MOMENTS AND CENTROIDS 43 
force per inch. Then the moment scale will be m xn units of moment 
per inch. For example, let the linear unit be one foot, and suppose that 
oh, measured with linear scale, is 4 feet. Let the force scale be 
100 Ibs. per inch, then the moment scale will be 100 x 4 = 400 foot-pounds 
per inch. 
It may be pointed out that the figure a’o’’ is the funicular polygon 
of the force AB with reference to the pole o. 
60. Resultant Moment of a System of Forces.—The resultant 
moment of a system of forces about a point is equal to the algebraical 
sum of the moments of the separate forces about that point, and it is 
obvious that this sum must be equal to the moment of the resultant of 
the system about the same point. Hence the graphical determination 
of the resultant moment of a system of forces about a point resolves into 
constructing the resultant of the system, and the determination of the 
Fie. 41. Fia. 42. 
moment of this resultant about the given point by the construction of 
the preceding Article. The two constructions may, however, be com- 
bined in one, as shown in Figs. 41 and 42. AB, BC, apd CD are three 
given forces, and M is a given point. It is required to determine the 
resultant moment of the given forces about the given point. . 
abcda is the force polygon ; ad, the closing line, gives the magnitude 
and direction of the resultant of the three given forces. A pole o is 
taken at a perpendicular distance oh from ad, which is a simple multiple 
or sub-multiple of the linear unit. The funicular polygon of the forces 
with reference to the pole o is next drawn, and the intersection of the 
closing sides OA and OD determines a point on the line of action of the 
resultant force AD. A line through M parallel to ad intersects the 
closing sides OA and OD of the funicular polygon at a’ and d’. The 
moment required is equal to a’d’ x oh. The triangle o’a’d’ is obviously 
similar to the triangle oad, and therefore, as shown in the preceding 
Article, the moment of AD about M is equal to a’d’ x oh. 
