BIFILAR BALANCE. 63 



The quantity C' may be called the coefficient of torsion of the 

 bifilar ; it is the moment of the couple which would produce a 

 deflection of 90. It will be seen that this moment is proportional 

 to the suspended weight, to the product of the distances of the 

 points of support, and inversely as the length of the wires. 



The sensitiveness of suspension, being inversely as this* couple, 

 may be measured by the ratio 



The torsion cannot exceed 90, for the couple would then 

 diminish. Snow Harris avoided this restriction by using a long 

 bifilar, the wires of which he connected at different heights by several 

 cross-pieces ; the apparatus formed thus a series of bifilars joined 

 end to end. For n identical bifilars, and a total deflection 0, the 

 value of the torsion couple is 



nC' sin . 

 n 



715. We may also allow for the rigidity of wires which cannot 

 always be neglected. When the system is twisted through the angle 

 6, each of the wires is twisted to the same extent. If then they were 

 without torsion in the original position, the two torsion couples CO, 

 which act in the same direction, must be added to the couple 

 C' sin 6 ; the equation of equilibrium becomes then 



I + 2 .JL . 

 |_ C sm 0J 





73- C 



As the angle is less than - , if the ratio , is very small we may 



2 \^ 



look upon the terms within the bracket as constant ; putting 



we get 



Q = C 1 sin6>; 



that is to say, the couple is still virtually proportional to the sine 

 of the angle of elevation. 



