one represented by BB'C'C (Fig. 94), and the other repre- 

 sented by AB'C', were filled with water, the pressure 

 on the bottom of each would be the same ; but if they 



