eledro-dynamic Phcenomcna. 37i 



of rotation, the continuous movement of the axis would take ' 

 place when one of the poles is between the two extremities of 

 the conductor, and the other pole without the space bounded 

 by these extremities. This result from my formula agrees with 

 that of the experiment made by means of the a]:)paratus 

 shown in Plate I. (fig. 1 ), although in this apparatus the lower 

 extremity N of the moveable conductor MABN, which is 

 immersed in the mercury of the cup PQ, is not terminated ex- 

 actly at the axis. This is occasioned, on one hand, by the co- 

 sines of the angles 9/ and 9,", relatively to the extremity N, 

 differing but very slightly from the values — 1 and + 1 which 

 these cosines would have if it were precisely in the axis ; and 

 on the other hand, by the value of the rotatory momentum, 

 expressed in functions of the angles 6', fl", 9/, 9," being applica- 

 ble to tliis case, because the various points of the conductor 

 are at much greater distances from the currents from the mag- 

 net than the radii of the circumferences described bv these 

 currents. But if we could suppose the conductor to penetrate 

 the magnet, and terminate at a point D of the axis situated in its 

 interior, we cannot say precisely what would be the result of such 

 a supposition, which however it would be impossible to realize. 

 For, the points of the portion CD of the moveable conduc- 

 tor being infinitely near to the currents from the magnet, the 

 radii of circumferences described by those currents could no 

 longer be considered as very small, relatively to the distances 

 between each other and the points we are speaking of: thence 

 the expression of the rotatory momentum which has been 

 calculated without reference to the powers of those radii, su- 

 perior to the third, would cease to give the value of that mo- 

 mentum. Therefore, if in the apparatus we have just described 

 we were to substitute for the magnet an electro-dynamic helix, 

 there would be still a continuous rotatory movement as long 

 as the lower extremity N of the moveable conductor was outside 

 of that helix, as it is outside of the magnet LL' (fig. 1 ) : but if 

 the helix having still for its axis that round which the moveable 

 conductor is made to revolve, the moveable conductor may be 

 disposed as in fig. 2, so that its lower extremity N should 

 be, in like manner as its upper M, precisely in the axis. By 

 making the horizontal portion BC of that conductor pass be- 

 tween the whorls of the helix, it would no longer have a ten- 

 dency to revolve round the axis of those whorls ; because for 

 each of them there would be upon BC a point O, such as the 

 rotatory momentum imparted by the action of the whorl to the 

 portion MA BO, in order to make it revolve in one direction, 

 will be destroyed by an equal momentum, and of a contrary 

 sign, resulting from the action of the same whorl to turn the 



3 A 2 portion 



