74 



ELECTRO-MAGNETISM. 



centres, as in fig. 135, or coincide with 

 it as in fig. 136, or have any other 

 inclination to it. 



228. If the centre of the moveable 

 circle be any where in a line drawn 

 through the centre of the former, and 

 perpendicular. to its plane, the moveable 

 circle will tend to arrange itself in a 

 plane parallel to the fixed circle, and 

 having its currents moving in a similar 

 direction. This is evident from fig. 137, 

 in which the same letters as before are 

 used to denote the corresponding points. 



(229.) In both cases an approxi- 

 mative force takes place, whenever the 

 moveable circle has arrived at its po- 

 sition of equilibrium; which force, in 

 the latter case, is particularly strong, 

 inasmuch as the attraction of the cor- 

 responding parts of the circles is uniform 

 throughout the whole circumference. 



(230.) For each position of the centre 

 of the moveable circle, intermediate to 

 those above described, there exists a 

 particular position of equilibrium, the 

 line of which, if prolonged, would inter- 

 sect the plane of the fixed circle at a 

 certain distance beyond it. 



(231.) All these positions of equili- 

 brium are determinate, and exclude the 

 possibility of any continued rotatory or 

 revolving motions. 



(232.) When an electric current, after 

 traversing a certain line of conducting 

 bodies, returns upon itself, so as to 

 arrive at the point from which it had 

 set out, or very near it, it has been de- 

 nominated a closed circuit. Such is 

 the case with the circles we have been 

 considering. One of the most import- 

 ant facts on which the theory of electro- 

 dynamics rests, is that the mutual action 

 of two closed circuits cannot produce, 

 in either of these circuits, a continued 

 rotatory motion in an invariable direc- 

 tion ; and, consequently, no assemblage 

 of closed circuits can ever be made to 

 produce such rotatory motion, in what- 

 ever manner they may be disposed. 



(233.) Experiments on the mutual 



actions of circular currents, either on 

 each other or on straight conductors, 

 are most advantageously made by means 

 of a flat spiral rendered astatic, by op- 

 posing to it a similar coil on the oppo- 

 site arm of the lever, from the middle of 

 which they are both suspended, as shown 

 in fig. 138, the spiral turns being in 



138. 



different directions in each, so that the 

 rotatory influence of the earth on the 

 one shall be exactly balanced by its in- 

 fluence on the other. 



8. Mutual Action of Heliacal and 

 Rectilinear Conductors. 



(234.) We have seen that the action 

 of conducting wires rolled into the form 

 of a flat spiral is similar almost in 

 every respect to that of a simple circular 

 wire; but when coiled round the sur- 

 face of a cylinder, so as to constitute a 

 helix, its action becomes much more 

 complicated. When the extremities of 

 the wire, after completing the helix, are 

 made to return along the axis, as de- 

 scribed in 105, and shown in fig. 71, 

 constituting what has been termed by 

 Ampere an electro-dynamic cylinder, 

 the whole may be considered as equiva- 

 lent in effect to a succession of circles, 

 whose planes are perpendicular to the 

 axis, and occupy the whole length of the 

 cylinder. In determining the forces 

 that are called into operation by such 

 an apparatus, we may, therefore, put out 

 of consideration the slight obliquity 

 which the turns of the spires have to 

 the axis, and the effect of which is 

 completely neutralized by the corre- 

 sponding portion of the wire that passes 

 along the axis ; and we may regard the 

 whole as composed of currents circu- 

 lating at right angles to the length of 

 the cylinder. 



(235.) Since we have seen that the 



