portant point, M. Colladon prepared an instrument, in which the wire was covered with two folds of silk, made 500 turns round the box, and had each separated from the others by oiled silk. With this instrument the effects were nearly tenfold what they were before, and as, in the former tase, the deviation of the needle, by the current from a machine, was only 3° or 4°, now it amounted to much larger quantities. When the point was at the distance of i decimetre (3.937 inches) the deviation was 18° ditto 10 5 3 2; 1 metre (39-371 inches) so that it was rendered sensible at the distance of a metre from the conductor. 474. It should be remarked that the withdrawing action of a point is sensibly proportional to its distance from the conductor. This is constantly the case with a cylinder machine, but seemed to be interfered with in a plate machine by the presence of four cushions. Experiments, instituted to illustrate this point, proved the correctness of this conclusion. When the motion of the cylinder machine was regular, the deviation remained constant as long as the experiment was continued. Operating with the battery, and slowly approaching the point, a constant deviation of 30° was obtained for sixty-five seconds. A jar, containing only two half-square feet of surface, deviated the needle 32°. 475. The ratios which these experiments establish between the action of currents produced by electrical machines, and those of a pile or a thermo-electric arrangement, afford the means of appreciating the absolute velocity with which the electricity moves in a closed electro-motive apparatus, when we know their electro-motive force, or the tension which may be produced by the contact of two metals, and the friction of cushions. In fact, in electrical machines, this velocity of circulation is determined by the motion of the glass plate, by which the electricity is transported to the conductors with a known velocity. If the tension of this electricity is ten thousand times stronger than the tension of a pair of Voltaic plates, having the same surface as the cushion, and nevertheless the effects produced by the two currents on a galvanometer are the same, the velocity of circulation of the electricity from the Voltaic arrangement would be evidently ten thousand times greater than that of the rubbed part of the plate; for it is an acknowledged opinion, that the deviation of the magnetic needle is proportional to the quantity of electricity which passes in the current. 476. Comparative experiments, made with piles and thermo-electric circuits, prove that the conductibility of metallic wires is not in the inverse ratio of their length. When the electromotive force is small, a metallic circuit of moderate length is sufficient to stop the electric current almost entirely. The intensity of the current rapidly increases as the length of the circuit is diminished to a certain limit, dependent on the energy of the electro-motive force. 477. M. Colladon observes also, that although bad conductors, as pure water for example, cannot be made part of a Voltaic circuit without stopping the motions of the galvanometer; yet a layer of air, of more than a metre in thickness, does not always prevent this kind of action, and that the results depend upon the energy of the electro-motive force; so that this becomes an important element, not to be neglected in experiments on the conductibility of bodies. 478. Taking advantage of some stormy weather, M. Colladon was enabled to obtain deviations of the magnetic needle by currents of atmospheric electricity, and has shown that the instrument may become a very precise and useful indication of the state of this agent in the atmosphere. A metallic point being raised on the observatory of the college of France, and connected with the galvanometer, whilst the other extremity of the instrument wire was communicated with the stem of a lightning-rod, deviations were obtained of 32°, 34°, and 37°. The direction of the needle indicated negative electricity, and by dismounting the apparatus, and using an electrometer, this was found to be the case. On another occasion the deviation was from 10° to 22°, and, during the twenty minutes that the instrument was observed, the direction of the current changed two or three times. On another occasion the deviation amounted to 87°. These results were obtained with the first and least sensible galvanometer. 479. These experiments prove that the galvanometer may be very useful in researches on atmospheric electricity. If it should be demonstrated that electricity contributes to the formation of hail, this instrument would be the only one which could indicate in a precise manner the quantities of electricity withdrawn by points more or less acute and elevated, and communicating more or less with the soil. 480. M. Nobili's galvanometer is a curious instrument. Its construction is founded upon the fact discovered by Oersted, the deviation of a magnetic needle by a wire conveying a current of electricity; and, as in most other instruments of this kind, the wire is passed several times round the frame, within which the needle is suspended, that the effect may be proportionally increased. It differs, however, from all made before it, in the use of two needles instead of one: these are equal in size, parallel to each other, magnetised in opposite directions, and fixed on a straw, so that the contrary ends of the two needles point in the same direction. Their distance from each other on the straw is regulated by the construction of the frame with its cover ing wire, in and about which they are to move. The frame of M. Nobili is twenty-two lines long, twelve wide and six high. The wire is of copper covered with silk, it is one-fifth of a line in thickness, from twenty-nine to thirty-feet long. It makes seventy-two revolutions about the frame. The needles are twenty-two lines long, three lines wide, a quarter of a line thick, and they are placed on the straw five lines apart from each other. An aperture is made in the tissue formed by the turns of the wire on the upper surface of the galvanometer, by thrusting them from the middle towards each side; the lower needle on the straw is introduced through this aperture into the interior, in consequence of which the upper needle remains a little above the upper surface of the wire. The aperture is retained open to a certain extent, to allow freedom of motion to the needles and straw, these being suspended in the usual way from the upper extremity of the straw. The graduated circle, on which the deviation is measured, is placed over the wire on the upper surface of the frame, having an aperture in its centre for the free passage of the needle and straw. The upper needle is the index, the lower being visible only from the sides of the instrument. 481. The sensibility of this instrument depends upon the addition of the upper needle. Being magnetised in an opposite direction to the lower one, it almost entirely neutralises the influence of terrestrial magnetism, leaving only so much of directive power as shall induce the whole arrangement to return to a constant position when uninfluenced by electrical currents, and yet combining with the lower needle, to cause deflexion when an electrical current is passing through the wire. 482. As an illustration of the delicacy of the instrument M. Nobili observes, that it is well known if Sebeck's combination of antimony and bismuth be attached to a common galvanometer, and the point of junction be cooled, only a very slight effect is observed on the instrument; whilst, if attached to the new galvanometer, the same influence is sufficient to make the needles revolve several times. If a piece of iron wire, five or six inches long, be used to connect the extremities of the copper wire of the instrument, by twisting the ends together, and one of the points of contact be warmed by touching it with the hand, the needle will move from 0°, and in the first oscillation extend to 90°. Even the mere approximation of the hand to the junction of the metals will produce a deviation of 20o. 483. It is necessary for the delicacy of the instrument that the needles used be magnetised as nearly as possible to the same degree, and two indications have been observed as useful in pointing out when this is the case; the first is the position taken up by the plane of the needles, when left to the earth's influence, this should not be in the plane of the magnetic meridian, but more or less inclined to it; the second is the manner in which the system oscillates about its line of equilibrium. These oscillations should be very slow compared with those of a common needle. 484. In consequence of the situation of the graduated circle above, and not within the frame, the folds of the wire may be brought much nearer to each other than in the common instrument, this renders it more compact, and, from the vicinity of the needle within to the wire, also more powerful. When fixing the graduation the zero should be placed so as to accord with the position of the needles, when left to the earth's influence; this will not be towards the true magnetic north, but will not be far from it, and will always be itself at a lower temperature than the ambient air, the difference being sometimes 2o, and resulting from the evaporation of the liquid. If a bar of bismuth be made to join the two extremities of the galvanometer wire, and one of the points of junction be plunged into a cup of water, the needle will immediatelydeviate several degrees proving that the instrument is capable of measuring the small degree of refrigeration produced by the evaporation of the liquid. I have actually submitted one of my galvanometers for fifteen days to an experiment of this kind, the deviation was about 15° in the morning and evening, but more considerable in the course of the day. This first attempt has made me suppose that the galvanometer might become, in the hands of an attentive and skilful philosopher, a kind of almidometer. If by means of a single couple of different metals, bismuth and copper, a deviation of 15° has been obtained, a much greater one would be produced by employing several pairs, conveniently immersed in the same vessel of water; and, perhaps, one might succeed by increasing the scale of observation, in ascertaining_more exactly the diurnal rate of evaporation. I propose, also, to ascertain the effect of a current of air, excited by any means over the surface of the water used in the experiment; it would, without doubt, augment the evaporation, and, by increasing the difference between the temperature of the air and the water, increase the effect on the instrument. 486. The theory of electro-magnetism remains to be illustrated. The phenomena developed were, at first view, not a little perplexing; and it was not till after repeated investigation, that, in 1820, any tangible view of the matter was furnished. The conducting wire was found to exert a magnetic force, not in a direction parallel to the wire itself, nor even in any plane pass ng through that direction, but in one that was perpendicular to it; and which, if circles were described in this latter plane, having the point at which it intersects the wire for their common centre, would have the direction of tangents to those circles. The following is another mode of conceiving the same thing. Imagine a cylinder of any diameter to envelope the wire,-the wire itself being in the axis; and conceive the surface of the cylinder to be covered on all sides with an infinite number of short lines touching the surface at different points, and situated transversely, that is, at right angles to its length. Suppose these lines to represent magnets, with the northern polarity of each turned in one inva riable direction, as we follow them round the cylinder. Then will these imaginary magnets indicate the direction and nature of magnetic forces, which emanate from the fire as long as the stream of Voltaic electricity is passing through it. The particular direction of the transverse, or, as it has been termed, tangential magnetic force will of course depend on that of the electric current in the wire, and may easily be traced in all cases by the recollection of the following fact. Supposing the wire to be in a vertical position-in which case the planes of the tangential forces will be horizontal-and supposing the stream of positive electricity to be descending along the wire, which of course im- of Sciences, for 1700; but was deemed of no plies that the negative electricity is ascending, importance. then that polarity which exists in the end of the magnetic needle, which naturally turns to the north, will be impelled round the wire in the circumference of a circle in a direction similar to the motion of the hands of a watch; that is, from the north to the east, and then to the south and west. The south pole of a magnet will of course be impelled in the contrary direction. A magnetic body in the vicinity of the wire will, by the influence of this force, tend to assume a position, shown in fig. 16, similar to one of the tangential lines we have been describing as placed on the cylinder. But further, the tendency of the electric current in the wire is to induce magnetism in soft iron or other bodies capable of receiving it; and the magnetism so reduced has the precise direction already indicated as that which a bar previously magnetised would assume by the influence of the wire. This direction is shown in the figure, where N and S denote respectively the north and south poles of steel bars, situated transversely with respect to a vertical conducting wire, in which the current of positive electricity is descending, as indicated by the arrows. 487. Most of the facts which have been brought to light by Oersted are the immediate consequences of the above general law. Mr. Barlow's enunciation of this law is as follows: he states that every particle of the galvanic fluid in the conducting wire acts on every particle of the magnetic fluid in a magnetised needle, with a force varying inversely as the square of the distance; but that the action of the particles of the fluid in the wire is neither to attract nor to repel either poles of a magnetic particle, but a tangential force, which has a tendency to place the poles of either fluid at right angles to those of the other; whereby a magnetic particle, suppos ing it under the influence of the wire only, would always place itself at right angles to the line let fall from it perpendicular to the wire, and to the direct on of the wire itself at that point.' 488. The transverse, or tangential action, which we have been describing is one of so extraordinary a nature, that it can be assimilated to no other principle in nature, of which we have any knowledge. It is not, therefore, surprising that it eluded the observation of former enquirers; although in the keenness of research, they almost stumbled upon the discovery. The fact which occurred to Beccaria, of the production of transverse magnetism in an iron bar, by the electric discharge of a battery, had, in fact, pointed out the precise direction of this inductive force; and the hint, if pursued, would have infallibly led to the discovery which Oersted made fifty years afterwards. It is curious that a circumstance extremely similar is on record, with regard to the observation which conducted Galvani to the discovery of the science which bears his name ; namely, the convulsive movements of the muscles of frogs, on taking sparks from a neighbouring prime conductor, charged with electricity. The very same fact had been noticed by Du Verney, about a century before, as appears from a memoir in the History of the French Academy 489. The relation which, this new magnetic power bears to the electrical, was also very singular and enigmatical. Considered as a magnet the conduct.ng wire acted differently, according to the side to which magnetic bodies were presented to it. What was attracted by the one side was repelled by the other; and, if the power were conceived to be derived from the impulse of a fluid, that fluid must be circulating perpetually round the wire in a kind of vortex, of which the wire is the axis. The consequence of such a vertiginous motion, as Dr. Wollaston has termed it, in the magnetic fluid, would necessarily, under certain circumstances, produce rotatory motions in the parts of certain combinations of magnets and of wires. The suggestion thus thrown out by Dr. Wollaston was soon after realized, by Mr. Faraday's discovery of the rotatory movements which had been predicted, and which we have already pretty fully described. By employing mercury as part of the Voltaic circuit, and placed so as to allow of perfect freedom of motion in the conducting wire, or in the magnet, according to the nature of the exper.ment, and so as to obtain the action of one pole only, Mr. Faraday succeded in effecting a variety of rotations, both in the magnet and the wire, in conformity with the law above stated. If the positive electric current be descending along the wire, the north pole of a magnet in its vicinity will revolve round it in the direction indicated by the arrows. As action and re-action are equal and contrary, the wire was seen to revolve round a fixed maguet, in a direction contrary to that in which the magnet would have moved, if the wire had been stationary; but, since these motions are to be estimated on opposite sides of a common centre, the direction in the circumference will remain the same. Thus, as a north pole revolves round a descending positive electric current in the direction of the hands of a watch, a wire in which a similar current is descending, will revolve in the same circular direction round a north pole placed in the centre of its motion. 490. The experiments of Mr. Faraday and professor Barlow, confirmed and extended as they have been by Barlow, Biot, and others, appeared to have conducted us to the most general fact belonging to the science; namely, the tendency to a transverse rotatory motion in the magnetic and electric fluids, when acting freely on each other. This fundamental principle once admitted, all the phenomena that had hitherto been discovered appeared to be easily explicable, and most of them were the immediate and necessary consequence of that principle. There was, indeed, one particular fact, for the discovery of which we are indebted to M. Ampere, to which it was less directly applicable, and which might not, perhaps, have been deduced as one of its results. This distinguished philosopher observed, that when two conducting wires were so arranged as that one or both of them were allowed a certain freedom of motion, they either attracted or repelled each other, according as the electric current which they transmitted was moving in the same or in opposite directions in the two wires, If, for example, two wires, which are transmitting currents of electricity, be situated within a certain distance, and parallel to each other; and if we suppose the currents of positive electricity to be passing from left to right in both the wires, they will manifest an attraction for each other. The same tendency of attraction will also appear when the positive currents are both moving in the contrary direction, that is, from right to left. But if the current in one wire is moving in a direction opposite to that of the current in the other wire, in that case a repulsive action will take place between the two wires. These were found to be constant and invariable effects of the transmission of electricity along conductors; and they were manifested equally, whether the two currents were obtained from separate Voltaic batteries, or were only two portions of the same current in different parts of its course. 491. To understand Ampére's theory, let us conceive a slender cylinder of iron intersected by an infinite number of planes, perpendicular to the axis, so as to divide it into as many circular discs, successively applied to each other, as represented in the engraving, at fig. 17: let us now imagine that, in consequence of some unknown action among the particles composing these circles, a current of electricity is perpetually circulating in their circumferences, as if they had composed a Voltaic circuit. Let us suppose the direct.on of these currents to be the same throughout the whole series of circles: the cylinder thus constituted may be considered as a magnetic filament; that extremity in which, when uppermost, the current of positive electricity is moving in a direction contrary to the hands of a watch, being the one which has the northern polarity, that is to say, which will, when suspended as in a compass-needle, point to the north. It is of course to be understood that the current of negative electricity revolves in the opposite direction. A magnet, then, is supposed to consist of an assemblage of similarly-constituted filaments; and, if these postulates be once granted, all the phenomena of magnetism will flow from them as corollaries; the magnetic power will be resolved into the electrical, and be henceforth erased from the list of original physical powers. 492. The facts belonging to the science of electro-magnetism may be classed under five heads-the first relating to the reciprocal actions of two electric currents when traversing a conduct.ng substance: the second, to the mutual action occurring between electric currents and magnets: the third, to the magnetic action of the earth on electrical currents: the fourth, comprising the actions of magnets on each other: the fifth, the action of the earth on magnets. These two last divisions of the subject constituted what was properly the province of the science of magnet sm; the three former having sprung up in consequence of the discovery of Oersted, and being of an intermediate character, had received the name of electro-magnetism. Ampére proposes to comprehend them all under the title of electro-dynamics. 493. Setting out, then, from the primitive fact, that parallel currents attract one another when their directions are the same, and repel one another when opposite, we have to study the law of modification which these forces undergo when the currents deviate from strict parallelism, and are inclined to one another at various angles, and in different planes. It is evident that the whole action of the currents must be the combined result of the actions of all their parts; and that in order to obtain the former, in every possible case, with mathematical precision, it is necessary to ascertain the simple law which governs the action of those elementary portions. 494. It is evident, in the first place, that the action will be in proportion to the intensities of the currents from which that action is derived; and it has been also determined, that the quantity of each action in each element, follows the same law as that of gravitation—namely, that it is inversely proportional to the square of the distance. The action, estimated in the direction of the line drawn from the one elementary portion of electric current to the other, and which, for the sake of conven ence, we shall term the line of junction, will be diminished by any obliquity in the direction of either of the currents-in the proportion of the radius to the sine of the angle which such direction forms with the line of junction. If, again, we consider the effects of a current, of. which the direction deviates from the plane that passes through the line of junction, and through the direction of the other current, and is situated in another plane, also passing through the line of junction, we shall find that, from being at a maximum when these two planes coincided, it will be reduced to the proportion of the cosine of the angle they form between them. Taking all these cons.derations, then, into account, and combining them in one formula, we obtain the following, in which a and b denote the respective intens.ties of the two elementary portions of each current; d their absolute distance from each other, measured of course on the line of junction; a, ß, the angles which their respective directions make with the Ine of junction, and y the angle between two planes, each passing through the direction of the respective current and the line of junction. Then the action of the two currents on each other, estimated in the direction of the line of junction, being expressed by A, A = ab (sin. a. sin. 3. cos. y.) 495. In the course of this investigation, Am pére found reason to conclude that the formula to the true law; for portions of the same, or o thus obtained was still only an approximation different currents, that were moving at very oblique angles, or even in the same continued line, were observed to exert a certain degree of repulsion on each other: he therefore introduced another term in the formula; and, as he was at first unable to ascertain the amount of its in fluence, prefixed to it the co-efficient k, the value of which was left for future determination. The whole formula will then stand thus: ab A= (sin. a. sin. B. cos. y. + k. cos. a. cos. B. d2 496. Ampère at first regarded the value of k as exceedingly small, and thought it might safely be neglected. Subsequent researches have led him to conclude that it was equal to-, so that the whole of that term has a negative value when the cosines of the two angles are themselves positive 497. The forces of electro-dynamical action, determined by the law above stated, are subject to the same laws of composition and resolution as all other mechanical forces, and afford, therefore, equal facilities for mathematical investigation. Many consequences important to the theory of particular facts are deducible from this consideration. Thus the action of a small portion of conducting wire, bent into any number of flexures and contorted forms, provided they do not extend to any great space, upon a distant current of electricity, will be equivalent to that of a similar wire proceeding in a straight course between the two extreme points of the contorted wire. 498. Another corollary deducible from the general law is, that the total action of a conducting wire of infinite length upon any portion of an electric current, moving in a direction parallel to the wire, is in the simple inverse ratio of the shortest distance intervening between the two currents that is, of the line drawn from one to the other, which is perpendicular to both, This consequence had been already deduced by Laplace, and was verified by direct experiment by Biot, as well as by Ampère. 499. Setting out from the simplest case, where a simple attractive or repulsive power is manifested, namely, that in which two currents are rectilineal, and in parallel directions, and in which the action is at its maximum in point of degree, we proceed to consider the variations which a change of inclination will produce. Let us first suppose one of the rectilinear currents, or wire which conveys it, to be inclined, as is shown at fig. 18, at a certain angle, and in a plane which does not pass through the other wire, or channel in which the other current is moving. In this case, a compound force, or at least one that may be resolved into two forces, is called into action. Let us suppose a line mn, fig. 18, drawn between the points, in each wire, which are the nearest to each other; a line which will, of course, be perpendicular to both the wires, and which may be called the line of junction: the points m, n, where this line meets the wires, will divide each wire respectively into two portions. Those portions of the wires, as a and b, or c and d, in which the currents are both moving, either towards those points or from them, will be attracted towards each other,―an action which will at first tend to turn them on the line of junction mn, as an axis, in planes perpendicular to that axis, so as to diminish the angle which they form, and to bring them into the parallel positions indicated by the dotted lines; and will also tend to make the two wires approximate. The former portion of this force, which produces a rotatory action, may be termed a directive force; the latter, which tends to the approach of the wires in the direction of the line of junction, may be termed the approximate force. This last force commences when the two wires are at right angles, and attains its maximum when they are brought by the directive force into a parallel position. When the corresponding portions of the wires, on the contrary, form an obtuse angle, the approximative force is negative, and is so in the greatest degree when the wires are parallel, with their current, moving in opposite directions. 500. This action will be considerably modified if, instead of supposing the two currents to be of equal length, and crossing one another at the line of junct.on, we take only a very limited portion of a rectilineal current, situated wholly on one side of the other current, which is itself of indefinite length; and we may now, for the sake of greater simplicity, assume them to be both in the same plane. If we analyse the forces which act on each side, and on each part of the limited portion of the current, the one set being attractive and the other repulsive, we shall find that the resultant is a force which will impel it in a direction perpendicular to itself, in the plane common to the currents, and so as to preserve its parallelism; and this will happen, whatever be the angle of inclination of the less current to the greater. Indeed we might show by experiment the direction in which the shorter wires will tend to move by the action of the current in the lower wire, supposed to be of indefinite length. The direction of this progressive tendency will be determined by that of the currents. When they are parallel to each other, they tend to approach or to separate, according as the direction of the currents is similar or dissimilar. When at right angles to each other, and the positive current in the shorter wire is receding from the longer wire, the shorter wire will be urged forwards in the same direction as the positive current is moving in the longer wire; and, vice versâ, it will be urged in the opposite direction when the current of positive electricity is moving towards the longer wire. Such then would be its motion were it free to move in all directions; but, if its motion be limited, in that plane, to a movement of rotation round one of its extremities, the same force will produce its continual revolution, with a uniformly accelerated velocity round this axis; because the force itself is independent of the angle of inclination of the currents, and is, therefore, uniformly exerted during the whole period of its revolution. It is to be observed, however, that the two cases we have here supposed, in which the effec of a straight current of indefinite length can be limited to a small portion of another current on one side only, are such as are not easily realised in practice. The difficulty lies in disposing of the remaining portions of the current, so that they shall not interfere with the effects intended to be produced. The only mode of obtaining this object is to provide for their subdivision and branching off in different directions, at the end which is nearest to the current whose action we are studying; so that these different portions shall act in opposite ways, and thus neutralise each other's effects. This object may be accomplished most conveniently and effectually by allowing the ends of the smaller portions of |