constant cell B2; its object is to produce inside the tube a magnetic field equal and opposite to that due to the earth’s magnetism. C is a “compensating coil” consisting of a few turns of wire through which the magnetizing current passes; it serves to neutralize the effect produced upon the magnetometer by the magnetizing coil, and its distance from the magnetometer is so adjusted that when the circuit is closed, no ferromagnetic metal being inside the magnetizing coil, the magnetometer needle undergoes no deflection. K is a commutator for reversing the direction of the magnetizing current, and G a galvanometer for measuring it. The strength of the magnetizing current is regulated by adjusting the position of the sliding contact E upon the resistance DF. The current increases to a maximum as E approaches F, and diminishes to almost nothing when E is brought up to D; it can be completely interrupted by means of the switch H.
The specimen upon which an experiment is to be made generally consists of a wire having a “dimensional ratio” of at least 300 or 400; its length should be rather less than that of the magnetizing coil, in order that the field H0, to which it is subjected, may be approximately uniform from end to end. The wire is supported inside the glass tube A with its upper pole at the same height as the magnetometer needle. Various currents are then passed through the magnetizing coil, the galvanometer readings and the simultaneous magnetometer deflections being noted. From the former we deduce H0, and from the latter the corresponding value of I, using the formulae H0 = 4πin/l and
| I = | d12 HE | × s, |
| 2nπr 2 1 − d1d23 |
where s is the deflection in scale-divisions, n the distance in scale-divisions
between the scale and the mirror, and r the radius of the
wire.
 |
| Fig. 10. |
The curve, fig. 10, shows the result of a typical experiment made upon a piece of soft iron (Ewing, Phil. Trans. vol. clxxvi. Plate 59), the magnetizing field H0 being first gradually increased and then diminished to zero. When the length of the wire exceeds 400 diameters, or thereabouts, H0 may generally be considered as equivalent to H, the actual strength of the field as modified by the magnetization of the wire; but if greater accuracy is desired, the value of Hi (= NI) may be found by the help of du Bois’s table and subtracted from H0. For a dimensional ratio of 400, N =0.00028, and therefore H = H0 − 0.00028I. This correction may be indicated in the diagram by a straight line drawn from 0 through the point at which the line of I = 1000 intersects that of H = 0.28 (Rayleigh, Phil. Mag. xxii. 175), the true value of H for any point on the curve being that measured from the sloping line instead of from the vertical axis. The effect of the ends of the wire is, as Ewing remarks, to shear the diagram in the horizontal direction through the angle which the sloping line makes with the vertical.
Since the induction B is equal to H + 4πI, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction. The general character of curves of magnetization and of induction will be discussed later. A notable feature in both classes of curves is that, owing to hysteresis, the ascending and descending limbs do not coincide, but follow very different courses. If it is desired to annihilate the hysteretic effects of previous magnetization and restore the metal to its original condition, it may be demagnetized by reversals. This is effected by slowly moving the sliding contact E (fig. 9) from F to D, while at the same time the commutator K is rapidly worked, a series of alternating currents of gradually diminishing strength being thus caused to pass through the magnetizing coil.
The magnetometric method, except when employed in connexion with ellipsoids, for which the demagnetizing factors are accurately known, is generally less satisfactory for the exact determination of induction or magnetization than the ballistic method. But for much important experimental work it is better adapted than any other, and is indeed sometimes the only method possible.[1]
Ballistic Methods.—The so-called “ballistic” method of measuring induction is based upon the fact that a change of the induction through a closed linear conductor sets up in the conductor an electromotive force which is proportional to the rate of change. If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q = δBns R, where δB is the increment or decrement of induction per square centimetre, s is the area of the coil, n the number of turns of wire, and R the resistance of the circuit. Under the influence of the transient current, the galvanometer needle undergoes a momentary deflection, or “throw,” which is proportional to Q, and therefore to δB, and thus, if we know the deflection produced by the discharge through the galvanometer of a given quantity of electricity, we have the means of determining the value of δB.
The galvanometer which is used for ballistic observations should have a somewhat heavy needle with a period of vibration of not less than five seconds, so that the transient current may have ceased before the swing has well begun; an instrument of the d’Arsonval form is recommended, not only because it is unaffected by outside magnetic influence, but also because the moving part can be instantly brought to rest by means of a short-circuit key, thus effecting a great saving of time when a series of observations is being made. In practice it is usual to standardize or “calibrate” the galvanometer by causing a known change of induction to take place within a standard coil connected with it, and noting the corresponding deflection on the galvanometer scale. Let s be the area of a single turn of the standard coil, n the number of its turns, and r the resistance of the circuit of which the coil forms part; and let S, N and R be the corresponding constants for a coil which is to be used in an experiment. Then if a known change of induction δBa inside the standard coil is found to cause a throw of d scale-divisions, any change of induction δB through the experimental coil will be numerically equal to the corresponding throw D multiplied by snRBa/SNrd. For a series of experiments made with the same coil this fraction is constant, and we may write δB = kD. Rowland and others have used an earth coil for calibrating the galvanometer, a known change of induction through the coil being produced by turning it over in the earth’s magnetic field, but for several reasons it is preferable to employ an electric current as the source of a known induction. A primary coil of length l, having n turns, is wound upon a cylinder made of non-conducting and non-magnetic material, and upon the middle of the primary a secondary or induction coil is closely fitted. When a current of strength i is suddenly interrupted in the primary, the increment of induction through the secondary is sensibly equal to 4πin/l units. All the data required for standardizing the galvanometer can in this way be determined with accuracy.
The ballistic method is largely employed for determining the relation of induction to magnetizing force in samples of the iron and steel used in the manufacture of electrical machinery, and especially for the observation of hysteresis effects. The sample may have the form of a closed ring, upon which are wound the induction coil and another coil for taking the magnetizing current; or it may consist of a long straight rod or wire which can be slipped into a magnetizing coil such as is used in magnetometric experiments, the induction coil being wound upon the middle of the wire. With these arrangements there is no demagnetizing force to be considered, for the ring has not any ends to produce one, and the force due to the ends of a rod 400 or 500 diameters in length is quite insensible at the middle portion; H therefore is equal to H0.
E. Grassot has devised a galvanometer, or “fluxmeter,” which greatly alleviates the tedious operation of taking ballistic readings.[2] The instrument is of the d’Arsonval type; its coil turns in a strong uniform field, and is suspended in such a manner that torsion is practically negligible, the swings of the coil being limited by damping influences, chiefly electromagnetic. The index therefore remains almost stationary at the limit of its deflection, and the deflection is approximately the same whether the change of induction occurs suddenly or gradually.
