146 REPORT—18638. 
Let a wire of any material be bent into an are of 574° with any radius, k. 
Let this are be placed in the magnetic meridian of any magnetic field, with a 
magnet of any strength freely suspended in the centre of the are. Let two 
vertical wires or rails, separated by a distance equal to /, be attached to the 
ends of the arc; and let a cross piece slide along these rails, inducing a current 
in the arc. Then it may be shown that the speed required to produce a 
deflection of 45° on the magnet will measure the resistance of the circuit, 
which is assumed to be constant. This speed will be the same whatever be 
the value of &, or the intensity of the magnetic field, or the moment of the 
magnet. In this form the experiment could not be easily carried out ; but 
if a length, 7, of wire be taken and rolled into a circular coil at the radius /, 
a2 
and the distance between the vertical rails be taken equal to fe then if the 
resistance of the circuit be the same as in the previous case, the deflection of 
45° will be produced by the same velocity in the cross piece, measuring that 
resistance ; or, generally, if the distance between the rails be p sn then p 
times the velocity required to produce the unit deflection (45°) will measure 
the resistance. The truth of this proposition can easily be established when 
the laws of magneto-electric induction haye been understood (31). 
31. Magneto-electric Induction.—Let a conducting cireuit be placed in a 
magnetic field. Let C be the intensity of any current in that circuit; E the 
magnitude of the electromotive force acting in the circuit. Let the circuit 
be so moved that the number of lines of magnetic force (11) passing through 
it is increased by N in the time ¢, then (23) the electromagnetic forces will 
contribute towards the motion an amount of work measured by CN. Now 
Q, the quantity of electricity which passes, is equal to Ct; so that the work 
done on the current is EQ or CEt. By the principle of conservation of 
energy, the work done by the electromagnetic forces must be at the expense 
of that done by the electromotive forces, or 
CN +CE:=0 "4 
or dividing by Ct, we find that 
E= — 2 > ° e . . , . . . . (15) 
or, in other words, if the number of lines of force passing through a circuit 
be increased, an electromotive force in the negative direction will act in the 
circuit measured by the number of lines of force added per second. 
If R be the resistance of the circuit, we haye by Ohm’s law (equation 6) 
E=CR; and therefore 
N=—Et=—RCi=—RQ; , 2 os» tp ee ho? 
or, in other words, if the number of lines of magnetic force passing through 
the circuit is altered, a current will be produced in the circuit in the direc- 
tion opposite to that of a current which would have produced lines of force 
in the direction of those added, and the quantity of electricity which passes 
multiplied by the resistance of the circuit measures the number of additional 
lines passing through the circuit. 
The facts of magneto-electric induction were discovered by Faraday, and 
described by him in the First Series of his ‘ Experimental Researches in 
Electricity,’ read to the Royal Society, 24th November, 1831. 
He has shown* the relation between the induced current and the lines of 
* Experimental Researches, 3082, ke. 
