The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 4 of 36

the direction of the induction, in that it is not the same for increasing as for diminishing induction when the magneto- motive force, and therefore the induction, is periodic ; and, in iiact, it is dependent upon the whole past magnetic history of the iron. It is impossible, therefore, to draw up a table of exact specific magnetic resistances of magnetic metals as we can draw up a table of specific electrical resistances, and reduce the calculation of the induction produced by a given steady magnetomotive force to the same simplicity that results from the apphcation of Ohm's law to electric circuits.

The reciprocal of magnetic resistance is magnetic cofidtictance, Faraday used the phrase ** conducting power for lines of magnetic force" to express the reciprocal notion to that of magnetic resistance. The reciprocal quality to specific magnetic resistance is also called magnetic permeability. This is generally denoted by the symbol /&. Hence the magnetic permeabihty is the magnetic conductance of a magnetic circuit of imit length and unit cross-section. If p stands for specific magnetic resistance and /a for magnetic permeability, we can say that

--M (18)

P

Consider a closed magnetic circuit of uniform specific magnetic conductance fi and of length I and section «, and let a uniform magnetic force H act in this circuit, producing a uniform induction B. Then by definition the magnetic resistance B of the circuit is given by

•D _^ H i ^ Magnetomotive force B 8 Total induction

where H Ms the magnetomotive force, and B s the total induction ; but

R =5 ^ and u = - ; therefore we have B«ftH (14)

This equation (14) is not only a fundamental equation in magnetism, just as Ohms law is in electro-kinetics, but it furnishes a definition of the method of measuring magnetic permeability

40 ELECTRO-MAGNETIC INDUCTION.

Experiment shows, as stated, that the ratio B to H,

B

expressed by the equation rj»/A, is not of a determinate

H

character, and that the value of /&, so far fi-om being constant,

is dependent on the whole previous magnetic history of the

iron, on the value of B, and on the nature of the magnetic

changes the iron is undergoing, viz., whether H is increasing

or diminishing. In fact, fi for iron varies from a value not

far from unity for strongly magnetised iron up to a ^'alue of

2,000 or 2,500 at a maximum for closed magnetic circuits of

best soft iron, and down to a value of about 100 for very

feeble magnetising forces.

In a cycle of magnetic operations, during which a bar of iron is exposed to increasing magnetising forces and then afterwards to decreasing ones, beginning and ending with the same force, the value of B is always greater on the descend- ing than on the ascending course, and hence the value of fi which is given by the ratio of B to H is also different. This phenomenon, which is exemplified familiarly by the retention of magnetism in a bar after withdrawal of the magnetising force, has been named by Prof. Ewing hysteresis (from wre/xo), to lag behind).

The magnetic permeability above defined is a quantity which is in magnetism the analogue of specific ind^ictive capacity in electrostatics, and of the conducting power of a body for heat. It was spoken of by Faraday as tJie conduct- ing power of a incujneiic viedium for lines of force (''Exp. Re- searches," Ser. XXVI., § 2,797 and § 2,846). More recently the reciprocal of /x has been called the magnetic reluctance. The term magnetic resistance has, however, become so sanc- tified by use that we shall continue to employ it in spite of certain objections which have been urged against it.

The magnetic resistance of a circuit, composed partly of iron and partly of air, is greater in proportion as the lengtti of the air path is increased in proportion to that of the iron. This fact is strikingly shown in experiments on the magnetic induction produced in closed rings and short bars of soft iron. Thus from some curves given by Prof. Ewing we find that in a certain soft iron ring a magnetising force of 7 C.G.S. units produced an induction of 11,000 C.G.S. units; whereas, in

ELECTRO-MAGNETIC INDUCTION. 41

the case of an iron rod, of which the length was 50 times the •diameter, the same force produced an induction of only 4,000 units. In the first case the circuit was a complete iron circuit, and the resistance small. In the second case the magnetic •drcait was partly iron and partly air, and therefore the total magnetic resistance was much greater.

The equation B^fi H is the expression of the fundamental relation hetween magnetic force and magnetic induction. For all ordinary non-magnetic materials the value of p and iJso of its reciprocal fi is taken as unity. Hence, in these cases the magnetic force and magnetic induction have the same value and are in the same direction. In the case of such diamagnetic hodies as bismuth and phosphorus, fi is very slightly less than unity and p very slightly greater, but so little as to be unappreciable except to refined experiments. In speaking of air circuits, or non-magnetic circuits generally, we can speak of lines of force or lines of induction indifferently, 3s the force and induction have everywhere the same numerical value and same direction, but in dealing with magnetic •dreuits of permeability greater than unity, the magnetic force and magnetic induction must be carefully distinguished, because they have not the same magnitude and may not have the same direction. In crystalline magnetic bodies the induc- tion might have a very different direction and value to the force, and as wo have seen in the case of soft iron, the induc- tion may be, numerically, two or three thousand times greater ■than the magnetic force.

• It should be borne in mind, therefore, that in the air-space outside a magnet or a mass of iron under induction the mag- netic force and magnetic induction have the same direction tmd same numerical value, but inside a magnet or mass of iron under induction they must be distinguished. The mag- netic force outside the magnet may be called the magnetic induction through the air, and generally in the non-magnetic material surrounding the magnet the magnetic force and magnetic induction are, for the purposes of measurement, one and the same. In the interior of a mass of iron under induction in a magnetic field, the magnetic force at each point is one compounded of that due to the external ox original field and that due to the induced polarity acquired,

42 ELECTBO-MAGNETIC INDUCTION,

and which acta to produce an opposing magnetic force. Hence the effect of the induced poles on any element in the interior of the iron is to tend to demagnetise it when the external ttiagnetising force is withdrawn. In the inside of a straight uniformly magnetised bar the magnetic force due to the influence of the poles themselves is from the end which pointa to the north to the end which points to the south, both within the magnet and in the space outside. The magnetic induction, on the other hand, is from the north pole to the south pole outside the magnet, and from the south pole to the north pole inside the magnet. A line of induction followed round, moving always in the positive direction, is found to be a closed loop or endless line.

It is a fftct of fundamental importance that a thin disc of iron or steel, magnetised so that at all points the magnetic axis of each small element of it is in a direction normal to its surface, produces a magnetic field identical with that produced by a wire conveying an electric current coinciding in form with the edge of the disc. In short, the magnetic field of a closed circuit conveying a current is identical with that of a magiutic shell filling up the aperture of the circuit. The magnetic field due to electric currents circulating in conductors is, however, of such a nature that each line of induction embraces or surrounds the axis of the circuit once or more. The magnetic field due to permanent or electromagnets is of such a nature that each line of induction passes through the magnet, giving rise to magnetic polarity at the places where it enters and leaves the iron or steel. Every line of induction either surrounds an electrie current or passes through magnetised iron.

The inUmity of magnetisation of any element of a magnet or mass of iron under induction is a term requiring definition.

The couple required to hold a very small magnet when placed with its axis of magnetisation perpendicularly across the lines of force of a uniform magnetic field in air of unit strength is a numerical measure of the moment of the magneto The moment of a magnet or of any element of a magnet may be considered numerically to be made up of two fetors — one its volume, and the other its intensity of magnetisa* tioHf or, simply, its magnetisation ; and hence, for a uniformly

ELECTRO-MAGNETIC INDUCTION. 43

magnetised small linear needle, we may define the intensity of its magnetisation by saying that it is the magnetic moment of unit volume of it. Intensity of magnetisation is, like force and induction, a vector quantity.* In the case of a very long thin wire of soft iron placed along the lines of force of a imiform field the three quantities — the magnetic force, the magnetic induction, and the magnetisation — are all in align- ment at any point.

It is important that the full meaning of the phrase <' mag- netic force at any point " should clearly be grasped. If there be any uniform magnetic field of strength Hq, and in it is placed a mass of iron in the shape of an elongated bar, the configuration of this uniform field is disturbed and magnetic polarity is developed in the iron. At any point in the interior of the iron there is a magnetising force, henceforth denoted by the letter H, which is due partly to the original magnetic field Ho and partly to the induced poles which create a force opposing Ho* This resultant magnetic force is spoken of as the magnetising force in the iron, and it is the resultant of the external magnetic forces and the internal magnetic forces due to the polarity. If the form of this bar is so chosen that there are no magnetic poles, as in the case of a ring lapped over with an endless solenoid, then the magnetic force in the iron is easily calculable, and it is that due to the external magnetic force alone. If the bar is straight and very long the induced magnetic poles may exert so httle effect at the centre of the bar that the induction there and the magnetic force also is that due to the external field alone.

At each point in the iron the magnetic force H must be thought of as producing magnetisation or magnetic displace- ment, just as in electrostatic phenomena electric force pro- duces in a dielectric electric displacement or electric strain, or joflt as mechanical stress produces in an elastic body oi*dinary strain or displacement at every point. This magnetisation is not necessarily in the same direction as the force.

S4. Lines and Tubes of Magnetic Indttction.--Faraday and Maxwell have raised the conception of a Une of magnetic

• A Tector quantity is one which is only precisely fixed when we know ita direction as well as magnitude.

44 ELECTRO-MAGNETIC INDUCTION.

induction from a simply directive notion to one which enables it to be used to convey a quantitative knowledge of the mag- netic field — ^in other words, have enabled lines of induction to be used not only to show the direction of the induction, but also its magnitude in certain units. By this means the mag- netic field can be mapped out into areas and volumes whidi have a definite dynamical signification.

In the twenty-eighth series of his '^ Besearches on Elec- tricity," Faraday lays stress on the fact stated above that every line of force (induction) is an endless loop (§ 3,117, **Exp. Bes.'*) : — " Every line of force must therefore be con- sidered as a closed circuit passing in some part of its course through a magnet, and having an equal amount of force in every part of its course. There exist lines of force within the magnet of the same nature as those without. What is more, they are exactly equal in amount to those without. They have a relation in direction to those without, and are, in fact, continuations of them."

Let a magnetic field have drawn in it a number of closely contiguous lines of induction. None of these lines can cut each other, because the resultant magnetic induction at any point can have only one definite direction.

In any region it is possible to describe a surface perpen- dicular to all the lines of induction. Such a surface is called a level surface.

In the case of a straight infinite current, these level surfaces will be planes radiating out from the axis of the wire, and their traces on a plane perpendicular to the axis of the wire will be a series of radial lines cutting all the circular loops of induction normally. Let A (Fig. 9) represent such a level surface, and let B be another, both cutting the same sheaf of magnetic lines of induction.

On the level surface A let any unit of area a be taken, and let this area a be projected on to the adjacent level surface B by lines of induction drawn through its boundary. We have then a tubular sur&Kie, the ends of which are formed of portions of level surfaces, and the rest of the tubular surface may be conceived to be formed of lines of magnetic induction, supposed to be very closely drawn through the bounding line. Such a geometrical conception is called a tube of induction.

ELECTRO-MAGNETIC INDUCTION, 45

The characteristic quality of a tube of induction is as follows. If the areas of the sections made by the two level surfaces A and B be called 8 and s', and if B be the mean magnetic induction over s, and B' that over s', then B«»B' s', or the product of a normal cross-section of tube and mean magnetic induction over that section is constant for all sections of the tube.

If any level surface be drawn, and on this surface be marked off contiguous small areas such that the magnitude of the area is inversely as the mean value of the magnetic induction over that little area, and if s and B are, as before, the numerical values of any small area and the mean indue* tion over it, then the product B a may be made equal to unity for each of these portions of that level surface. From these

Fjg. 9.

small areas let tubes of induction be supposed to take their rise, the whole field will be cut up into contiguous tubes of induction. Each of these tubes is called a unit Uihe of indnc- tion. By their mode of description these tubes will have small cross-section at pi aces where the field is strong and widen out in section at places where it is weak, and by the fundamental property of the tubes the value of the mean magnetic induction at any place is inversely as the cross- section of the tubes of induction force at that place.

From Faraday's point of view, a magnet of any form must be mentally pictured as surrounded with and as having its whole field filled up by a closely packed arrangement of such unit tubes of induction, the tubes being intersected at right fuigles by the equipotential or level surfaces, and each having

46 ELECTRO-MAGNJETIC INDUCTION.

at any point a nonual cross-section which is inversely as the magnetic induction at that point. This system of tubes must be supposed to be rigidly attached to the magnet, and to inove with it wherever it goes. Furthermore, in accordance with Faraday's conception, each tube is an endless tube, or, as it were, a pipe returning into itself and passing in some part of its course through a magnet or round an electric current. In <;onstructing what may seem to the student to be a highly artificial conception, we are not postulating necessarily any physical existence for these tubes. They should be regarded simply as a device for plotting out the space round a magnet according to a definite rule, and may, in the first place, be regarded as no more than analogous to such subdivisions of ihe earth's surface as we make by lines of latitude and longi-

FiG. 10.

tude. Having thus divided up a magnetic field into unit tubes of induction, it is simpler in thought to suppose a single line of induction to run down the axis of each tube, and then to mentally disregard the tubular system, and, instead of speaking of a unit tube, to speak of each as a single line of induction. If we imagine a system of induction tubes starting from an equipotential surfEice and draw any irregular curve on this surfeice, we shall find that this curve encloses a certain number of tubes or lines of induction (Fig. 10). Bearing in mind that the cross-section s of the tube where it sprouts out from the equipotential sur&ce is inversely as the magnetic induction B at the centre of this cross-section, it is at once evident that the greater the average induction over the area defined so much the more numerous will be the

ELECTRO-MAGNETIC

47

number of tubes or lines of induction which pass through it.

If the cross-section s of each tube should happen to be equal,

and there be n tubes passing altogether through an area equal

to S, bounded by the black line, then by the very definition of

a unit tube

Ba = l,

or nSs — n\

but ^* •*» ** S,

hence BS = 7i;

and the number of tubes passing through any area S on such an equipotential surface in a uniform field is numerically equal to the product of the whole area and of the induction at any point on that area.

Fio. 11.

The characteristic quaUty of a tube of induction is that the flux of induction along it is constant throughout its length. That is to say, the product B « = induction x cross-section is constant, and, since what is true of one tube is true of all, we may say that in a space wholly made up of tubes of magnetic induction ^e total magnetic induction or flux of induction is the same across all sections of this mass of tubes.

The lines of induction of a permanent steel magnet are to be thought of as closed loops which pass in their course partly through the steel and partly through the air. The lines of induction of a circuit conveying an electric current are closed

48 ELECTRO-MAGNETIC INDUCTION,

loops entirely surrounding the axis of the w'ire. If this circuit is a straight wire, with the return wire at a very great distance, the lines of induction are concentric circles described on a plane perpendicular to the axis of the wire, and having their centre in that axis.

If a circuit is formed by coiling up into a circular coil a length of insulated wire, the coil having n turns, then to a first degree of approximation we may say that each line of induction forms a closed curve embracing the circuit n times. Thus, if the wire forms a coil of one turn (Fig. 11) each line of induc- tion (represented by the dotted line) is a closed loop em- bracing or linked with the circuit once. If we take a circuit

of two turns (Fig. 12), then nearly all loops of induction belonging to one single turn embrace not only that turn but the adjacent turn, and if the circuit could be supposed to be opened out straight (Fig. 18), without destroying the loop of induction, it would be found to be twisted twice round that circuit. By similar reasoning, if a loop of induction embraces or is linked with n turns of a conducting circuit, it is in fact the same as linking each loop of induction n times with the single circuit.

Let a conducting circuit have the form of a helix (Fig. 14), then the lines of induction are closed loops, which embrace

ELECTRO MAGNETIC INDUCTION.

49

some or all the turns of the spiral, and, if the helix have n turns, then each loop of induction, according to its length and

position, in reality embraces that circuit 1, 2, 8 orn times.

If there be two circuits, in one or both of which currents are flowing, then each circuit is surrounded by lines or loops of induction, and of those belonging to one circuit some or all are

•^U'

i i

I ,'

Fio. 13.

linked in as well with the other circuit, so that a certain number of all the loops of induction are common to the two circuits, and are called the loops or lines of mutual induction. It is exceedingly convenient to think of these lines or tubes of induction as linked with various circuits. A line of induc- tion is always linked with an electric circuit or else passes

through a magnet in some part of its course. If any closed conducting circuit is placed in a field of magnetic induction, it may be thought of as linked with a certain number of unit lines or tubes of induction. If the circuit is moved or the field is changed, the number of linkages is altered or may be altered. If at any instant N unit tubes or lines of induction are linked with any circuit, and at a very short interval of time

60

ELECTRO-MAGNETIC INDUCTION.

afterwards, say after an inierval t, the number of linkages is

N-N' N', then N - N' is the change in the linkage, and — - — is the

rate of change of linkage, and this, by Faraday's law, is the numerical value of the electromotive force set up in the circuit. If during any period of time a circuit is exposed to magnetic induction the rate of change of which varies, then from instant to instant the impressed inductive electromotive force varies and may be represented graphically as follows : Let the straight line 0 X (Fig. 15) be an axis on which lengths are marked off to represent intervals of time, and let ordinates perpendicular to it represent the instantaneous value of the flux of induction through, or lines of induction included by,

a circuit ; then, if the variation of induction is continuous, it may be represented by a curve drawn between these axes. This curve may be called a curve of induction. If at any point P a tangent PT is drawn to this curve, the trigono- metrical tangent of the angle PTM represents the rate of variation of P M with respect to 0 M, and if P M represents at any instant the induction N, then the slope of the tangent at

P represents --, or the rate of change of N with respect to time. "^^

In the practical application of the above rule it must be borne in mind that if N, or the number of lines or linkages, is measured in units based on the centimetre, gramme, and second system, then the electromotive force is given in the same units.

ELECTRO MAGNETIC INDUCTION. 51

Since one volt is 10^ C.6.S. electromagnetic units, to get the electromotive force in volts we must divide the time rate of change of induction by 10^. Thus, if the change of induction be such that N C.G.S. lines are removed uniformly from the circuit per minute, the electromotive force in volts set up will be

§ 5. Ourves of Magnetisation.— One of the most important practical problems in magnetism is to discover the manner in which the induction B varies with the magnetising force H in different cases. Since this variation is often very complicated, it is best represented by a curve of which the ordinates are taken as proportional to the induction and the abscissas as proportional to the magnetising force. Such curves are called curves of magnetimtion. We shall consider a few special cases and describe the mode of practically determining these curves. The principal instance is the curve of magnetisation of a closed iron ring. Let an iron ring be made of circular cross-section radius a and be circular in form, the radius of the mean circular central axis being B. Let a be very small compared with B. Let such a ring be wound over uniformly with N turns of insulated wire, and let a current of strength A amperes be sent through this wire. The magnetic force creates an induc- tion in the iron, and the lines of induction are circles lying wholly in the iron. Inside the circular solenoid the mag- netic force is nearly the same in value everywhere, and is

equal to --^ » A, where n is the number of turns of the wire

N per unit length of the solenoid; or n^- — ^. Hence we

Air rC

can calculate the magnetic force acting everywhere on the iron. Let the ring be also wound over with a second insulated coil of wire of N' turns, and let this secondary coil be connected to a ballistic galvanometer or a galvano- meter suitable for measuring quantity of electricity. If the current in the primary coil is altered in strength or reversed, the magnetic force undergoes a change, and the induction changes also. Since the lines of induction all pass through, or are linked with, the turns of the secondary coil, this

e2

52 ELECTRO-MAONETIC INDUCTION.

chaoge in induction will, by Faraday's law, create a flow of electricity in the secondary circuit. If the current in the primary coil is suddenly changed from one value A amperes to another value A' amperes, a certain quantity of electricity will flow through the secondary coil and galvanometer, and it will cause the galvanometer needle to deflect through an angle 6, If /p is the galvanometer constant {see Appendix, Note C), then the whole quantity of electricity which flows through

the galvanometer is equal to Q, where Q^k sin- (l + ^j,

X being the logarithmic decrement of the galvanometer.

If R* is the total resistance of the secondary coil on the ring, together with that of galvanometer coils and connec- tions, then, as above shown, the total change in the induction through the secondary circuit is equal numerically to B' Q. If B is the mean induction density in the interior of the circular solenoid, S the mean cross-sectional area of the primary coil, and N' the number of turns on the secondary coil, then it is clear that B S N' represents the total induction passing through the secondary circuit, or the number of lines of induction which are linked with the galvanometer circuit.

Hence if the induction is suppressed by stopping the current the total change in induction is B S N', and this is equal to B' Q. If the current, instead of being simply stopped, is reversed, then the total change in induction is 2 B S N'. Therefore we have

B S N' « R' Q for stoppage of current ; or 2 B S N' = R' Q for reversal of current.

By our fundamental equation

B^/xH.

In the above case the average magnetic force H is equal to

4ir N A

— — — -, in which formula N is the number of primary turns,

A the primary current in amperes, and I the mean perimeter of the primary solenoid, which last is equal to 2v R, where R is the mean radius of the primary solenoid. Hence we find that

ELECTRO-MAGNETIC INDUCTION. 53

sN'iS^£=«'Q (^«)

according as the primary current is stopped or reversed. Taking the latter as the usual case, we find finally that

6 *-B'.B.Bm|(l4.^)

Hence fi is determined in terms of nine quantities, all of which can be easily and exactly measured. If all quantities are measured in centimetres and seconds, then it must be particularly noted that the galvanometer constant k is the number by which the corrected sine of half the angle of throw has to be multiplied in order to obtain the quantity of electricity producing that throw, estimated m absolute C.G.8, electromagnetic meamre, which has flowed through the gal- vanometer. Generally speaking, it is most convenient to find k by determining the throw produced by a discharge through the galvanometer of a certain number of mtcrocou- lombs, obtained by charging a condenser of known capacity in microfarads with a certain number of volts. Then it must be remembered that a microcoulomb is 10~^ of an electromag- netic unit of quantity in C.G.S. measure.

By the help of the above formula we can deduce the values of fi for the iron ring corresponding to certain values of B or H, and tabulate them. For instance, taking a perfectly new iron ring, we can apply gradually increasing values of H, increasing by small steps, and obtain the corresponding values of B, and then draw curves representing the relation of B and H and of B and fx. Such curves have been given by many observers: Rowland, Hopkinson, Ewing, Shelford Bidwell, and others. For the sake of showing what are the sort of values of B and /a corresponding to certain values of H, a table is given on the next page o! results of an experiment by Shelford Bidwell on a soft iron ring, and in Figs. 16 and 17, page 55, are given diagrams showing the forms of the curves of induction and permeability for such a ring.

o4

ELECTRO-MAGNETIC INDUCTION.

Values of the Pe^^meability and Induction corresponding to various Magnetising Forces for Closed Iron Magnetic Circuits,

H.

B.

A*-

MagnetisiDg Force.

InductioD.

Permeability.

0-2

80

400

0-5

300

600

10

1,400

1,400

20

4,800

2,400

3-9

7,390

1,899

5-7

9,240

1,621

10-3

11,550

1,121

177

13,630

770

22-2

14,450

651

30-2

16,100

500

40

15,460

386

78

16,880

216

115

17,330

151

145

17,770

122

208

18,470

89

293

18.820

64

362

19,080

62-7

427

19,330

45

465

19,470

42

503

19,480

38-7

585

19,820

34

24,500 (Ewing)

45,300

1-9

It will be noticed that the value of the permeability rises very rapidly to a maximum, but that with increasing magnet- ising force it finally diminishes again, and that in very strong magnetic fields iron becames scarcely much more permeable than air. Although there is apparently no limit to the induction or number of lines of force which can be forced through iron, yet it seems as if the excess of lines of force generated in the iron, over and above that which would exist if the iron were not there, is limited. Hence, if we consider the strength of the original field as numerically defined by a certain number, the number expressing the induction when a closed circuit of iron is placed in that field is obtained by using a certain multipher, which becomes less and less as the magnitude of the field increases.

On looking at these permeability curves it will be seen that the permeability rises to a maximum for a certain value of the

ELECTttO'MAQJ^ETlC INDVCTIO:^.

56

indnction and then falls again. It has been shown by Lord Bayleigh that for very small magnetic forces soft iron has an

12,000

2 4 6 8 10

Magnetising Force.

FlO. 16.

Curve of Hagnetiaation for rising and falling magnetisation in a

Soft Iron Ring.

initial permeability of about 100. Its maximum permeability is about 2,500, and for very great inductions it falls again to something not much greater them unity. Hence the specific

3.000

2,600 2.000

; 1.600

w 1.000

600

/*

/

\

/

f

\

/

\

/

\

\

B

\

"S,

0 6,000 laOOO 15,000 20.000

Induction.

Pro. 17. Permeability Curve for Soft Iron Ring (Rowland).

magnetic resistance curve is the inverse of the above curves, and the specific magnetic resistance has a minimum value which for a soft iron ring appears to correspond to an indue-

66

ELECTRO-MAGNETIC INDUCTION.

tion density of about 6,000 C.G.S. (lines per square centi- metre). At less or greater induction densities the specific magnetic resistance is increased.

Experiments to determine /i can only be performed properly on very long bars or rings of iron placed in uniform predeter- mined magnetic fields by lapping over the ring with insulated wire or placing the bar in a heUx, so that an electric current traversing this wire generates a field having known values at

300

OHfX

/

■^S

V'

220»

c.

/

/^

^

200

//

f

^

V

!ol60

7

\

\

15<» (

^100

/

V

\

60

B

\

\

\

2.000 4.000

Induction.

Fio. la

8.000

Permeabiltty Curves for Nickel (RowlaDd).

each point in the interior of the coil. Such experiments have been carried out extensively by various experimentalists, and the results embodied in curves called pemieabUity curvet,* The form of these permeability curves is considerably affected

• Accounts of experiments and investigations on the form of the permea- bility and susceptibility curvei( for iron and other paramagnetic metals will be found in the foUowing memoirs :— Weber, Electrcdyfutmiiche Maoi- beitimmwtgen, Bd. III., §26 ; Von Quint u<« Icilius, Poggendorf8 AnnaUnt CXXl., 1864 ; Oberbeck, Pogg, Ann., CXXXV., 1868 ; Riecke, Ftigg. Ann,, CXLL, 1870 ; Stoletow. Fogg. Ann., Ergbd. V., 1870 ; Rowland, PhU. Mag., Ser. IV., 1873, p. 336, 1874, p. 254 ; Bouty, Qmptei Xendus, 1875 ; Fromme, Pogg. Ann., Ergbd. VII., 1875 ; Warbutg, Wiedemann's Annalen, XIII., 188L ; Bidwell, Proe. Boy. Soc Lond., No. 245, 1886 ; BidweU, iVoc. Roy. Soe. Land., Vol XLIII., 1888; Bidwell, Proc Hoy. Soe. Land.. No. 242, 1886 ; Ewing, Tram. Roy. Soe. Lond., Part. II., 1885 ; Hopkinsou, Tian$. Roy. Soe. Lond., Part II., 1885.

ELECTllO-MAGNETIG INDUCTION. 57

bj temperature, and for each magnetic metal there appears to be a temperature at and beyond which it is not much more permeable than air. The permeability of nickel and cobalt varies very much with temperature. In Figs. 17 and 18 are shown the permeability curves for iron and for nickel for two very different temperatures. At about 750''C. iron, and at about 400''G. nickel, possess a permeability not much greater than air.* In cobalt, permeability appears to be increased up to about 150''C. and then diminished.