64 MEASUREMENT OF COUPLES. 



716. The conditions of symmetry assumed in the preceding 

 calculation can never be absolutely fulfilled, and it is necessary to 

 investigate the consequences of a want of adjustment. Whatever be 

 the length of the wires, and the arrangement of the points of sup- 

 port, there is no position of equilibrium other than that in which the 

 wires are in the same plane containing the centre of gravity of the 

 system. If the system is moved from this position, and kept at an 

 angle 0, under the action of a horizontal couple, the only forces 

 which are acting independent of the external couple and the torsion 

 couple of the wire are the weights of the system and the tensions of 

 the two wires. The vertical components of the tensions counter- 

 balance the weights; the horizontal components form a couple which 

 with the torsion couples are in equilibrium with the external couple ; 

 these components are therefore equal and parallel. 



It follows from this, that if we project the system on a horizontal 

 plane (Fig. 135) the projections of the two wires A^ and A^D' are 



always parallel ; the projections DD' and AjA^ of the lines which 

 join the points of attachment, will cut at O, on the vertical which 

 passes through the centre of gravity of the system, and are divided 

 by this point into parts which are inversely proportional to the 

 vertical components of the tensions. 



If / and p' are these vertical components, q the common value of 

 the horizontal components, h and h' the vertical projections of the two 

 wires, A and \ their horizontal projections, and, finally, 20, and zb 

 the projections of the distances of the points of attachment ; we have 

 the ratios 



