APPENDIX. 



EXPLANATION OF THE ENGRAVINGS. 



LESSON 17. 



Centre of Gravity. Engraving I. — If the centres of gra- 

 vity^ of two bodies, A and B, fig. 12. be connected with the 

 right line A B, then the common centre of gravity, C, will be 

 as much nearer to A than to B, as the ball A is heavier than 

 the ball B. If the ball A weigh 12 pounds, and the ball B only 

 4 pounds, and the length A B be 20 inches, then, because the 

 ball A is three times heavier than the ball B, the distance 

 A C will be three times less than the distance B C, that is, 

 A C will be 5 inches and B C 15 inches ; the point C, there- 

 fore, is the common centre of gravity of the two bodies A 

 and B, and if supported by this point they will balance each 

 other. As 12-|-4=:16 is to 20, so is 4 to 5, or so is 12 

 to 15. 



The inclining body A B C D, fig. 4. whose centre of gra- 

 vity is E, stands firmly, because the line of direction E F 

 falls within the base. But if the body A B G H be placed 

 upon it, the centre of gravity will be raised to L, and then 

 the line of direction L D will fall out of the base towards I : 

 the centre of gravity, therefore, is not supported, and thQ 



whole body must fall. 



LESSON 19. 



Compound Motion. — The body A, fig. 1. acted upon by a 

 force in the direction A B, and at the same time by another 

 force in the direction A C, will move in the direction A D. 

 If the lines A B and A C be made in proportion to the 

 forces, and C D and D B be drawn parallel to them, then 

 A D, the diagonal, will represent the force with which the 

 body will move ; and this force will be as much greater than 

 either of the two forces by which it was impelled as A D is 



