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produced in the derivation, and are inverse on the closing, direct on the opening of the circuit.

We should add that, from our present point of view, a very feeble coil is equivalent to a conductor of enormous capacity.

2. On the Magnetization of Steel. A steel needle, recently tempered, is transported from infinity into the interior of a spiral animated by a curreut, and then extracted from the spiral and transported to infinity in the opposite direction. This needle is attracted into the spiral; and during its introduction the work absorbed by the magnetization of the steel is added to the work of the attractive forces developed between the spiral and the needle. These two effects in the same direction produce in the wire outside the coil an induced current opposite in direction to the principal current. When the needle is withdrawn from the coil, the work restored by the loss of the temporary magnetization is added to the negative work of the attractions—whence a direct induced current outside the coil*

The considerations unfolded in the preceding article concerning the extra currents apply also to the induced currents. It is probable that these currents are without effect withiu the coil from which they emanate. In all cases, if the needle is introduced or extracted very slowly, the intensity of the induced currents is very feeble; and in this case, at least, their magnetic effect within the coil may be neglected. We have therefore good ground for admitting that the magnetism carried away by a needle which is passed once to the spiral is due solely to the action of the principal current.

I. The circuit comprises only a pile with a constant current and the coil within which the magnetizing takes place.

(1) If the needle be introduced and extracted slowly, and the permanent magnetic moment which it has carried away be measured, we find that repetition of the passing of the needle augments the residual moment. It tends, through the repetition, towards a limit A; and the magnetic moment y, after x passages, is sufficiently well represented by the empiric formula

B

(1) ac * This direct current is equal in quantity to the inverse current ; whence this proposition :-The work absorbed by the production of permanent magnetization is equal to the excess of the work of the attractive forces during the extraction of the magnet from the spiral above the work of the same forces during its introduction. The permanent magnetizationhas therefore a mechanical origin, and derives nothing from the current.

th

y=A

en

roduced in the derivation, and are inverse on the closing, direct n the opening of the circuit.

We should add that, from our present point of view, a very eble coil is equivalent to a conductor of enormous capacity.

in which A-B represents the residual magnetic moment after the first passage. The degree of accuracy of the formula will be seen from the following examples. TABLE I.—Needle 2 millims. in diameter, magnetized by

1 Grove's element.

Magnetic moment.

Difference.

Number of passages to the spiral.

Observed.

Calculated.

2. On the Magnetization of Steel. A steel needle, recently tempered, is transported from infinity co the interior of a spiral animated by a current, and then excted from the spiral and transported to infinity in the oppoe direction. This needle is attracted into the spiral; and ring its introduction the work absorbed by the magnetization the

steel is added to the work of the attractive forces developed tween the spiral and the needle. These two effects in the me direction produce in the wire outside the coil an induced rrent opposite in direction to the principal current. When the edle is withdrawn from the coil

, the work restored by the loss the temporary magnetization is added to the negative work of e attractions—whence a direct induced current outside the il* The considerations unfolded in the preceding article concern

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TABLE II.—Needle 1.3 millim. in diameter, magnetized by

1 Bunsen element.

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& the extra currents apply also to the induced currents. It is
obable that these currents are without effect withiu the coil
om which they emanate. In all cases, if the needle is intro-
ced or extracted very slowly, the intensity of the induced cur-
ats is very feeble; and in this case, at least, their magnetic
ect within the coil may be neglected. We have therefore good
und for admitting that the magnetism carried away by a
dle which is passed once to the spiral is due solely to the
pn of the principal current.

The circuit comprises only a pile with a constant current
the coil within which the magnetizing takes place.
1) If the needle be introduced and extracted slowly

, and the
janent magnetic moment which it has carried away be mea-
1, we find that repetition of the passing of the needle aug-
& the residual moment. It tends, through the repetition

, 'ds a limit A; and the magnetic moment y, after x passages, ficiently well represented by the empiric formula

B y=A

(1) x

A=41:52, B=4:02.

The curious augmentation in question has been already observed by Hermann and Scholz* They wrongly confound, in their researches, the effect of a magnetizing spiral and that of a horseshoe magnet, to the poles of which they apply the needle to be magnetized. In the first case, indeed, if the needle is thin enough, it may be regarded as placed in a magnetic field of constant intensity, which it certainly is not in the second; and as it is impossible to place the needle in precisely the same manner in a great number of successive experiments, the law of the increase is masked by a phenomenon of a different kind. These authors

* Hermann and Scholz, locis citatis.

his direct current is equal in quantity to the inverse current; whence oposition :-The work absorbed by the production of permanent tization is equal to the excess of the work of the attractive forces

the extraction of the magnet from the spiral above the work of the orces during its introduction. The permanent magnetizationbas ire a mechanical origin, and derives nothing from the current.

were therefore unable to find an empiric formula fitted to represent the results of their experiments; but, taking only the numbers obtained by means of the magnetizing spiral, we shall see from the following Table that they agree as well as possible with our own empiric formula *.

TABLE III.

Number

First needle.

Second needle.

Third needle.

of pas.

sages.

Observed. Calculated. Observed. Calculated. Observed. Calculated.

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The augmentation of the magnetic moment by repetition of the passages is independent of the duration of the immersion, as Hermann and Scholz had ascertained; it is essentially connected with the intermission of the action of the current. then, be admitted, since the induced currents themselves are without sensible effect, that the magnetic equilibrium which succeeds the action of the currents modifies the distribution of the magnetism in such wise that a second application of the same force, acting under the same conditions, may add to the total residual magnetismt.

(2) Three other processes may be employed to magnetize a steel needle within a coil :

a. The needle is introduced, the current established, and the needle withdrawn slowly (establishment).

b. The needle is introduced slowly, the current passing; the current is interrupted, and the needle withdrawn (interruption).

c. The needle is introduced; the current is established, and * The authors do not state what is the limit of the errors of experiment in their measuring-process; but it is certain that they exceed the greatest differences between the numbers in the column of the observations and in that of the calculated numbers.

With the exception of the three experiments contained in this Table, the authors confine themselves to the observation of the magnetic moments corresponding to 1, 2, and oo passages. The application of the empiric formula gives the third number by means of the two first, with sufficient approximation whenever the magnetization has been obtained by the spiral. In the opposite case the calculated third number is notably less than the number observed. They found that the degree of tempering, the length of the needles, and the duration of the immersions are without influence on the results.

† The fact we are describing should be compared with the known fact

then interrupted; and then the needle is withdrawn (disruptive discharge).

The repetition of each of these processes furnishes an increment of magnetism to the needle; and, provided that all the operations effected are of the same sort and the conditions identical, the results of the experiments are well represented by a hyperbolic formula such as formula (1). The limit A appears to be the same for the passages and the interruptions, but less for the establishments. TABLE IV.-Needle 2 millims. in diameter, magnetized by

1 Grove's element.

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After the tenth passage, interruptions having been produced unawares, the moment of the needle suddenly rose to 55.96, and was not carried beyond that limit by 50 establishments. Ten passages with the spiral then raised the magnetic moment to 57.56, and twenty more passages to 57.88. TABLE V.- Needle 2 millims. in diameter, magnetized by

1 Grove's element.

Magnetic moment.

Number of interruptions.

Differenee.

Observed.

Calculated.

1
2
32

53:15
55.93
58.73

53.15
55.93
58.55

0.00

0.00 +0:18

that the permanent magnetism produced by a current A becomes more considerable when the needle, after magnetization, has been submitted to the action of a current B, feebler and in the opposite direction. If B is made to tend to 0, the phenomenon still continues ; and this is not at all surprising, since partial demagnetization (corresponding to loss of the temporary magnetism) is the consequence of the cessation of the current A.

Thirty passages to the spiral did not raise much the magnetic moment of this needle*. The results obtained by the disruptive discharges are less regular than the preceding, although the empiric formula still represents them. The irregularities doubtless proceed from the difficulty of working these discharges in perfectly identical conditions.

The preceding experiments already establish that the extra currents are without magnetic action within the coil which produces them. If it were otherwise, interruption would be a more efficacious process of maguetization than passing the needle to the spiral; now augmentation of the magnetic moment has never been observed when needles magnetized by a great number of passages have been submitted to repeated breakings of the circuit.

II. The circuit comprises, besides the pile, two coils P and Q.

The phenomena observed on account of slow passages are the same as in the case of a single coil; but the effect of the extra currents complicates the phenomena arising from interruption. We will suppose the coil P much more powerful than Q. If the two coils are placed one after the other, two needles p and q, magnetized, each in the corresponding coil, to the limit relative to the passages, acquire a greater magnetic moment through the interruptions; but the relative increment is much greater in the less powerful coil. Example :

TABLE VI.--Needles 142 millims. long and 2 millims.

in diameter.

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First passage:
17.51 First passage

3:22
Second passage.

18:21
Second passage

3.63
Twentieth passage .. 18.70 Twentieth passage ... 4:15
21 interruptions 18.91 21 interruptions ....

5.61

......

The extreme magnetization corresponding to the passages, from the first two observations of each column, would be, according to our empirical formula, 18.61 for p, and 4:04 for q. The increment of the magnetic moment produced by the interruption is, for p 0.21 in absolute value, and about 94 in relative value; for the needle q the values are 1.46 and 1.

* The two preceding experiments were made immediately after those of Table I., with needles almost identical and in the interior of the same spiral. The establishments and interruptions are effected by means of a cup containing mercury, into which the extremities of the conducting wires dipped.

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