direction both the wires a b and a' b'.

When we wish to have

a short and thick wire galvanometer, we connect by a metal arc a and a', and do the same for b and b'; we make the current enter by the two united ends (a and a'), and come out by the two others (b and b'); so that it traverses simultaneously the two wires in the same direction, which amounts to the same thing as if it traversed only one of the same length as one of them, and of double the sectional area. Finally, by using but one of the wires, namely, by making the current enter by a and come out by b, or else enter by a' and come out by b', we have a galvanometer of short and fine wire. The same instrument may thus fill the office of three galvanometers at the same time that it serves the purpose of a differential galvanometer. The letters A and B marked on the frame, indicate that the current enters by a or a' if the north pole of the upper needle deviates towards a, and by b or b' if it deviates towards B.

Fig. 135. represents a differential galvanometer, constructed of large dimensions, on account of the facility we have of seeing its indications from a distance. With this view, the upper magnetised needle is covered with a long and very light slip of fine whalebone cut into the form of an arrow, which, by moving over a white frame upon which the divisions are traced, is extremely visible. This instrument is very sensible; for, on placing two very clean plates of platinum, communicating with the ends of the wires, the one under the tongue and the other over, we obtain a current capable of producing a deviation of several degrees.

Comparable Galvanometers.

We have hitherto regarded the galvanometer as an instrument fitted for detecting the presence of even the most feeble current, and of indicating its direction; it now remains to us to examine how it may determine its intensity.

This intensity may be appreciated approximately by means of the amplitude of the deviation; but it is far from being proportional to it, at least on as far as 90°; although from 0° to 20° we may, without sensible error, as experiment has proved,

admit this proportionately; so that a current that produces a deviation of 12° has a double intensity to that which produces a deviation of only 6°, and triple of that which produces one of only 4°, and so on.

The most simple means for determining in a galvanometer the relation existing between the forces and the angle of deviation, is to roll around the frame several wires independently of each other, placed similarly in respect of the needles, and to pass the current first through one, then through two, then through three, and so on; so that we thus act upon the needle with forces as 1, as 2, as 3, &c. It is merely necessary that the wires be sufficiently large and not too numerous, so that the current, in traversing them all successively, does not experience any sensible diminution in intensity by the effect of their resistance of conductibility. By operating in this way, we may satisfy ourselves that just below 20°, and for stronger reasons beyond it, the deviations are no longer proportional to the force of the current, but proportionately less considerable.

Beyond a limit which cannot surpass 20°, and which frequently does not attain to that, there are two circumstances which prevent the intensities of the currents being proportional to the angle of the deviations. One is, that the directive force of the globe, which, by tending to bring back the system of needles into the magnetic meridian, produces equilibrium with the force of the current that moves it from it, is proportional not to the angles, but to the sines of the angles of deviation; and that from about 20° the difference between the arc and its sine, which was but little sensible until then, becomes too considerable to permit of their being taken indifferently for each other. The second circumstance is, that as soon as the needle or the two needles recede from the magnetic meridian in which they are naturally retained, and in which the movable frame is to be placed, so that they may be parallel to the wires, their position in respect to these wires is no longer the same; and, consequently, the currents can no longer act upon them in the same manner. It is easy to see that if, in the normal position, that in which the wires are

parallel to the needles, the force possesses its whole intensity, as soon as there is a deviation from the meridian it acts only by a component less in proportion as the angle of deviation is greater. This circumstance, the influence of which is but little sensible for the first degrees of deviation, becomes excessively so as soon as this deviation increases. In order to remedy this, M. Peltier had proposed to substitute for each of the two needles of the astatic system two needles crossed at a right angle in the same plane. It follows, from this arrangement, that, when the needles that are parallel to the frame are driven from it, the others tend to enter into it, and that one of the effects almost compensates for the other. M. Peltier found that the indications of this instrument up to 45° are exactly proportional to the intensities of the current.

But if we desire, for measuring currents, to have galvanometers in which this proportionality is perfectly exact, we must employ the sine galvanometer or the tangent galvanometer. It is true that as these two instruments contain but a single magnetised needle, they lose in sensibility what they gain in accuracy. They are therefore essentially applicable to the determination of certain laws in which we act upon currents that may be procured as intense as is necessary.

The sine galvanometer (Fig. 136.), the principle of which I

Fig. 136.

had described as far back as 1824*, and which M. Pouillet *Mém. de la Soc. de Phys. et d'Hist. Nat. de Genève, tom. iii. part I. p. 117.

has constructed more recently under a slightly different form, consists of a compass needle from 4 in. to 6 in. in length, furnished with an agate cap, by which it rests upon a steel point placed exactly in the middle of a low and narrow metal frame, around which is carefully wound a wire or a ribbon covered with silk, which makes a greater or less number of convolutiens, according to the degree of sensibility that we desire to impart to the apparatus. The multiplier and its needle are fixed upon the movable transom of a divided circle; and when they are both in the plane of the magnetic meridian, the apparatus is at the zero of the division. The needle, by its position in the interior of the frame of the multiplier, to which its axis must remain parallel, accommodates itself with difficulty to the exact determination of its real direction. In order to obtain the direction with precision, and in a convenient manner, we add to the needle, perpendicularly to its length, a thin and light slip of wood, upon which we have traced an index-line, that enables us to judge of the true position of the needle itself. We are sure that it is exactly parallel to the mean plane of the multiplier, when the index-line, of which we have just spoken, falls beneath the wire of a lens that is fixed to the movable piece upon which the galvanometer is adjusted. In order to operate with this instrument, we begin by placing it at the zero of the division, the needle being quite parallel with the wires, and, at the same time, in the magnetic meridian. We then pass the current through the wire of the multiplier. The needle is deviated; and we turn the transom that carries the multiplier until the wire of the lens coincides with the index-line the division traced upon the fixed circle indicates the number of degrees it was necessary to turn it from the 0°, in order to obtain this coincidence. This is the exact measure of the deviation of the needle, namely, the angle that it forms with the magnetic meridian. But, in this new direction, the needle has preserved the same position in respect to the wires of the multiplier; that is to say, in respect to the current, which consequently acts upon it in the same manner. The amplitude, therefore, of the deviation of

the needle can depend only upon the intensity of the current. The forces between which equilibrium is established, and which consequently are equal, are thus, on the one hand, that of the current, on the other hand, the directive force of the earth, which tends to bring the needle back to the meridian from which the former had removed it. Now the latter being proportional, as we have seen, to the sine of the angle of deviation, the former, that is to say, the intensity of the current, is the same also. By means of this instrument, therefore, taking care to operate with precision in each case, we may determine with accuracy the relations of intensity existing between the different currents that are transmitted through the wire of the multiplier.

We may, as may be imagined, give the sine galvanometer various degrees of sensibility, either by bringing the wire nearer to or farther from the needle, or by increasing or diminishing the number of convolutions; we may even cause the wire to make but a single turn. It is convenient to have multipliers fulfilling these divers conditions, which may all be fixed in the same manner upon the movable transom, and in the interior of which the same needle may be placed. It is necessary to take every precaution in the fabrication and the magnetisation of this needle, which should be a good compass-needle without consecutive poles.

The tangent galvanometer (Fig. 137.) consists of a large circle, open within, of from fifteen to twenty inches in diameter, provided with an exterior groove not more than in. wide, wherein a wire is placed, or, which is better still, a copper ribbon covered with silk, and which is made to have one or several convolutions around the circle. The two extremities of the wire or the ribbon, being bent back very near to each other, are prolonged below in the direction of the vertical diameter, so as each to plunge into a cup filled with mercury, in order that the transmission of the current may so be brought about. The circle, whose circumference is traversed by the current, is fixed vertically upon a divided and horizontal circle, the centre of which coincides with its own; this circle is intended for measuring the deviations of a