FORCE AND MOTION. 39 



the aid of trigonometrical formulae. When the com- 

 ponents act at right angles to each other, the resultant is 

 the hypothenuse of a right-angled triangle. (See Olney's 

 Geometry, paragraph 346.) When the components are 

 equal and include an angle of 120, the resultant divides 

 the parallelogram into two equilateral triangles. It is 

 equal to either component, and makes with either an angle 

 of 60. (Let the pupil draw such a diagram.) 



86. Equilibraiit. A force whose* effect is to 

 balance the effects of the several components is 

 called an equilibrant. It is numerically equal to the 

 resultant, and opposite in direction. Thus in Fig. 10, the 

 gravity of the weight V is the equilibrant of W and w\ 

 it is equal and opposite to the resultant represented by 

 AD. 



87. Triangle of Forces. By reference to Fig. 9, 

 it will be seen that if AC represent the magnitude and 

 direction of one component, and CD the magnitude and 

 direction of the other component, the line AD, which 

 completes the triangle, will represent the direction and 

 intensity of the resultant. Where the point of application 

 need not be represented, this method of finding the rela- 

 tive magnitudes and directions is more expeditious than 

 the one previously given. If the line which completes the 

 triangle be measured from D to A, that is to say, in the 

 order in which the components were taken, it represents 

 the equilibrant ; the arrow-head upon AD should then 

 be turned the other way. If this line be measured from 

 A to D, that is, in the reverse order, it represents the 

 resultant. 



