Page:Elementary Text-book of Physics (Anthony, 1897).djvu/145

§ 117] after each addition, until the tube is filled. The boiling must not be carried too far; for there is danger, in this process, of expelling the air so completely that the mercury will adhere to the sides of the tube, and will not move freely. For rough work the tube may be filled with cold mercury, and the air removed by gently tapping the tube, so inclining it that the small bubbles of air which form can coalesce, and finally be set free at the surface of the mercury.

115. Archimedes' Principle.—If a solid be immersed in a fluid, it loses in weight an amount equal to the weight of the fluid displaced. This law is known, from its discoverer, as Archimedes' principle.

The truth of this law will appear if we consider the space in the fluid which is afterwards occupied by the solid. The fluid in this space will be in equilibrium, and the upward pressure on it must exceed the downward pressure by an amount equal to its weight. The resultant of the pressure acts through the centre of gravity of the assumed portion of fluid, otherwise equilibrium would not exist. If, now, the solid occupy the space, the difference between the upward and the downward pressures on it must still be the same as before,—namely, the weight of the fluid displaced by the solid; that is, the solid loses in apparent weight an amount equal to the weight of the displaced fluid.

116. Floating Bodies.—When the solid floats on the fluid, the weight of the solid is balanced by the upward pressure. In order that the solid shall be in equilibrium, these forces must act in the same line. The resultant of the pressure, which lies in the vertical line passing through the centre of gravity of the displaced fluid, must pass through the centre of gravity of the solid. Draw the line in the solid joining these two centres, and call it the axis of the solid. The equilibrium is stable when, for any infinitesimal inclination of the axis from the vertical, the vertical line of upward pressure cuts the axis in a point above the centre of gravity of the solid. This point is called the metacentre.

117. Specific Gravity.—Archimedes' principle is used to determine the specific gravity of bodies. The specific gravity of a body