KESCLTAJTT COUPLE. i . 





t* the rr* r rAr owpto w**dk act tt jWtviSfl ol r.V/Al 



an^fef to eacA other. 



Let -I/A AC, AD be the axes of the given couples (see 

 fig. to Art. 24). Complete the parallelogram C/A and drew 



iie diagonal. Th.-n J A' in tin- a couple which 



resultant of the two couples of which the axes are 

 AB, AC. Complete the parallelogram / 

 the dia# M couple 



the resultant of the couples of wi, . ixes are 



or of those of which the axes are AB % AC. AD. 



Now AF*-AE 9 + AI?-AB' + AC* + s\ 



Let be the moment of the resultant couple; /., M, .V 

 those of the given couples ; 



therefore 0--Z,'+JT + 



an i it \, /A, r be the angles the axis of the resultant makes 

 those of the components, 



AB L V 



oosx "25 i "^ ; ***-G' "*" 



Hence conversely any couple may be replaced by 

 three couples acting in planes at right angles to each other; 



tlu-ir in--: i'<Mi cos*; when 



the moment of the given couplr, and X, M, v the angles its 



axis makes with the axes of the three couples. 



Thus couples follow, as t -mposition and resolution, 



laws similar to those which apply to fort**, the axis of the 

 couple corresponding to the direction of the force and the 

 moment of the coupK i'nie*ty of the force. Heoee 



xample, by Art. 29, the resolved part of a resultant 

 couple in any direction is equal to the sum of the resolved 

 part* of the component couples in the same direction. 



