ON STANDARDS OF ELECTRICAL RESISTANCE. 141 
20. Weber's Electro-Dynamometer.—The measurement described in the last 
paragraph is only accurate when D is very great, and therefore the moment to be 
measured very small. Hence it is better to make the experimental measure- 
ments in another form. For this purpose, let a length (/) of wire be made into 
a circular coil of radius /; let a length (/,) of wire be made into a coil of very 
much smaller radius, &,. Let the second coil be hung in the centre of the 
first, the planes being vertical and at the angle 6. Then, if a current C tra- 
verses both coils, the moment of the force tending to bring them parallel 
will be 
lk 
G=4C? + sin 0. apne? a dan deitireuate S| 
This force may be measured in mechanical units by the angle through 
which it turns the suspended coil, the forces called into play by the mecha- 
nical arrangements of suspension being known from the construction of the 
instrument. Weber used a bifilar suspension, by which the weight of the 
smaller coil was used to resist the moment produced by the action of the 
currents. 
21. Comparison of the Electro-magnetic and Electro-chemical action of 
Currents.—Currents of electricity, when passed through certain compound 
substances, decompose them; and it is found that, with any given substance, 
the weight of the body decomposed in a given time is proportional to the 
strength of the current as already defined with reference to its electromagnetic 
effect. The voltameter is an apparatus of this kind, in which water is the sub- 
stance decomposed. Special precautions have to be taken, in carrying this 
method of measurement into effect, to prevent variations in the resistance of 
the circuit, and consequently in the strength of the current. This subject is 
more fully treated in Part V. $$ 53, 54. 
22. Magnetic Field near a Current.—Since a current exerts a force on the 
pole of a magnet in its neighbourhood, it may be said to produce a magnetic 
field ($ 6), and, by exploring this field with a magnet, we may draw lines of 
force and equipotential surfaces of the same nature as those already described 
for magnetic fields caused by the presence of magnets. 
When the current is a straight line of indefinite length, like a telegraph- 
wire, a magnetic pole in its neighbourhood is urged by a force tending to turn 
it round the wire, so that this force is at any point perpendicular to the plane 
passing through this point and the axis of the current. 
The equipotential surfaces are therefore a series of planes passing through 
the axis of the current, and inclined at equal angles to each other. The 
number of these planes is 47 C, where C is the strength of the current. 
The lines of magnetic force are circles, haying their centres in the axis of 
the current, and their planes perpendicular to it. The intensity of the mag- 
netic force at a distance, /, from the current is the reciprocal of the distance 
between two equipotential surfaces, which shows the force to be a 
The work done on a unit magnetic pole in going completely round the 
current is 47 C, whatever the path which the pole describes. 
23. Mechanical Action of a Magnetic Field on a closed Conductor conveying a 
Ourrent—When there is mechanical action between a conductor carrying a 
current and a magnet, the force acting on the conductor must be equal and 
opposite to that acting on the magnet. Every part of the conductor is there- 
fore acted on by a force perpendicular to the plane passing through its own 
direction and the lines of magnetic force due to the magnet, and equal to the 
