COMPOSITION OF COUPLES 



105 



a force 2 R at C, the middle point of A'B. These two forces 2 R, 

 2 R are equal and act in opposite directions at the same point C. 

 There is therefore equilibrium, proving that two couples are equiv- 

 alent if they have equal moments and if the planes in which they 

 act are parallel. 



81. The direction perpendicular to the plane in which a couple 

 acts is called the axis of a couple. Thus : 



Two couples having the same axis and the same moment are 

 equivalent. 



COUPLES COMPOUNDED ACCORDING TO THE PARALLELOGRAM LAW 



82. A couple, as we have just seen, is determined by a quantity 

 (its moment) and a direction (its axis). Thus it may be fully 

 represented by a straight line, the direction of this line being that 

 of the axis, and the 

 length representing, 

 on any scale we 

 please, the magni- 

 tude of the moment 

 of the couple. 



We shall now 

 show that couples 

 can be compounded 

 according to the 

 parallelogram law. 



THEOREM. Two couples, represented in magnitude and direction 

 ly two lines AB, A C, will have as resultant a couple represented in 

 magnitude and direction ~by AD, the diagonal of the parallelogram 

 of which AB, A C are edges. 



Let AB, AC be lines representing by their direction and magni- 

 tude the axes and moments of two couples. Let 8 AS' be a line 

 perpendicular to the plane ABC, A being its middle point. Let 

 us draw planes through S, S' parallel to the plane ABC, and let 

 the couple AB be replaced by two forces PS, P' S' in these two 



FIG. 57 



