62 APPLIED SCIENCE 



62. Force Expressed Graphically. Sometimes it is neces- 

 sary to express or measure a force or forces graphically, 

 that is, by means of lines. This is particularly true in the 

 building of machinery and structures,* where the results of 

 the application of force and skill may be obtained with less 

 labor than by calculation. Graphic expression also gives ac- 

 curacy sufficiently near for good practice. Force is mea- 

 sured in this way by considering the beginning of a line to 

 be the point at which the force is applied, the length of the 

 line to be its magnitude, and the direction of the line to 

 be the direction of the force. 



To illustrate: If a force of 10 Ibs. is applied at a certain point A 

 in an easterly direction, it would be represented by the line AB 

 drawn 10 units in length. If there are two forces acting on a body 

 at A and at right angles, one with an easterly direction of 10 Ibs. 

 and another with a northerly direction of 5 Ibs., the actual direction 

 of the motion of the body may be repre- 

 sented by the following parallelogram, the 

 lines of which are parallel to each other 

 (Fig. 39). If AC represents a force of 5 

 Ibs. (called a component force) and AB 



represents a component force of 10 Ibs., 

 Fia. 39. Parallelogram .t. . , A e ,, 



of Forces. AD W1 ^ represent the resultant of the 



two forces. To maintain the forces AB 



and AC in equilibrium a force must be applied at A equal to 

 AD and acting in the opposite direction AF. 



AF = AD 

 AF is called the equilibrant. 



The above principle may be worked backwards. For 

 example: If one force is given, it is always possible to find 

 two others in given directions which will balance it. 



