This series presents four changes in the direction of the magnetism. The first takes place at less than a millimetre from the wire; the second at 2 mill.; the third at 8 mill., 4; the last at 21 mill, 5. We see that needles which were negative in the first series are positive in this, and vice versa. The latter maximum, which is found at the height of 3 cent., is 4 cent. Its value is less; it being only 34".

In the same circumstances, for needles ten millimetres long, the same changes of signs take place at 0 mill., 5; 2mill., 5; 9mi mill., 5; and about 20 mill., 5. For needles of five millimetres in length, at 0 mill., 5; about 3 mill, 2; 10 mill., 5; and about twenty millimetres. These distances are almost the same as were obtained with needles of fifteen millimetres.

I now proceed to a third example. For the same distance charge a platinum wire, rather thicker than the preceding one, of Omill., 37 diameter, and of the same length (one metre), gave changes in the sign four times, nearly at the distances of three, five, nine, and twelve millimetres from the wire. From thence up to 2 cent. we only find the needles very feebly magnetised; between which, with stronger discharges, a third period was manifested, except at the changes of the signs, at least by the variations of the intensity, just as I have observed it in a series obtained with a brass wire of an equal sensible diameter. For the platinum wire of which I have just spoken, the needle the most magnetized was that found at a distance of about 6 cent. from the wire. It took 56" to make sixty oscillations. The needle possessing the most magnetism for a finer wire, and of the same length as before specified, made the same number of oscillations in 34", and was at a distance of 4 cent. from the wire.*

On the same platinum wire of 0 mill., 57 diameter, but 0 met., 65 lengths only, and for a discharge stronger than the preceding ones, small needles of five millimetres have changed the direction of their magnetism five times;

In order to finish the comparison between different platinum wires I chose one much finer than the preceding ones. It was of a millimeter in thickness. A meter in length of this wire, with a discharge equal to the preceding one, gave the following results :

the

This series presents no changes in the sign. At the commencement the variations of intensity are scarcely observable. It is important in this respect: 1st, the maximum of magnetic intensity is found at the height of 11 mill. about five times nearer wire than when we employed a platinum wire three times as thick; 2ndly, this maximum is the state of saturation which we obtain by the magnets, and its value is nearly six times greater than the value given by a wire of triple its diameter. At the same time that the maximum approaches the wire the decrease of the intensities of this maximum from thence becomes more rapid.

If we pass through a wire of a millimetre in thickness and one metre in length, a series of discharges, diminishing their strength by degrees, we should see the maximum very slowly diminish as it approached the conductor; but we never obtain changes in the sign of the magnetism, and never any analogous series to those presented by the other wires. On the other hand, by gradually diminishing the discharges, we never obtain with the other thicker wires, and of the same length, the series just presented to us by the finest wire. The changes of sign quite disappear then, and we only observe variation of intensity in their place, but at the same time the value of maxima diminish in proportion as they are found at less heights.

the last change took place at twenty-eight millimetres from the wire. The needles in contact with the wire were even magnetized negatively, and the most magnetized of all. It was necessary to remove to a distance of 10 cent. from the wire to obtain a slight degree of magnetism.

If, on the contrary, we cause to traverse these wires of a still greater diameter, without changing their lengths, discharges of a stronger character than those whose effects have been described in the preceding paragraph, we shall see the maximum of magnetism augment a little in value; but this is by increasing the distance more and more, and the series changes in form, but without coming into any of the other series, at least in the limits of the electric force of the battery employed.

In the preceding experiments a given discharge has always produced a magnetism as much stronger as the length of the wire was greater in proportion to its diameter. This increase has a limit to its effect. The following series gives for a similar discharge, but much more feeble than the preceding ones, their lengths of the same platinum wire of of millimetre in diameter.

A needle placed at a considerable distance from the third, and apparently at the same distance from the conducting wire, was. equally negative, and made 60 oscillations in 54" 8.

Needles 15 mill. long.

Length of the same wire 1 met. 0, and 4 met. 30.

We see in comparing the three preceding series, 1st, that the wire of a metre in length gave absolutely the most elevated maximum; 2ndly, that the relative maxima in each series were found nearer the wire in proportion as this wire was increased in length, the diameter still remaining the same.

In general, with the same battery, and with wires of the same nature, and with similar needles, the form of the series depends on three things: the intensity of the discharge, the diameter, and length of the wire. The discharge and the length of the wire being made constant, there is a diameter at which the maximum of magnetism has the highest value; for diameters greater or smaller than this the maximum is less. The discharge and the diameter being kept the same, we find a length at which the maximum is greater than for any other length either greater or smaller.

The length and the diameter which thus give the greatest degree of magnetism, is the one which is the smallest, and the other that which is the greatest, in proportion as the wire has less conducting properties.

The maximum of magnetism is further from the wire, the number of changes in the sign in the interval much more considerable, as the length of the wire is less in proportion to its diameter.

We obtain similar series by means of equal discharges, by varying at once the length and the diameter of the wire in a certain proportion. When the length and the diameter of two wires are not satisfactory on this point, we can not in general, by means of discharges, either equal or different, obtain from the two wires exactly parallel series. The disparity is especially manifested when the wires and the discharge are in the necessary conditions for producing change in the sign of the magnetism with a change of distance.

I have not yet made a complete series with wires whose thickness was less than a millimetre. But I am convinced that a brass stem of five millimetres in thickness, will give needles magnetized in different directions according to the intensity of the discharge.

Hence that part of the conducting wire extended in a right line to a sufficient length, and the form of that part which is not so extended, exerts no influence on the magnetism, whilst its length does so to a considerable extent, as we have just seen.

All the points of the wire exercise equal actions, at least in these inconsiderable lengths. In fact, at the same height, those needles which were at a great distance from each other, providing that they were not too near the extremities of the rectilinear part, received exactly the same quantity of magnetism, and in the same direction. This is true again when amongst the needles, some of them are

• This proportion differs sensibly from the simple proportion which, according to the researches of M. Davy and M. Becquerel, ought to exist between two conducting wires of the same nature, because they transmit with an equal intensity a voltaic current of equal strength. We know then that the relation of these wires to their transverse sections ought to be constant.

enveloped in glass tubes, sealed with gum lac, and the others exposed without envelope to the action of the current. This latter proof is only a repetition of one of the first experiments of M. Arago. It does not permit me to suppose that a part of the discharge, when the wire is very fine, is transmitted by the air and the neighbouring bodies, or at least that such a part could have any sensible influence. In fine, in order to discard the supposition that the strips of dry wood placed under the wires could exert any influence, it will suffice to dispose the needles some above and some below the horizontal conductor, in such a manner that the latter are very near the plane which serves for a support. We find, as we might easily foresee, at equal distances from all parts of the wires that there is the same magnetic intensity and contrary polarities.

In order to study the mutual influence of the different parts of a circuit, I disposed three series of needles of three brass wires, placed one after the other, and joined together at their extremities. Each wire was a metre in length: the first, situated between the two others, Omil., 125, the second Omil., 375, the third Omil., 75, in diameter. The first needle had a maximum of positive intensity, which gave 60 oscillations in 36"; for the finest and farthest insulated wire, the maximum would have sensibly the same value; it would have been for the other two about 57", and 1'4". The changes in the signs were found in the three wires, the first between 3 and 4 millemetres in height, the second between 13 and 14 millimetres. The negatively magnetized needles were affected a little less on the thickest wire. On being acted upon singly, the two latter needles gave, with an equal discharge, changes in the signs of the magnetism four times. The very fine wire only exhibited them twice, one at 4mil, the other at about 11mil. in height.

The equality of the action which took place at all points of a similar wire conductor, still subsists then almost wholly throughout the extent of a circle composed of several wires of different diameter, at least at some distance from the points of junction. The form of the periods is the same on all, saving the slight displacements in the position of the changes of the sign, and the same as on a wire equal in length to the sum of all the lengths, and of a diameter that is intermediate between all the diameters. If one of the wires be very fine, whatever place it occupies in relation to the others, it communicates to them nearly its own properties, whilst its manner of acting only undergoes feeble modifications. Circumstances

transpire with regard to this wire, as if it was lengthened a very little, but with regard to the others as if their extent was much augmented. The invariable conductors of a battery, then, ought to be sufficiently large to permit of their influence being neglected.

It is not necessary to understand what has just been said of the equality of action observed in a complete circuit, relating to a system of wires of very different diameters, comparable to the distances where the changes of sign take place; neither to a case where during the discharge one of the wires changes its state and becomes entirely volatilized.