46 



WELLS'S NATURAL PHILOSOPHY. 



the center of gravity no longer corresponds with the center 

 of magnitude, or the central point of the bulli of the body. 



Fig. 11. Thus, in a sphere, a cube, or a cylinder, the center of grav- 



ity is the same as the center of the body. In a ring of uni- 

 form size and density, the center of gravit}- is the center of 

 the space inclosed in the ruig (see Fig. 11). This example 

 shows that the center of gravity is not necessarily included 

 in that portion of space occupied by the matter of the body. 

 In a w'lieel of wood of unilbrm density and thickness tho 

 •enter of gravity will be the center of the wheel, but if a part of the rim be 

 made of iron, the center of gravity will be removed to some point aside from 

 the center. 



"WTien two bodies are connected together, they may be regarded as one 

 body, having but one center of gravity. If the two bodies be of equal weight, 

 the center of gi-avity will be in the middle of the line which unites them ; 

 but if one be heavier than the other, the center of gravity will be as much 

 nearer the heavier body, as the heavier exceeds the lighter one in weight 

 Pj(j_ ]^2. Thus, if two balls, each weighing four pounds, be 



connected together by a bar, the center of gravity 

 will be a point on the bar equally distant from 

 each. But if one of the balls be heavier than the 

 other, then the center of gravity will, in propor- 

 tion, approach the larger ball. This is illustrated by reference to Fig. 12, in 

 which the center of gravity about which the two balls support themselves, is 

 seen to be nearest to the heavier and larger ball. 



89. The center of gravity of a body being regarded as the 

 point in which the sum of all tho forces of gravity acting upon 

 the separate particles of the body are concentrated, it 

 be considered as influenced by the attraction of the earth 

 in a greater degree than any other portion of the body. It 

 follows, therefore, that if a hody has freedom of motion, it can not be brought 

 into a position of permanent equilibrium, until its center of gravity occupies 

 the lowest situation which the support of the body will allow; that is, the 

 center of gravity will descend as far toward the center of the earth as possible. 



_ 90, By Equilibrium we mean a state of rest 



What do we J ^ 



nieanbyEquui- produccd by the counterpoise, or balancing, of 

 opposite forces, 



I Thus when one force tending to produce motion in one direction, is oppa'sed 

 by an equal force tending to produce motion in an exactly opposite direction, 

 the two balance each other, and no motion results. To produce any action, 

 there miat be an inequality in the condition of one of the forces. 

 J, , The truth of this principle may be illustrated by certain ex- 



periment can perimonts which at first seem to be contradictory to it. Thus 

 This priQci^e ? '^ cylinder may be made to roll up an inclined plane. Fix a 

 piece of lead, I, Fig. 13, on one side of the cylinder a, so that 



When will the 

 Center of Grav- 

 ity be in perma- 

 nent rest, or 

 equilibriuiu '! 



