this degree of magnetization is sensibly the same in two helices of different diametres, provided that they be sufficiently long and their pitch be equal and sufficiently short. When the spirals are a little removed from each other, to 3 millimetres for example, the helices have much greater action than when their diameter is smaller, but this increase of energy is extremely feeble. It is almost insensible, and may be altogether neglected with a pitch a moiety less, 15 millimetres. The most exact means of proving these small differences is by placing one in the other, two helices which turn in the same direction, as was done by M. Arago, and to bring into communication by their extremities the wires which they cover. The current then traverses them in contrary directions; they act in contrary directions on the needles placed in the interior helix, and these needles, either remaining unmagnetized or only acquiring, with very strong discharges, a feeble magnetism in the direction which the helix of the smallest diameter gives them. However, this magnetism increases little by little with the intensity of the discharge.

If the two helices, placed one in the other, and always of the same pitch, in place of turning in the same direction, turned in contrary directions, the one dextrosum, the other sinistrosum, the current traverses them longitudinally in opposite directions and transversely; their actions, always pretty nearly equal, are added together, instead of being destroyed as in the preceding case. We may thus measure double, triple, or quadruple forces. It is sufficient if we make the discharge arrive at first at a simple helix, from that to a system of two, three, or four helices of the same pitch, one enclosed in the other, and alternately turning in contrary directions. The mutual action of helices which envelope each other is here, however, as we shall hereafter see, a cause of error, but this error is very small, if the wire of which they are formed is sufficiently fine.

Here I give, for electric charges of which the intensity may be represented in the gross by the numbers 2, 3, 4, 4, and 5, the durations of oscillations measured by the magnetism of magnetized needles; the one in the simple helix, of which I before made use of, the others in the system of two helices of the same pitch, which I shall call, for the sake of brevity, the double helix.

We see already by these estimates, inasmuch as they are still very large, not only that the action of a double discharge is very different to double the action of a simple discharge; but further, that the

relation of these two forces is variable, and depends on their absolute intensity.

A double helix acts sensibly as a simple helix of a pitch a moiety shorter, the length of wire being the same for them both.

We may be assured that if a portion of a discharge is passed from one spiral to another, without following the contrary, this portion may be altogether neglected, at least for the heights of pitch that I have employed. It will suffice if we isolate with gum lac the spirals of an helix for a short extent, in any part of its length, we obtain on passing a discharge through this helix, exactly equal magnetic intensities in both of the moieties, whatever be the direction of the magnetism; whether it attains its maximum, or whether it be almost null. Since in the whole interior of a helix similar needles are equally magnetized, every point of these needles are submitted to equal actions. The differences of magnetization which the different parts of the same needle present must only be attributed to the reaction of these parts upon each other. In order to appreciate the influence of these reactions, I took needles of the same temper and of the same diameter, but of three lengths: 15 mill., 10 mill., and 5 mill.. I place in one and the same helix three new needles, one of each length. After having magnetized them they were made to oscillate. The mean needles were afterwards broken in two; those of fifteen millimetres into three equal parts, and these fragments, equal to small needles, were made to oscillate. These are the effects then remarked: the fragments of the same needle, equal to each other, are always magnetized in the same direction, that of the entire needle, and are equally magnetized; at least the differences, which are in general very small, always preserve the same sign from one extremity to the other, which solely announces a gradual inequality in the temper of the different points of the needle; an inequality almost inevitable, since in general these points are only successively plunged into the cold liquid.

The numbers which in the following table express the durations of the oscillations of the fragments of the same needle, are the means of durations almost equal, obtained by making them oscillate successively. The signs always indicate the direction of the magnetism.

We see that the needles of different lengths are always magnetized in the same direction. Perhaps the shorter needles change the sign with forces a little less. It will be remarked that these needles of five millimetres are less magnetized in one direction as well as in the other, than the equal fragments of needles of ten millimetres; and that the latter are themselves less magnetized than the fragments of longer needles.

There can be no doubt but that in breaking the needles we alter the magnetism of their parts, but in a quantity which is not very considerable. One of the needles of fifteen millimetres, that made sixty oscillations in 28", 5, was placed in a small glass tube of the same length as itself, extremely light, into which it entered with friction. This caused it to make the same number of oscillations in 37", 8. It was then withdrawn; it was broken in three pieces, of which each separately made sixty oscillations in 11", 8. The three pieces having been replaced, one after the other, in the small tube of glass, it then took 41", in place of 37", 8, to oscillate the same number of times.

I will cite, while noticing these latter researches, an analogous experiment. I magnetized, it is now a long time ago, to saturation, with two strong magnets, an untempered steel needle of about one millimetre in diameter, and thirteen centimetres long, on which I had previously traced, at the end of each centimetre, with a fine line, annular marks of but slight depth, but sufficient to determine the rupture of the needle when a slight pressure was exercised on any part of it. I convinced myself that the entire needle had only one magnetic centre. I then broke it into thirteen equal parts. The extreme fragments were then smaller than the distance of the poles from the two ends of the needle. Their magnetic distribution changed in a manner almost instantaneously. For after some minutes, and excepting some very feeble and irregular differences of intensity, all the fragments possessed the same quantity of magnetism, and almost the maximum to which it was possible they could obtain. The entire needle made sixty oscillations in 3′′, 16′, 3. The fragments of that part from the north pole to the centre, made the same number of oscillations in 47′′, 2; 49′′, 2; 48′′, 8; 47′′, 2; 47", 3; 50′′, 2; 48′′, 0, fragment from the middle; the following fragment 47", 0. In a state of saturation, these fragments made sixty oscillations in 44", and 46′′.

I now return to the phenomena of magnetism produced by electricity. In what has been already said, I have supposed that all discharges, the feeblest as well as the strongest, being drawn from the same battery, that equal charges corresponded to the same tensions : In giving to electrized surfaces of very different extents, and gradually decreasing in proportion, that with equal charges the tension is more elevated. I found, by some trials, that the maximum of magnetic intensity, the helix and wire being the same, have a less value. Now has decrease any limit? How does the influence of tension combine with the influence of the length of the wires: with

their diameter, and the distance between the spirals? These elements of the question I have yet to study. In fact I have only spoken of the effects produced by an unique discharge. I ought as the basis of a possible explication, point out the effects obtained in helices by means of successive discharges. If these discharges are very feeble, such as simple sparks drawn from a machine, and very near, their action is added to each other, with certain limits of magnetization, which depends on the nature of the needles. Any number whatever of the same sparks will not raise it beyond the limit of magnetism already produced. The resistance which is opposed to its development increases then with the magnetism already developed. This resistance which is, perhaps, great enough in needles still unmagnetized to prevent a continuous series of sparks sufficiently feeble from ever exerting any sensible influence.

If instead of increasing, the sparks traversing the wire in a contrary direction tend to produce opposite effects, the resistance, in proportion as we approach the first maximum of magnetization, becomes more and more unequal in the two directions, and the force necessary to destroy the magnetism produced is only a very feeble portion of the force lost when we seek to augment it.

And again as soon as the discharges pass beyond the degree of intensity capable of giving the needles this first maximum of magnetism, which may be very far from the state of saturation, the direction and the degree of magnetism which they give them are very near, and more and more independent of the magnetic state in which those needles were found before the experiment.

On the action of other bodies, as Steel and Iron, submitted to the action of electric discharges, but isolated from the conductor which they traverse.

One of the first observations of M. Arago, at the time of his researches on magnetism, was, that the influence which magnetises iron and steel, very different from that of other electric actions, is transmitted through wood, glass, and other insulating substances, without undergoing any appreciable change. Two needles (Ann. de Chem. et de Phys., 1820), placed in the same helix, the one enclosed in a crystal tube, the other out of this tube, received exactly the same quantity of magnetism. These trials, which M. Arago had intended to have varied and extended, were pursued no farther until the time when he discovered the very remarkable action that all the substances, and especially the metals in a state of movement, exercised on the needle. I expressed to him, a short time after, the desire I had to know what might be the influenc eof this latter class of bodies on the magnetism developed by the electric currents, and he was very desirous to engage me to follow out a class o fresearches which he himself had intended to repeat.

I at first placed two needles in a helix, the one without envelope, the other enveloped in a thick cylinder of red copper, isolated from the conductor. The effect of a discharge which strongly magnetized

the first was insensible on the second. There was nothing transmitted through the copper. I substituted a needle already magnetized for the needle without magnetism enclosed in the metallic tube. I then placed it in such a manner that a new discharge ought to change its poles, or at least to enfeeble its magnetism, if the envelope did not destroy all its effects. The duration of the oscillations, measured before and after this trial, were found to be exactly the same. It is useless to say, that in order to eliminate the influence due to terrestial magnetism, the needles were always placed, during the discharge, in a direction perpendicular to the magnetic meridian.

I gradually diminished the thickness of this metallic envelope; the intensity of the discharges always remaining the same, the envelope needles commenced exhibiting an action more and more sensible. For a certain thickness the enclosed needle and that entirely naked, if I may be so allowed to express myself, were equally magnetized. For thickness gradually decreasing, the enveloped needle became the most strongly magnetized of the two, attaining a maximum of intensity, and then it afterwards approached anew, by successive diminutions, to the degree of magnetization of the other needle.

In proportion as the intensity of the discharges augment, the thickness of the metallic envelope with which the needle was covered, and the one that was not, received the same degree of magnetism, and may be gradually increased. At the same time the increase of magnetism due to a diminution of the thickness of the envelopes is more and more considerable. With very feeble discharges the thickness which has no action is very small.

These experiments were made with plates of pewter, rolled round the needles. This disposition permitted the thickness of the envelope to be gradually diminished. I assured myself besides, that a cylinder of cast pewter and a cylinder formed of leaves of rolled pewter, as nearly equal in volume and in weight as the greater density of the plate pewter would permit, exercised sensibly the same action.

The eighth part of leaf of beaten silver, weighing 08, 005, was rolled round a needle of two centimetres in length, and five times heavier. This very thin envelope, when submitted to a discharge from a Leyden jar, raised by one-third the degree of magnetism which the same discharge communicated to a similar needle by its direct action.

When in a given helix, the first maximum attained by the needles without envelope is very far from the state of saturation; with discharges increasing in strength, and which magnetize them in decreasing ratios, the maximum of similar needles in a convenient envelope continues considerably to raise itself beyond the maximum of the first ones. It will even become raised when these are magnetized in a contrary direction. This is a new proof that even at high tensions the electric fluid does not pass, at least in appreciable quantity, from one spiral to another of the helices, without following the turnings therein.