N, for a great number of values of N. For the intermediate values proportional parts are taken,

The masses of iron distributed, in fixed positions, in the laboratory where the operations are carried on, have no influence on the measurements, provided that they are not too near the apparatus; they merely modify the azimuth of equilibrium, which we take for our magnetic meridian.

In short, a space of ten minutes is sufficient for accomplishing a good experiment; and the result of several successive measurements of the same needle furnishes, in general, numbers equal within of their value. Moreover the operation becomes so simple and convenient with practice, that we prefer to employ this method even in those cases in which the oscillation method would give good results.

Comparison of several Apparatus, and Absolute Measures.-One has often to compare several apparatus. This is accomplished by effecting the measurement of the moment of one and the same needle by means of two apparatus which we wish to compare. Another needle, suitably selected (larger, for instance), will permit the comparison of the second apparatus with a third, and so on.

Further, all the relative measures can be converted into absolute measures for this it is sufficient to determine, by the oscillation method, the magnetic moment of a needle, and afterwards measure it by means of the apparatus which have been compared.

II. ON MAGNETIZATION BY CURRENTS.

1. On Extra Currents.

A coil of conducting wires possesses magnetic properties as long as it is traversed by a current. During the time occupied in establishing the current the production of this magnet absorbs a certain quantity of work in addition to that which would be necessary to establish the current in an equal linear resistance. This absorption of work is manifested outside the coil by the in

verse extra current.

When the current is interrupted, the destruction of the magnetic property of the coil restores the work absorbed in its production; hence the direct extra current, equal in quantity to the inverse. As experiment shows that the first is shorter in duration than the second, we can affirm that the magnetic property of the coil is lost more quickly than it is produced.

When a coil of conducting wires is furnished with a core of soft iron, the extra currents retain their character, but are much augmented in intensity. This augmentation measures the work absorbed by the magnetization, or restored by the demagnetiza

tion of the soft iron. The inequality of duration of the extra currents authorizes us to affirm that the demagnetization of soft iron is more rapid than its magnetization *.

Analogy has led physicists to regard the coil, which gives rise to the extra currents, as the seat of temporary electromotive forces the same in direction as, or contrary in direction to the principal current; but it does not authorize us to identify in all points the interior of a coil with that of an element of a pile and, consequently, to regard the extra currents as having the same effects inside the coil as in the rest of the circuit. We shall see that the extra currents are without effect within the coil from which they

emanate.

A condenser C (fig. 3) placed in a voltaic circuit, on a derivation, is, like an induction-coil, the seat of temporary electromotive forces at the time of the opening or closing of the circuit. We will examine only the two following cases.

1st. The condenser C is placed on a derivation without resistance, on which the interruptions are made. The points of bifurcation, A and B, have the same potential when the current passes, since the derivation

is destitute of resistance and consequently the condenser is not charged. When the current is interrupted the difference of potential in A and B becomes equal to the electromotive force of the pile P. Thus the condenser discharges itself during the period of the establishment of the current, and becomes charged at the time of the interruption, whence there result in the principal circuit BN PA an inverse and a direct extra current.

2nd. The condenser C is placed on a derivation the resistance of which is sufficiently great for that of the rest of the circuit, including the pile, to be negligible. The interruption is made at N, apart from the derivation. In this case the points of bifurcation are at the same potential when the current is interrupted; but when it is passing, the difference of their potentials is sensibly equal to the electromotive force. The extra currents are

* Villari (Pogg. Ann. 1873) has determined directly the time taken by flint, a diamagnetic substance, to gain or lose its magnetic rotatory power, the correlative of its magnetization. He found that the demagnetization is more rapid than the magnetization, and assigns to this latter a duration of 0.0024" (see Journal de Physique, vol. ii. p. 422). This is the only experimental determination I know of in regard to the duration of magnetization.

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 current, 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 within 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 a passages, is sufficiently well represented by the empiric formula

*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 magnetization has therefore a mechanical origin, and derives nothing from the current.

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.

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

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.

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 *.

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

sages.

1234568

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. It must, 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 magnetism t.

(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 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