2527] 



EQUIVALENT SYSTEMS. 



29 



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

 vector is thus replaced by vectors X, Y, 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< -y 



Fig. 26. 



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

 equivalent to component couples about the axes, whose moments 

 are ^(yZ zY), ^(zX xZ), ^(xYyX}, where X, F, Z are 

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

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

 in which that vector is localised. 



