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 ( UNIVERSITY J 



VSi^WX 



UPON THE SIDES AND BOTTOM OF A CYLINDRICAL VESSEL. 163 



density and specific gravity express the same thing" under different aspects ; the 

 former being' more accurately restrained to the greater or less vicinity of particles, 

 the latter to a greater or less weight in a given volume ; hence, as weight depends 

 upon the closeness of the particles, the density varies as the specific gravity, and 

 the terms may in most cases be indiscriminately used. 



The specific gravities of fluids are usually considered without any regard to the 

 empty spaces between the particles, though if the particles of fluids are spherical, 

 the vacuities make at least one fourth of the whole bulk. But it is sufficient that 

 we know precisely in what sense the specific gravities of fluids are understood. 



PROBLEM XXV. 



163. A cylindrical vessel whose sides are perpendicular to 

 the horizon, has a certain quantity of fluid in it; which fluid, 

 by reason of a sudden change of temperature, has its magnitude 

 or bulk increased by a certain part of itself : 



It is therefore required to determine what will be the 

 alteration of pressure on the sides and bottom of the vessel. 



Let ABCD, and abed respectively, represent vertical sections of 

 the cylindrical vessel, of which the sides are perpendicular and the 

 base parallel to the horizon ; then in 

 the first instance, let E F be the height 

 to which the vessel is filled, and ef 

 the height to which the fluid rises, 

 by reason of the change that takes 

 place in the temperature. 



Draw the diagonals EC, FD and 

 ec, fd intersecting respectively in 



the points G and g, and through the points G, g, draw the Vertical lines 

 MN and mn ; then are MG and mg, the respective depths of the centres 

 of gravity of the cylindric surfaces, in contact with the fluid before 

 and after the expansion, and MN, mn, are the depths of the centres 

 of gravity of the bases or bottoms D c and dc. 



Through the points G and g, draw the straight lines GT and gs, 

 parallel to the horizon and to one another; then is GS or rg the 

 height which the centre of gravity of the cylindric surface is elevated, 

 by reason of the expansion of the fluid. 



Put d = DC or dc, the diameter of the cylindric vessel, 



h = MN, the height to which the vessel is originally filled, 

 h'mn, the height at which the fluid stands in the vessel after 

 expansion, 



M 2 



