54 GRA VITA TION. 



legs, as a chair, the base is the polygon formed by joining 

 the points of support. 



116. Stability. W7ien the line of direction 

 falls within the base, the body stands ; when with- 

 out the base, the body falls. 



In the case of the tower represented in Fig. 23, if the 

 upper part be removed, the line of direction will be as 

 shown by the left hand dotted line. It falls within the 

 base, and the tower stands. When the upper part is fast- 

 ened to the tower, the line of direction is represented by 

 the right hand dotted line. This falls 

 without the base, and the tower falls. 

 The stability of bodies is measured 

 by the amount of work necessary to 

 overturn them. This depends upon 

 the distance that it is necessary to 

 raise the centre of gravity (equivalent 

 to raising the whole body), that the 

 line of direction may fall without the 

 base. When the body rests upon a 

 point, as does the sphere, or upon a 

 line, as does the cylinder, a very slight 

 force is sufficient to move it, no elevation of the centre of 

 gravity being necessary. The broader the base, and the 

 lower the centre of gravity, the greater the stability. 



117. Illustrations of Stability. Let the figure 

 represent the vertical section of a brick placed upon its 

 side, its position of greatest 



stability. In order to stand f 

 the brick upon its end, g, the 



centre of gravity must pass a 



over the edge c. That is to FIG. 24. 



