FUNDAMENTAL THEORY OF COUPLES. 



By A. G. Greenhill, M.A. 



Two equal, parallel, unlike forces make a couple. 



The arm of a couple is the perpendicular distance 

 between the forces. 



The moment of a couple is the product of either force 

 into the arm. 



I. The moment of the forces of a couple about any 

 axis perpendicular to the plane of the couple is constant 

 and equal to the moment of the couple. 



The moment of the forces (fig. 33) in the direction of 

 the rotation of the couple about 



O is P. - P. O - P. A 



II. A couple may be replaced by any other like couple 

 of equal moment in the same or a parallel plane without 

 altering the effect. 



This is proved by shewing that two unlike couples in 

 the same or parallel planes will balance if their moments 

 are equal. 



Let each force of one couple be P and of the other Q 

 (fig. 34). Let ABCD be the parallelogram formed by the 

 lines of action of the forces. 



