employed in the construction of the thermomultiplier, furnish sufficiently simple means of solving the question in each particular case. Indeed there is nothing easier than to keep the index of the galvanometer at any degree of deviation. All that is required for this purpose is to place a lighted lamp at proper distance from either side of the thermoelectrical pile. To prevent the possibility of mistake on this point, let us suppose the axis of the pile to be perpendicular to the magnetic meridian, and the communications so fully established that, when the left or the right side of the pile is heated, a corresponding deviation will be exhibited by the galvanometer. Let there be now produced a sufficiently marked deviation by placing a lamp near enough at the same side. Let this deviation be 44°. After having brought the needle back to 0° by interposing a metallic screen, let us make it move to the 42nd degree of deviation on the left, by means of a second lamp placed on the other side. To bring the needle back again to the zero point of the scale, we have only to stop the radiation by means of a metallic screen, as before.

It is natural to ask what will be the effect now produced by the heat of both lamps being brought to bear simultaneously upon the opposite sides of the pile. The calorific effects will be partially destroyed, and the instrument will mark but their difference. If the same force were always required to make the needles describe arcs containing the same number of degrees, the index would stop at the second degree of deviation to the right; but we know that these effects continually increase to the right and to the left of zero. The difference of two degrees just now observed between the partial deviations of 44° and 42° was owing to the application of a force greater than what is required to make the index traverse the first two degrees of the scale. The position marked 2° will therefore be exceeded, and the more so in proportion as the first force is greater than the second, and the arc described will, when compared with the difference of the two deviations, immediately give the measure of the corresponding force. If, for instance, the needle stops at 8°, it will be inferred that the force required to make the needle pass from 42° to 44° is four times greater than that required to make it pass from zero to 2°. This effect would be five times greater if the needle stopped at 10°, and so of the rest.

I shall not attempt to conceal the fact, that in this process the proportionality of the forces to the degrees in the arc employed as a comparative measure is tacitly assumed. But the assumption is fully justified by experience; for we find that in galvanometers whose astatic system has been brought to a high degree of perfection, the magnetic needles, through the whole extent of the arc comprised between zero and the twentieth degree nearly, describe arcs proportional to the action of the electric current to which they arc subjected. To be convinced of this,