62 STATICS OF SYSTEMS OF PARTICLES . 



Thus we have a new definition of a moment, which is exactly 

 equivalent to that previously given, namely: 



The moment about a line L of a force R acting at A is equal 

 to AM, the perpendicular from A on to L, multiplied by the com- 

 ponent of R in a direction perpendicular to AM and to L. 



48. From this conception of a moment we have at once the 

 theorem : 



The sum of the moments about any line L of any number of 

 forces acting at a point A is equal to the moment of their resultant 

 about L. 



For, let R lf R z , be the forces, and R their resultant. Let AM, 

 as in 47, be the perpendicular from A on to L, and let AS be a 

 direction perpendicular to AM and to L. The theorem to be proved 



is that 



AM x component of R^ along AS 



+ AM X component of R 2 along AS -\- 

 AM x component of R along AS. 



On dividing through by AM the theorem to be proved is seen 

 to be simply that the component of R along AS is equal to the 

 sum of the components of R, R z , - along AS, which is known 

 to be true. 



We can now see more clearly how it is that the moment of a 

 force, defined as we have defined it, gives a measure of the tendency 

 to turn. In fig. 32 we are taking moments about a line L which 

 is at right angles to the plane of the paper and meets this plane 

 at M. The force whose moment is being considered is a force R 

 acting at the point A. At A we have three directions mutually at 

 right angles, namely 



AS, AM, and the direction of a line through A parallel to L. 

 The moment of R about L has been defined to be 

 AM x component of R along AS. 



