MECHANICS. 39 
be represented by h’, the pressure upon I will be represented by FA’. 
Suppose the partition wall now replaced by a layer of water, this will ex- 
perience a pressure from above of FA’, and a pressure from below of FA; 
equilibrium can therefore only exist when h=h’', or when the level is 
equally high in both vessels. If the liquid in the different vessels be 
different, however, the level will be unequal. If, for example, in fig. 8, one 
vessel contain water and the other mercury, they will meet each other in the 
plane passing through g. Below the plane gh there is only mercury ; above 
it in the one vessel there is water, in the other mercury, the water pressing 
upon the mercury so as to force it into the smaller vessel in proportion to 
its height, never, however, attaining to the same level. The heights of the 
liquids will naturally be inversely as their specific gravities, and as these are 
as 1:14, the column of water must be 14 times the height of that of 
mercury. 3 
b. Law of Archimedes ; Specific Gravity. 
Under certain circumstances, heavy bodies may move in a direction 
opposite to that of gravity. Thus wax and wood rise from the bottom to the 
top of a vessel filled with water ; a piece of brass rises in mercury, &c. All 
these phenomena depend upon that important law first discovered by 
Archimedes, and named after him. A body immersed in a fluid loses in 
weight by an amount equal to the weight of the fluid displaced. This may 
be explained by means of fig. 9, pl. 18, where a combination of several ver- 
tical prisms is immersed in a fluid. The proposition is readily proved for 
a single right prism ; as in this case the pressures on the different sides of the 
prism mutually balance each other, it is only necessary to consider that 
upon the top and bottom. The upper surface experiences a downward 
pressure equal to that of a column of fluid whose base is this upper surface, 
and whose altitude is the height of the fluid above the surface of 
the prism. The lower surface, on the other hand, is pressed upwards by 
a force equal to the column of fluid whose base is the lower base of the 
prism, and whose height is that of the fluid above this base, equal, therefore, 
to the height of the fluid above the prism, plus the height of the prism itself. 
The heights of these two columns differ, therefore, by the height of the 
prism, and it is therefore evident that the pressure from below, or the up- 
ward pressure, exceeds the pressure from above or the downward pressure, 
by the weight of a column of fluid equal in volume to the prism immersed. 
This excess of upward pressure acting contrary to the weight of the body, 
or to its gravitation, necessarily relieves the latter of an amount of weight 
equal to that of the fluid displaced. All bodies, of whatever irregularity of 
shape, may be considered as composed of right prisms, to each of which, 
and consequently to whose sum, the above reasoning will apply. <A con- 
vineing proof of the accuracy of this law, which applies to both liquids and 
gases, may be had by means of the apparatus figured in fig. 10. At one 
end of a common balance is suspended a hollow cube of metal, beneath 
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