38 PHYSICS. 
The same proposition holds good in reference to the walls of the vessel ; 
for, supposing an aperture made in the side of the vessel by cutting out a 
piece equal in surface to the piston, the same weight as is placed upon the 
piston would be required upon this piece to prevent the liquid from escaping 
and the resistance would be in proportion to the surface of the piece cut off. 
If the piston itself were pierced, the liquid would escape through it ; liquids, 
therefore, transmit pressure uniformly in all directions. The laws thus 
developed for weightless liquids apply equally to those with weight, as it is 
here the single molecules which receive and transmit the pressure. rie 
Another proposition with regard to liquids is the following: when a 
liquid is in equilibrium, its surface must be perpendicular to the direction 
of gravitation. When liquids are in equilibrium, they exert upon each other 
and all solid bodies with which they are in contact, a greater or less pres- 
sure : this pressure upon the bottom of a containing vessel being, without 
any regard to its shape, equal to the weight of a vertical column of the same » 
liquid, which has the bottom of the vessel for its base, and the perpendicular 
height of the water for its altitude. Haldat’s apparatus (p/. 18, fig. 1) 
serves as an illustration of this law. It consists of a bent tube fastened ina 
box and so adjusted as to admit of attachments of various forms (figs. 2—4) 
being screwed on at one end instead of dh. Mercury is now poured into the 
tube, and the height, 2, noted to which it rises in the armc. The cylindrical 
vessel, d, is screwed on to the left hand and filled to a given height, 4, with 
water, and the increased height, p, of the mercury observed in the other arm. 
The rise of the mercury is evidently the result of pressure exerted upon it by 
the water in d. Let off the water by means of the cock, r, and exchange 
the vessel, d, successively for figs. 2—4, filling them with water to the same 
height, the mercury will each time rise to the same height, p, although the » 
amount of water in the different cases is very unequal. 
The pressure experienced by any portion of the side of a vessel is repre- 
sented by the weight of a column of liquid, whose horizontal base is equal 
to the area of the portion in question, and whose altitude is the depth of its 
centre of gravity below the surface of the liquid. Jig. 5 illustrates the 
pressure upon the different points of the vertical side of a vessel. Erect at 
any point, a, a perpendicular to rs, and make this equal to ar, or the depth 
of the liquid at this point below the surface, then ab represents the pressure 
experienced by the point, @; suppose similar perpendiculars erected all 
along rs, then the entire isosceles right-angled triangle thus produced, will 
represent the entire pressure exerted upon the side in question. Ifo be the 
centre of gravity of the triangle, then a line drawn horizontally from o will 
intersect the wall in a point, c, called the centre of pressure: its height 
above the bottom is one-third of the height of the surface of the liquid. 
In vessels communicating with one another in any manner, figs. 6 and 7, 
for instance, the surfaces will stand at the same height, if the same liquid be 
contained in both vessels. Suppose in fig. 6 a horizontal partition to be passed 
through m, then, if I represent the area of this partition, and / the height 
vv, the pressure on the partition wall from below will be = Fh. In the 
broader vessel, if the height, am, at which the water is supposed to stand 
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