it is by no means necessary to review in succession all the degrees that contribute to the formation of this arc. The application of our method to the angles of 20° and 10° will be quite sufficient. This being done, we shall find an equal quantity between their difference and the effect produced by the simultaneous action of the moving forces. In other words, let us produce a deviation of 20° to the right and one of 10° to the left: let us then simultaneously expose the two opposite faces of the pile to the two radiations which produce these galvanometric indications: the index will move to the right, and stop precisely at 10°. Hence we infer that the force necessary to make the needle describe the arc comprised between 10° and 20° is equal to the force required to make it pass over the first ten degrees of the scale. Thus the proportion of the degrees to the forces is perceptible as far as the 20th degree on each side of zero.
This fact seems opposed to the inference which might have been made in examining the nature of the galvanometric action; for, in the successive rotation of the astatic system, the poles of the magnetic needles depart from the mean line of the electric currents. The intensity of the repulsive forces, therefore, decreases in proportion as the angle of deviation increases. Whence we should conclude that the effort necessary to make the needles exceed a given arc should change as soon as the first degrees of the scale are passed. This would undoubtedly take place if all the electric currents lay in a vertical plane passing through the line marked 0°; but the circumvolutions of the metallic wire which is wound on the frame placed under the graduated circle are distributed to a certain extent on each side of this plain. In the galvanometer which I have employed in my experiments, they cover the two opposite arcs of 76°, the chords of which are perpendicular to the line marked 0°. Thus so long as the oscillations take place within certain limits there will always be electric currents situated on each side of the needles. Now when the intensity of these currents is extremely feeble, their sensible effect on the needles must cease at a very short distance. Let us suppose this distance to be 18° of the division of the galvanometer intended to show the degrees of electric action which cause the deviations to the right and left for the first 20° of the scale. These degrees of action must be extremely feeble in a very delicate galvanometer. If, during these oscillations, the system of the needles is confined within the two initial arcs of 20°, it is clear that it will always be subject to the same action, whatever may be the position in which it is placed; for there will always be near its plane a series of currents extending to 18° on each side, even when the system will occupy the extreme limits. The influence of the currents that are further distant will, according to our hypothesis, be nothing. As the moving force will therefore have a constant value, we shall have to consider only the