54 MEASUREMENT OF COUPLES. 



and therefore for the times of oscillation 



From this is deduced 



PT 2 



-rr _ _ * x _ -rr > 



~ (P + P')T' 2 - PT 2 



(P + P')T' 2 -PT 2 ' 



706. UNIFILAR BALANCE. The unifilar balance, or torsion balance, 

 was devised by Coulomb, who showed the advantage that could be 

 drawn from it in the measurement of small forces ;* it consists 

 essentially of an elastic wire, ordinarily of metal, fixed at the top, and 

 carrying a movable system for instance, a needle with an electrified 

 sphere, a magnetised bar, etc. 



The wire is attached at the top to a graduated drumhead, which 

 measures the rotation imparted to the end of the wire by being 

 movable against a mark or vernier. When the system is free, and 

 has not of itself any directive force, its position of equilibrium is that 

 in which the wire is without torsion. If the system is exposed to any 

 extraneous directive action if it supports, for instance, a magnet 

 under the action of the earth, then by suitably turning the drumhead, 

 we may bring the system into that direction which it would acquire 

 under the directive force of the earth alone, the wire being without 

 torsion. This condition is clearly realised if the position of equi- 

 librium does not change when the external directive force is sup- 

 pressed when, for instance, the magnetised bar is replaced by a 

 copper one of the same weight. Any angular displacement a of the 

 body from this position produces a torsion of the same angle in the 

 wire if the top is fixed ; if, on the contrary, the upper micrometer 

 is turned through an angle A in the contrary direction, the total 

 torsion of the wire is equal to the sum of the two angles, and 

 therefore equal to A + a. 



707. LAWS OF TORSION. When a system suspended to a metal 

 wire is moved from its position of rest and left to itself, it makes 

 oscillations on each side of this position. The experiments of 



* COULOMB. Mem. des savants etrangers, Vol. x., 1777; and Mem. de 

 V Acad. pour 1784. 



