S72 M. Ampere's Letter on Electro-dynamic Phenomena. 



portion OC in a contrary direction. The opposition of those 

 tTvo actions evidently takes place only from the circumstance 

 that the portion OC of the moveable conductor is in the in- 

 terior of the helix ; whereas the portion MABO is on the out- 

 side : but that circumstance cannot take place unless there 

 be points of the moveable conductor at a distance from the 

 two whorls between which it passes, less than that from one 

 whorl to another; and then the value of the rotatory mo- 

 mentum in the function of the angles 6', 6", 6',, fl", is no longer 

 applicable, as it rests upon these two suppositions; 1st, that 

 the distance between two consecutive circular currents is infi- 

 nitely small ; and, 2d, that the distance from the several points 

 of the moveable conductor to those currents is very gi'eat, re- 

 latively to the radii of the circles which they describe. The 

 case, however, in which the value found for the rotatory mo- 

 mentum no longer exists, is peculiar to the electro-dynamic 

 helices, and cannot be applied to magnets, since the moveable 

 conductor cannot pass between the electric currents to which 

 they owe their properties, and since the radii of the circles de- 

 scribed by those currents are of a minuteness corresponding 

 to the order of dimensions of the particles of bodies. 



Thus no real difference appears between the action of a 

 magnet and that of an electro-dynamic solenoid. It may be 

 seen that the helix which is substituted for the latter, acts like 

 a magnet, with the exception of that case only where a por- 

 tion of the moveable conductor passes between its whorls, and 

 extends into the interior of that helix ; which circumstance 

 cannot take place with respect to the magnet, of which the 

 circular currents surround each particle. It may at the same 

 time be perceived why the value of the rotatory momentum 

 mentioned above ceases at the same time to express the action 

 of the helix, although it always represents precisely that of the 

 magnets; and how the continuous rotation of the moveable 

 conductor (disposed as in fig. 1) is by no means opposed to 

 the case of equilibrium which I have deduced between the two 

 constants k and n of my formula, the relation 



21- ■{■ n = 1, 

 and which I have proved by the experiment described at 

 pages 311 and 312 of my Recucil. In that experiment the 

 equilibrium takes place between the two actions formed by 

 the circular horizontal conductor ; the first, in one direction, 

 upon the portion of the moveable conductor which coi'responds 

 to the interior of this circular conductor; the second, in a 

 contrary direction, upon the portion of the moveable conductor 

 which is exterior to it. Now, in the apparatus (fig. 1) the lat- 

 ter is quite exterior to the magnet ; there is therefore action in 



one 



