Page:Scientific Memoirs, Vol. 1 (1837).djvu/25

Rh modifications which the active part of this force is made to undergo by the different inclination of the needles to the direction of the currents; and these modifications are quite analogous to those which take place in the portion of gravity that acts on the pendulum in different arcs of oscillation.

Now the force necessary to make the pendulum vibrate from one inclination to the other, is proportional to the difference of the cosines of the angles which the two directions form with the vertical. Whence it is clear that it remains sensibly constant in the arcs that are not far removed from the line of rest. The same effect must therefore be produced in the galvanometer also; or, in other words, the force required in this apparatus to increase the deviation of the index by a degree will be constant near the line of zero, as is shown by experiment.

From what we have just said it will be easy to see that the relation between the degrees of the galvanometer and the forces which cause the deviations of the needles, must depend on the sensibility of the astatic system and the distribution of the wire on the frame In order to understand this clearly, it is sufficient to suppose a galvanometer in which the circumvolutions of the wire are move numerous towards the extremities than towards the central part. It is evident that under the action of such a system the forces which produce the deviations, instead of increasing or being merely proportional in the arcs near zero, must decrease as we approach the extremities of the frame, in order to increase afterwards when the index haspassed these positions.

As to the influence of the sensibility of the astatic system, we shall be able to form a tolerably exact idea of it, if we imagine a galvanometer with the two needles possessing very different degrees of magnetism. Then the terrestrial globe will very powerfully affect both combined; and, in order to produce the least deviations, electric currents must be employed possessing much greater force than those required to produce small deviations in a more perfect astatic system. In the positions near zero, the electro-magnetic action produced by the most distant currents, that is, the action of the currents situated at the extremities of the frame, will possess an energy sufficient at least to overcome the resistance arising from the twisting of the suspension thread and the inertia of the astatic system. It will therefore always contribute to move the oscillating mass. Hence it is evident that if the needles are displaced in the slightest degree, the consequence will be a loss in the moving force; for if the system approaches a certain arc at a certain extremity, it recedes at the same time double the distance from the opposite extremity. Now we have already seen that, in delicate galvanometers, the moving force is constant when the angles are small; and we have assigned the cause of this fact upon the incontestible principle that, in small deviations of the instrument, the action of the currents situated towards the extremities of the frame must be disregarded, not indeed because they have no value, but because it becomes, in consequence of its distance, extremely feeble, and incapable of surmounting the obstacles opposed to it by the torsion of the silk thread and the inertia of the needles. . It will vary, therefore, according to the construction of the instrument, but may be always determined by the method we have mentioned.

Experiment having shown that in my galvanometer the proportion of