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arrangements of the circuit are shown to balance each other, 
and from the arrangements necessary to produce this equi- 
librium the desired laws are deduced. 
I. If the current be reversed the force is reversed. Intro- 
duce the current at A. J oin BD and lead away at C. Then 
the same current goes in opposite directions round the coils 
(1) and (2), and since the needle is not deflected the reversal 
of the force when the current is reversed is proved. 
II. The force is proportioned to the length of current 
acting. This is proved by the last, for the two coils (1) and 
(2) exert equal forces on the needle. If the current went 
round them in the same direction we should have twice the 
force which each exerted singly, with twice the length of 
current. This assumes that the current in different parts 
of the circuit is the same, which might be shown by slightly 
modifying I, thus, introduce between B and D various re- 
sistances and the equilibrium is not disturbed. 
III. The force is proportional to the strength of the cur- 
rent. Introduce at A and connect A with C and B with 
D, and connect D with F and lead off from E. There will 
be two equal currents in the same directions in coils (1) and 
(2), for they are exactly similar to each other and similarly 
situated. These two currents unite to give a double current 
in the opposite direction in coil (3), and the double current 
in a single wire exerts twice the force exerted by each single 
current, since there is no deflection. 
IY. The force is inversely proportional to the square of 
the distance. Introduce at A, connect B with H, and lead 
off at G. Then since we have two turns to the coil (4) we 
have a current of four times the length at twice the distance 
acting in opposition to the same current through (I). Since 
there is no deflection, the two exert equal forces, and there- 
fore the force is inversely proportional to the square of the 
distance. 
