The relation between exciting power and magnetic moment is very complicated, depending not only on the dimensions and shape of the core and the manner of winding, but also on the chemical constitution of the iron of the core. It is not possible, or at least it has hitherto not been found possible, to embody all these various elements into an exact mathematical formula, which would give the magnetic moment as a function of the exciting current; but the above mentioned experiments have shown that within certain limits, and in the neighborhood of the point of saturation, the relation between the two is that of an arc to its geometrical tangent. It will be seen that for large angles the arc increases much slower than the tangent; that is, for strongly excited cores, a very large increase of the exciting current will produce only a slight increase of magnetic moment. If Mueller's formula were correct for all currents, absolute saturation could only be reached with an infinite current. Whether this be the case or not, it is certain that the greater the exciting current the less will a variation in it affect the magnetic moment of the core. To imitate as nearly as possible permanent steel magnets, it is therefore necessary to use electro magnets, the cores of which are easily saturated.

The core should be thin and long and of the horseshoe type; the amount of wire wound round it should be large in comparison with the size of the core.

Here is a magnet partly wound which was used in one of our earliest experiments, but which was a failure on account of having far too much mass in the core in comparison with the amount of copper wire wound round it. Since then we have greatly diminished the iron and increased the copper. The cores of the instruments on the table are composed of two or three No. 18 b.w.g. charcoal iron wires, and are wound with one layer of 0'120 inch wire in the case of the current indicators, and eighteen layers of 0.0139 inch wire in the case of the potential indicator. If from the diagram, Fig. 1, we plot a curve the abscissae of which represent exciting current, and the ordinates magnetic moment of the soft iron core, we find that a considerable portion of the curve is almost a straight and only slightly inclined line. If it, were a horizontal straight line the core would be absolutely saturated, but such as it is, it answers the purpose sufficiently well, for with a variation of exciting current from 10 to 100 amperes the magnetic moment varies but slightly.

If a small soft iron or magnetic steel needle, n s, be suspended between the poles, S N, of an electro magnet of such proportions as described above, and the current, after exciting the electro magnet, e e, be lead round the coils, DD, it will be found that for all currents between 10 and 100 amperes the needle, n s, shows a definite deflection for each current. Here we have a galvanometer with permanent calibration. In this case the deflection of the needle will not strictly follow the law of tangents, because the directing power of the electro magnet is not absolutely constant; but whatever the exact ratio between deflection and current may be, it must always remain the same, and to each angle of deflection corresponds one definite strength of current.

The force with which the electro magnet tends to keep the needle in its zero position, that is, in line with the poles, S N, is due partly to the magnetism of the core, which is nearly constant, and partly to the magnetic influence of the coils, ee, themselves, which is, of course, simply proportional to the current. The total magnetic force acting on the needle is, therefore, represented by the sum of these two forces, and consequently not nearly so constant as might be desired in order to get a good imitation of a tangent galvanometer with a permanent magnet. In the diagram, Fig. 2, the curve, O A B, represents the magnetic moment of the iron core, the straight line, ODE, that of the exciting coils per se, and the dotted line, O F M, the sum of the two, obtained by adding for every current, O C, the respective ordinates, CD and C A.

 CF = CD + CA 

The rise of this curve shows that the force which tends to bring the needle back to its zero position increases with the current, though at a slower ratio than the deflecting force of the current. It follows from this that for large currents the increment in the angle of deflection is comparatively small, and the divisions on the scale whereon the current is to be read off would come too near together to allow accurate readings to be taken. In other words, the range of accurate reading in an instrument so constructed would only be limited. But it is very easy to eliminate the magnetic effect of the coils of the electro magnet on the needle, by introducing an opposite magnetic effect, so that only that part of the force remains which belongs to the soft iron core proper. One way of doing this is by surrounding the needle with a coil, the plane of which is at right angles to the line, S N, and coupling this coil in series with the deflecting coil, D D. If the proportions of this transverse coil and the direction of the current through it be properly chosen, its magnetic effect can be made to exactly counterbalance that of the exciting coils, e e, without perceptibly weakening the magnetism of the iron core.

But instead of employing two coils, one parallel and the other transversely to the zero position of the needle, we can obtain the same result in a more simple manner with one coil only, if this be placed at such an angle that its magnetic effect can be substituted for the combined effects of the two coils. In other words, we set the deflecting coil, D D, at a certain angle to the zero position of the needle.