200 LECTURE XXI. 



the same height in both of them, in order to remain in equilibrium : for if 

 any portion be supposed to stand, in either leg, above the surface of the 

 fluid in the other leg, it is obvious that its centre of gravity may be lowered, 

 by removing so much of it as will raise the fluid in the opposite leg to its 

 own level, the situation of the fluid below remaining unaltered ; conse- 

 quently the centre of gravity of the whole fluid can never acquire its lowest 

 situation, unless both the surfaces are in the same level. 



The air, and all other elastic fluids, are equally subject with liquids to 

 this general law. Thus, a much greater force is required, in order to 

 produce a blast of a given intensity with a large pair of bellows, than with 

 a smaller pair ; and for the same reason, it is much easier to a glassblower, 

 when he uses a blowpipe, to employ the muscles of his mouth and lips, 

 than those of his chest, although these are much more powerful. If we 

 estimate the section of the chest at a foot square, it will require a force of 

 seventy pounds to raise a column of mercury an inch high, by means of the 

 muscles of respiration, but the section of the mouth is scarcely more than 

 eight or nine square inches, and a pressure of the same intensity may here 

 be produced by a force of about four pounds. The glassblower obtains, 

 besides, the advantage of being able to continue to breathe during the 

 operation, the communication of the chest with the nostrils remaining 

 open, while the root of the tongue is pressed against the palate. 



It is obvious that the pressure on each square inch of the side of a vessel, 

 or on each square foot of the bank of a river, continually increases in 

 descending towards the bottom. If we wish to know the sum of the 

 pressures on all the parts of the side or bank, we must take some mean 

 depth by which we can estimate it ; and this must be the depth of the 

 point which would be the centre of gravity of the surface, if it were 

 possessed of weight. Thus, if we had a hollow cube filled with water, the 

 centre of gravity of each side being in its middle point, the pressure on 

 each of the upright sides would be half as great as the pressure on the 

 bottom, that is, it would be equal to half the weight of the water contained 

 in the cube. 



If, however, we wished to support the side of the cube externally by a 

 force applied at a single point, that point must be at the distance of one 

 third of the height only from the bottom. For the pressure at each point 

 may be represented by aline equal in length to its depth below the surface, 

 and a series of such lines may be supposed to constitute a triangle, of 

 which the centre of gravity will indicate the place of the centre of pressure 

 of the surface ; and the height of the centre of gravity will always be one 

 third of that of the triangle. It is easily inferred, from this representation, 

 that the whole pressure on the side of a vessel, or on a bank, of a given 

 length, is proportional to the square of the depth below the water to which 

 it extends. (Plate XIX. Fig. 245.) 



The magnitude of the whole pressure on a concave or convex surface 

 may also be determined by the position of its centre of gravity ; but such 

 a determination is of no practical utility, since the portions of the forcbs 

 which act in different directions must always destroy each other. Thus 

 the perpendicular pressure on the whole internal surface of a sphere filled 



