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 battery, and a piece of wire in the cylinder is flexibly connected to it, the lower end of this last piece just touching the mercury. When a current is passed in at the top wire and out at the lower end of the bar magnet, the loose wire revolves round the magnet pole. All text-books on physics contain in their chapters on electromagnetism full accounts of various forms of this experiment. In 1825 another important step forward was taken when William Sturgeon (1783–1850) of London produced the electromagnet. It consisted of a horseshoe-shaped bar of soft iron, coated with varnish, on which was wrapped a spiral coil of bare copper wire, the turns not touching each other. When a voltaic current was passed through the wire the iron became a powerful magnet, but on severing the connexion with the battery, the soft iron lost immediately nearly all its magnetism.

At that date Ohm had not announced his law of the electric circuit, and it was a matter of some surprise to investigators to find that Sturgeon’s electromagnet could not be operated at a distance through a long circuit of wire with such good results as when close to the battery. Peter Barlow, in January 1825, published in the Edinburgh Philosophical Journal, a description of such an experiment made with a view of applying Sturgeon’s electromagnet to telegraphy, with results which were unfavourable. Sturgeon’s experiments, however, stimulated (q.v.) in the United States, and in 1831 he gave a description of a method of winding electromagnets which at once put a new face upon matters (Silliman’s Journal, 1831, 19, p. 400). Instead of insulating the iron core, he wrapped the copper wire round with silk and wound in numerous turns and many layers upon the iron horseshoe in such fashion that the current went round the iron always in the same direction. He then found that such an electromagnet wound with a long fine wire, if worked with a battery consisting of a large number of cells in series, could be operated at a considerable distance, and he thus produced what were called at that time intensity electromagnets, and which subsequently rendered the electric telegraph a possibility. In fact, Henry established in 1831, in Albany, U.S.A., an electromagnetic telegraph, and in 1835 at Princeton even used an earth return, thereby anticipating the discovery (1838) of C. A. Steinheil (1801–1870) of Munich. Inventors were then incited to construct powerful electromagnets as tested by the weight they could carry from their armatures. Joseph Henry made a magnet for Yale College, U.S.A., which lifted 3000 ℔ (Silliman’s Journal, 1831, 20, p. 201), and one for Princeton which lifted 3000 with a very small battery. Amongst others J. P. Joule, ever memorable for his investigations on the mechanical equivalent of heat, gave much attention about 1838–1840 to the construction of electromagnets and succeeded in devising some forms remarkable for their lifting power. One form was constructed by cutting a thick soft iron tube longitudinally into two equal parts. Insulated copper wire was then wound longitudinally over one of both parts (see fig. 2) and a current sent through the wire. In another form two iron disks with teeth at right angles to the disk had insulated wire wound zigzag between the teeth; when a current was sent through the wire, the teeth were so magnetized that they were alternately N. and S. poles. If two such similar disks were placed with teeth of opposite polarity in contact, a very large force was required to detach them, and with a magnet and armature weighing in all 11·575 ℔ Joule found that a weight of 2718 was supported. Joule’s papers on this subject will be found in his Collected Papers published by the Physical Society of London, and in Sturgeon’s Annals of Electricity, 1838–1841, vols. 2-6.

The Magnetic Circuit.—The phenomena presented by the electromagnet are interpreted by the aid of the notion of the magnetic circuit. Let us consider a thin circular sectioned ring of iron wire wound over with a solenoid or spiral of insulated copper wire through which a current of electricity can be passed. If the solenoid or wire windings existed alone, a current having a strength A amperes passed through it would create in the interior of the solenoid a magnetic force H, numerically equal to $$4 \pi / 10$$ multiplied by the number of windings $$\text{N}$$ on the solenoid, and by the current in amperes $$\text{A},$$ and divided by the mean length of the solenoid $$l,$$ or $$\text{H} = 4\pi \text{AN} / 10l.$$ The product $$\text{AN}$$ is called the “ampere-turns” on the solenoid. The product $$\text{H}l$$ of the magnetic force $$\text{H}$$ and the length $$l$$ of the magnetic circuit is called the “magnetomotive force” in the magnetic circuit, and from the above formula it is seen that the magnetomotive force denoted by (M.M.F.) is equal to $$4\pi \, 10 $$ (= 1·25 nearly) times the ampere-turns (A.N.) on the exciting coil or solenoid. Otherwise (A.N.) = 0·8 (M.M.F.). The magnetomotive force is regarded as creating an effect called magnetic flux (Z) in the magnetic circuit, just as electromotive force produces electric current (A) in the electric circuit, and as by Ohm’s law (see ) the current varies as the E.M.F. and inversely as a quality of the electric circuit called its “resistance,” so in the magnetic circuit the magnetic flux varies as the magnetomotive force and inversely as a quality of the magnetic circuit called its “reluctance.” The great difference between the electric circuit and the magnetic circuit lies in the fact that whereas the electric resistance of a solid or liquid conductor is independent of the current and affected only by the temperature, the magnetic reluctance varies with the magnetic flux and cannot be defined except by means of a curve which shows its value for different flux densities. The quotient of the total magnetic flux, $$\text{Z},$$ in a circuit by the cross section, $$\text{S},$$ of the circuit is called the mean “flux density,” and the reluctance of a magnetic circuit one centimetre long and one square centimetre in cross section is called the “reluctivity” of the material. The relation between reluctivity $$\rho = 1 / \mu$$ magnetic force $$\text{H},$$ and flux density $$\text{B},$$ is defined by the equation $$\text{H} = \rho \text{B},$$ from which we have $$\text{H}l = \text{Z} (\rho l / \text{S}) = \text{M. M. F.}$$ acting on the circuit. Again, since the ampere-turns (AN) on the circuit are equal to 0·8 times the M.M.F., we have finally AN/l＝0·8 (Z/S). This equation tells us the exciting force reckoned in ampere-turns, AN which must be put on the ring core to create a total magnetic flux Z in it, the ring core having a mean perimeter and cross section S and reluctivity $$\rho = 1 / \mu$$ corresponding to a flux density $$\text{Z} / \text{S}.$$ Hence before we can make use of the equation for practical purposes we need to possess a curve for the particular material showing us the value of the reluctivity corresponding to various values of the possible flux density. The reciprocal of $$\rho$$ is usually called the “permeability” of the material and denoted by $$\mu.$$ Curves showing the relation of $$1 / \rho$$ and $$\text{Z S}$$ or $$\mu$$ and B, are called “permeability curves.” For air and all other non-magnetic matter the permeability has the same value, taken arbitrarily as unity. On the other hand, for iron, nickel and cobalt the permeability may in some cases reach a value of 2000 or 2500 for a value of B＝5000 in C.G.S. measure (see ). The process of taking these curves consists in sending a current of known strength through a solenoid of known number of turns wound on a circular iron ring of known dimensions, and observing the time-integral of the secondary current produced in a secondary circuit of known turns and resistance R wound over the iron core N times. The secondary electromotive force is by Faraday’s law (see ) equal to the time rate of change of the total flux, or E＝NdZ/dt. But by Ohm’s law E＝Rdq/dt, where q is the quantity of electricity set flowing in the secondary circuit by a change dZ in the co-linked total flux. Hence if 2Q represents this total quantity of electricity set flowing in the secondary circuit by suddenly reversing the direction of the magnetic flux Z in the iron core we must have RQ＝NZorZ＝RQ/N. The measurement of the total quantity of electricity Q can be made by means of a ballistic (q.v.), and the resistance R of the secondary circuit includes that of the coil wound on the iron core and the galvanometer as well. In this manner the value of the total flux Z and therefore of Z / S＝B or the flux density, can be found for a given magnetizing force H, and this last quantity is determined when we know the magnetizing current in the solenoid and its turns and dimensions. The curve which delineates the relation of H and B is called the magnetization curve for the material in question. For examples of these curves see.

The fundamental law of the non-homogeneous magnetic circuit traversed by one and the same total magnetic flux Z is that the sum of all the magnetomotive forces acting in the circuit is numerically equal to the product of the factor 0·8, the total flux in the circuit, and the sum of all the reluctances of the various parts of the circuit. If then the circuit consists of materials of different permeability