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. [Illustration] 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