NATURAL PHILOSOPHY. 



[Lesson XIII 



the single force (the rope) would be the 

 resultant of the three forces. 



167. T. How can you explain the 

 action offerees ? 



P. By means of diagrams. Thus, the 

 various lines are made to represent the 

 quantity or intensity of the forces, the 

 eilbcts produced, and the directions in 

 which they act. 



168. T. When several forces act in 

 concert upon a given point, what are they 

 termed? 



P. The system of forces. If, however, 

 we speak of them in reference to the 

 equivalent or resultant force, they are then 

 termed latent or component forces. 



169. T. How can you determine the 

 resultant of forces ? 



P. When two or more forces act in the 

 same direction, their resultant is the sum 

 of the separate forces ; but if they act in 

 opposite directions upon one point, their 

 resultant is equal to the difference of the 

 two, and the line of action is in the direc- 

 tion of the greater force. 



170. T. Suppose that two forces act 

 upon one point, and make an angle with 

 each other, how will you find the resultant 

 of them ? 



P. By means of the law called the 

 parallelogram of forces, which is explained 

 by this diagram. Suppose that a ball is 

 placed at the point a, and two forces are 



Fiy. IS. 



acting upon it at the same moment, the 

 one in the direction a f, the other in the 

 direction a d. Now let us take it for 

 granted that the one force will move the 

 ball of itself in a second from the point a to 

 b, while the other force will only move it from 

 a to c in the same space of time. It is, there- 

 fore, very evident that the same result would 

 ensue, as if one force acted upon the ball 

 in the direction of the line a c, because if 

 in one second the ball would !>< impelled 

 as far as a b, and then the action of ihe 

 force cease, and the ball only subjected to 

 the action of the second force, it would 



reach e in another second. Therefore it 

 is certain, that if the two forces acted at 

 the same instant, that the ball would reach 

 the point e, and the single force that 

 would produce the same Jesuit, if applied 

 in the direction of the line a e, in the re- 

 sultant. 



171. T. What is meant by the com- 

 position of forces ? 



P. It is the process of finding a single 

 force that is equivalent to two or more 

 forces. 



172. 2'. What is the resolution of 

 forces ? 



P. It is the process by which we can 

 find forces that will produce a motion 

 equal to that of a single force. 



173. T. Give me an example of this. 

 P. Let ^/represent a boat,/ithe rope 



by which it is drawn along, and also the 



Fiy. 19. 



force of draught. It may then be assumed 

 that there are two forces acting, /#, which 

 draws the boat forward, and f //, which 

 would draw the head in the direction f h 

 were it not counteracted by the helm e d, 

 which is parallel to the line/z. When the 

 boat is moving the resistance of the water 

 acts upon the helm, which may be explained 

 thus. If c a represents the resistance, it 

 may be resolved into a d and e c. Now, as 

 a d produces no effect upon the helm, it is 

 evident that the pressure is in the line e c t 

 which tends to turn the stern of the boat in 

 the direction b c k, and thus counteracts 

 the force f h. 



174. T. How can you prove the correct- 

 ness of the law of the parallelogram of 

 forces ? 



P. By experiment. For example, sup- 

 pose that we have three forces, each equal, 

 and opposed to the resultant of the oilier 

 two, a state of equilibrium will be the re- 

 sult. You observe that I have two \ 

 pieces of wood attached to the table, and 

 that each of them has a movcable slide, to 

 which apv.lley, that turns easily upon its axis 



