Royal Academy of Sciences of Paris. 387 



7°. The action exercised upon an indefinite current by an 

 upright cylinder composed of small circular currents united 

 upon a common axis perpendicular to the indefinite con- 

 ductor, may be represented in all cases by supposing the con- 

 ductor to be subjected to the action of the two forces, the in- 

 tensities of which are in an inverse ratio of the distances to 

 the two extremities of the cylinder, and whose directions are 

 perpendicular to the signs which measure those distances. 

 This result agi-ees perfectly with the experiment, for M. Pouil- 

 let has established, by the needle's positions in equilibrio, that 

 law which M. Biot had deduced from its oscillations ; that the 

 action of a magnet upon a Voltaic conductor perpendicular to 

 its axis, is represented in all cases by supposing the conductor 

 to be subjected to the action of two forces, whose intensities 

 are in an inverse ratio of the distances to the two poles of the 

 magnet, and whose directions are perpendicular to the lines 

 which measure those distances. 



If we suppose that the circular currents liave their centres 

 in a curve of any form, to which their planes are perpendicular, 

 a disposition which a horse-shoe magnet represents ; and if 

 we take for this curve the circumference of a circle, we have 

 that which the circular magnet employed by Messrs. Gay- 

 Lussac and Weither represents. The calculation applied to 

 these two systems leads to two new theorems. 



8°. A magnet bent into a circle has no action at any di- 

 stance upon an indefinite conductor perpendicular to the plane 

 of the circle. 



9°. The action exercised upon an indefinite conductor by 

 a magnet, whose axis forms any curve symmetrical Avith re- 

 gard to a diameter, is directed into this diameter every time 

 the indefinite current passes through one of its points, and is 

 perpendicular to the curve of its centres. 



From this last theorem it follows, tliat if a vertical con- 

 ductor is susjjended upon a vertical axis around whicl; it can 

 revolve freely, and if it is subjected to the action of a 

 horse-shoe magnet placed horizontally, and in such a 

 manner that its diameter meets the axis of rotation ; the 

 conductor is constantly brought into one of the two jwsitions 

 in which it meets the diameter of tlie magnet: of these two 

 positions, the one is always that of stable equilibrium ; the 

 other of unstable equilibrium ; the conductor, from the iuipos- 

 sibility of its fixing itself except in this latter, is made to pass 

 from one to the other, either in reversing the direction of 

 the current, or iti turning the magnet in such a manner as 

 Oiat the upper surface becomes the louci ; or by presenting 

 aiternatciv to the conductor the concavity and tiic convexity 

 3 C 2 oi 



