of the bar must pass back
through the air to the other end of the bar, as indicated by dotted
lines and arrows. The path followed by the magnetic lines of force is
called the _magnetic circuit_, and, therefore, the magnetic circuit of
the magnet shown in Fig. 90 is composed partly of iron and partly of
air. From what has been said concerning the relative permeability of
air and of iron, it will be obvious that the presence of such a long
air path in the magnetic circuit will greatly reduce the number of
lines of force that a given magnetizing force can set up. The presence
of an air gap in a magnetic circuit has much the same effect on the
total flow of lines of force as the presence of a piece of bad
conductor in a circuit composed otherwise of good conductor, in the
case of the flow of electric current.

Reluctance. As the property which opposes the flow of electric
current in an electrical circuit is called _resistance_, so the
property which opposes the flow of magnetic lines of force in a
magnetic circuit is called _reluctance_. In the case of the electric
circuit, the resistance is the reciprocal of the conductivity; in the
case of the magnetic circuit, the reluctance is the reciprocal of the
permeability. As in the case of an electrical circuit, the amount of
flow of current is equal to the electromotive force divided by the
resistance; so in a magnetic circuit, the magnetic flux is equal to
the magnetizing force or magnetomotive force divided by the
reluctance.

[Illustration: Fig. 90. Bar Electromagnet]

Types of Low-Reluctance Circuits. As the pull of an electromagnet
upon its armature depends on the total number of lines of force
passing from the core to the armature--that is, on the total flux--and
as the total flux depends for a given magnetizing force on the
reluctance of the magnetic circuit, it is obvious that the design of
the electromagnetic circuit is of great importance in influencing the
action of the magnet. Obviously, anything that will reduce the amount
of air or other non-magnetic material that is in the magnetic circuit
will tend to reduce the reluctance, and, therefore, to increase the
total magnetization resulting from a given magnetizing force.

_Horseshoe Form._ One of the easiest and most common ways of reducing
reluctance in a circuit is to bend the ordinary bar electromagnet
into horseshoe form. In order to make clear the direction of current
flow, attention is called to Fig. 91. Th