MECHANICS 49 



that PE is the resultant, which we see exactly balances 

 the remaining force PF 3 . Thus is formed a many-sided 

 figure or polygon, consisting of the lines PF 1 , F 1 ^ CD, 

 DE, and EP, the five sides of which represent the five 

 forces, because a parallelogram must have its opposite 

 sides equal. 



PF 1 expresses the intensity of the force acting 

 along PF 1 . 



F X C expresses the intensity of F 2 , because F J C is the 

 side of a parallelogram whereof PF 2 (expressing the 

 intensity of F 2 ) is the opposite side. 



Similarly CD must equal PF 3 and DE must equal PF 4 , 

 while PE - F 5 . 



There may be two forces acting side by side, as in 

 a two-horsed carriage. Two such powers are called 

 parallel forces. The resultant of two parallel forces 

 acting in the same direction is equal to their sum, and, 

 when such forces are equal, the resultant of their com- 

 bined force acts midway between the points of application 

 of each; when unequal, it is in a definite degree (as we shall 

 shortly see) nearer to the stronger force. 



When the parallel forces are equal but act in 

 opposite directions, their result is to produce rotation, 

 and this tendency cannot be counterbalanced by any 

 single force. 



A practical knowledge of rudimentary mechanics was 

 no doubt early obtained, since human ingenuity would 

 readily suggest the application of a strong stick, as a lever, 

 to raise a heavy body from the ground, and would lead 

 to the perception that it is easier to push such a body 

 up a sloping surface, than to raise it in men's arms and 

 carry it. Though we^aiiitrteaduce the reader but to the 

 first elements of mechanics, we must nevertheless offer 

 some explanation with respect to the principle of the 



