44 APPLIED MECHANICS 
It may be observed that the moment of any one of the forces, say 
BO, is obtained by drawing through M a parallel to BC to intersect the 
sides of the funicular polygon which meet on BC at 0’ and c’ ; b’c’ x oh 
is the moment of BC about M. 
61. Principle of Moments.—When a number of forces acting on 
a rigid body are in equilibrium, then the moments of all the forces about 
any given axis being taken, the sum of the moments of those forces 
which tend to turn the body in one direction about the axis is equal to 
the sum of the moments of those forces which tend to turn the body in 
the opposite direction about the same axis. 
62. Couples.—A couple consists of two equal parallel forces acting in 
opposite directions. The arm of a couple is the perpendicular distance 
between the lines of action of the two forces. The moment of a couple 
is the product of the magnitude of one of the forces and the arm of the 
couple. A couple tends to cause a body to rotate. 
Two couples will balance one another when (1) they are in the same 
plane or in parallel planes, (2) they have equal moments, and (3) their 
directions of rotation are opposite. 
63. The Centre of Parallel Forces.—If a system of parallel forces 
acts at fixed points, the resultant will act through another fixed point, 
called the centre of the system. ‘This centre is independent of the 
Fig. 43. 
direction of the forces so long as the sense of each in relation to the sense 
of one of the forces is unaltered. 
In Fig. 43, P, Q, R, and S§ are parallel forces acting at the fixed 
points A, B, C, and D respectively in a plane. By means of the force 
and funicular polygons the line of action LK of the resultant is deter- 
mined. Let the direction of the forces be changed so that they act as 
shown by P’, Q’, R’, and 8’. The line of action MK of the resultant is 
determined as before. The point K, where LK and MK intersect, is the 
centre of the parallel forces P, Q, R, and S acting at the points A, B, C, 
and D respectively. If the construction be repeated with the forces 
acting in any other direction, it will be found that the new resultant 
will act through the same point K. 
In Fig. 43 the forces P, Q, R, and § have all the same sense, and 
