66 MEASUREMENT OF COUPLES. 



for which the apparatus has the least sensitiveness that is to say, 

 those which give the most rapid oscillations. 



The points of attachment are in general at the same height, and 

 on the other hand, the lever AA l is by construction perpendicular to 

 the straight line which joins its middle to the centre of gravity of the 

 movable system, and it is only then necessary to make the wires of 

 the same length. All difficulty is got rid of if only two points of 

 support are retained, either above or below, for the two ends of a 

 single wire, which passes over a pulley. When the two wires are 

 independent, use is made of the property of the minimum duration 

 of oscillations, and the adjustment is more easily made the lower is 

 the centre of gravity of the movable system. 



When the apparatus has been once adjusted, the same condition 

 serves to bring it into position after it has been displaced; the 

 levelling screws are adjusted until the minimum sensitiveness is 

 obtained. 



* 717. If the wire is rigidly fixed to the points of support so that 

 the first element at each end is kept vertical, it is no longer 

 rectilinear.* In these conditions the system, under the action of a 

 given horizontal couple, undergoes a less displacement than if the 

 wire were quite flexible. For a symmetrical suspension the lower 

 end of a perfectly flexible wire, the top of which was fixed, would 



be displaced by a quantity 8 = -L When the two extreme elements 



/ 



are kept vertical, it is found that the value of the displacement is very 

 nearly 



(9) 



E being the first modulus of elasticity, and K the moment of inertia 

 of the section of the wire in respect of an axis passing through the 

 centre of gravity, and perpendicular to the plane of flexure. 



irr^ 

 In the case of a circular wire of radius r y we have K = , 



4 

 and therefore 



(ID) 5 1 = 



* KOHLRAUSCH, Wiedemanri 1 s Annalen, Vol. xvn., p. 741. 1882. 



