[Illustration: Fig. 40. F. The centre. A B C D E. Plummet-lines, all pointing to the centre, and therefore diverging from each other.] [Illustration: Fig. 41. P P P. Inclined planes, gradually decreasing in height, cut out of inch mahogany, with a groove at the top to carry an ordinary marble. B B B. Different positions of the marble, which starts from B A.] In a sphere of uniform density, the centre of gravity is easily discovered, but not so in an irregular _mass_; and here, perhaps, an explanation of terms may not be altogether unacceptable. _Mass_, is a term applied to solids, such as a mass of lead or stone. _Bulk_, to liquids, such as a bulk of water or oil. _Volume_, to gases, such as a volume of air or oxygen. [Illustration: Fig. 42. A B D, The three points of suspension. C, The point of intersection, and, therefore, the centre of gravity. P, The line of plummet.] To find the centre of gravity of any mass, as, for example, an ordinary school-slate, we must first of all suspend it from any part of the frame; then allow a plumb-line to drop from the point of suspension, and mark its direction on the slate. Again, suspend the slate at various other points, always marking the line of direction of the plummet, and at the point where the lines intersect each other, there will be the centre of gravity. [Illustration: Fig. 43.] If the slate be now placed (as shown in Fig. 43) on a blunt wooden point at the spot where the lines cross each other, it will be found to balance exactly, and this place is called the _centre of gravity_, being the point with which all other particles of the body would move with parallel and equable motion during its fall. The equilibrium of bodies is therefore much affected by the position of the centre of gravity. Thus, if we cut out an elliptical figure from a board one inch in thickness, and rest it on a flat surface by one of its edges (as at No. 1, fig. 44), this point of contact is called the point of support, and the centre of gravity is immediately above it. In this case, the body is in a state of secure equilibrium, for any motion on either side will cause the centre of gravity to ascend in these directions, and an oscillation will ensue. But if we place it upon the smaller end, as shown at No. 2 (fig. 44), the position will be one of [Page 35] equilibrium, but not stable or secure; although the centre of gravity is directly above the point of support, the slightest touch will displace the oval and cause its overthrow. The famous story of Columbus and the egg suggests a capital illustration of this fact; and there are two modes in which the egg may be poised on either of the ends. [Illustration: Fig. 44. The point of support. C, The centre of gravity.] The one usually attributed to the great discoverer, is that of scraping or slightly breaking away a little of the shell, so as to flatten one of the ends, thus--