" A1»PEND1X. 291 



longer than A C, or any other single side of the parallelo- 

 gram. This is called the composition and resolution of mo- 

 tion. [Note. Several things in this Lesson may be obscure 

 to some students : the teacher should explain and illustrate 

 them by familiar " verbal instructions," and by such figures 

 and diagrams as he may have in his possession, or may 

 easily draw upon paper or a slate.] 



LESSON 20. 



Levers. — First kind, ^g. 7. C E is the lever, and B the 

 prop. A the stone to be raised = 1000 pounds, and the 

 strength of a man at C = 100 pounds. Since the strength 

 of the man is only one tenth the weight of the stone, that the 

 power and weight may balance each other, the arm of the 

 lever B C must be ten times as long as the arm B E. Second 

 kind, fg. 9. If the hand C be nine times as far from A as 

 the point X, then one pound at C will balance nine pounds 

 at B. Fig- 5. a burden on a pole. Weight W three 

 times nearer to a than to b, a then will bear three times as 

 much of the weight as b. Third kind, Jig. 10. Distance 

 P F 3 inches ; W F 12 :— then 20 pounds at W will require 

 the force of 80 at P in order to balance it, for 12 is four 

 times 3. Fig. 2. man's arm, — D centre of motion, — the 

 power is the muscle inserted at C, — A the weight : — now as 

 the distance D C is one tenth part of C A, the muscle, there- 

 fore, must exert a power equal to 100 pounds in order to 

 raise 10 pounds. 



LESSON 21. 



Pulley. — Fig. 13. single moveable, — in order to raise the 

 weight W one inch, the power P must draw the strings B 

 and C one inch each : the whole string, therefore, is short- 

 ened two inches, while the weight is raised only one. Fig. 

 15. System of pullies. While the weight W rises one inch, 

 each of the four ropes must be shortened an inch, and P, 

 therefore, must move four inches : 5 pounds at P will ba- 

 lance 20 at W. Wheel and Axle, Fig. 11. If the diame- 

 ter of the wheel be 4 feet, and that of the axis only 8 inches, 

 then the power P of 100 pounds will balance the weight W 

 of 600 pounds ; for 6x8=48 inches which make 4 feet, the 

 diameter of the wheel. Inclined Plane. Fig. 8. If B C= 



m 



