2527] 



EQUIVALENT SYSTEMS. 



29 



magnitudes of these components are X, F, Z. The original 

 vector is thus replaced by vectors X, F, Z localised in the axes, 

 and by three couples about the axes, whose moments (by last 

 Article) clearly are 



yZ-zY, zX-xZ, xY-yX 

 respectively. 



Hence any system of vectors localised in lines can be replaced 

 by a single vector localised in a line through the origin, whose 



Y&amp;lt;- - 



Fig. 26. 



resolved parts parallel to the axes are 2X, 2F, *ZZ, and by a couple, 

 equivalent to component couples about the axes, whose moments 

 are *Z(yZ-zY) t ^(zX-xZ), 2(a?F-yZ), where X, F, Z are 

 the resolved parts of any one of the original vectors parallel to 

 the axes, and a?, y, z are the coordinates of any point in the line 

 in which that vector is localised. 



