ELECTRO-MAGNETISM. 



69 



portions A P and C Q. The portions 

 P B and Q D will also attract one an- 

 other, because the currents are proceed- 

 ing from the points P and Q, in each 

 respectively. But the portions A P and 

 Q D will repel one another, as will also 

 the portions P B and C Q ; because the 

 currents are moving: in a different man- 

 ner in the two that compose each of 

 these pairs. 



All these forces concur in producing 

 a rotatory motion round the axis P Q. 

 The wire A B will tend to assume the 

 position a b, parallel to C D ; and the 

 wire C D will be urged to take the posi- 

 tion c d parallel to A B. If only one of 

 these be moveable, it will place itself in 

 a line parallel to the other ; if both be 

 moveable, they both will take an inter- 

 mediate position ; so that, in either case, 

 they will become parallel to one another. 

 That part of the force which produces 

 this rotatory effect, and acts in a plane 

 perpendicular to the axis, may be termed 

 the directive force. It varies as the 

 sine of the angle A P a ; but another 

 part of the force still remains, namely, 

 that which acts in a direction perpendi- 

 cular to this plane that is, parallel to 

 the line P Q, the nearest distance of 

 the wires. It is evident that this force 

 varies as the cosine of the angle A P a. 

 Whenever that angle is less than a right 

 angle, this force is attractive ; and as it 

 tends to bring the currents nearer to 

 each other, it may be distinguished from 

 the former by the designation of the 

 approximative force. Commencing 

 when the positions of the wires, from 

 being perpendicular, are slightly inclined 

 to each other, this latter force attains its 

 maximum when they have been brought 

 by the directive force into a parallel 

 position. When the corresponding por- 

 tions of the wires, on the other hand, 

 form an obtuse angle, the approxima- 

 tive force is negative, and is so in the 

 greatest degree when the wires are 

 parallel, so that their currents move in 

 opposite directions. This is an obvious 

 consequence of the change of sign which 

 the cosine of the angle A P a experiences 

 when the latter changes from an acute 

 to an obtuse angle. 



(211.) If the movements of either of 

 the wires be restricted to rotation round 

 an axis different from P Q, such as X, 

 fig. 121, some part of the directive force 

 will be destroyed by the opposing action 

 of the current passing through the por- 

 tion X P, which intervenes between the 

 axis and the perpendicular. This oppo- 



sition of forces will increase according 

 as the axis is further removed from the 

 perpendicular : so that all action may 



Fig. 121. 



come to be entirely neutralized, if its 

 distance is sufficiently great in propor- 

 tion to the length of the other branch, 

 P B, of the current situated on the other 

 side of P Q. In estimating the result- 

 ing effect, however, it is necessary to 

 take into account the mechanical advan- 

 tage which the rotatory force, impelling 

 the remote part PB, has over that which 

 impels XP, in consequence of the greater 

 length of lever by which it acts. When 

 the contrary rotatory momenta thence 

 arising are equal, the currents will be in 

 a position of equilibrium, which posi- 

 tion will tend the more nearly to coin- 

 cide with that of parallelism, in propor- 

 tion as the axis approaches to a coinci- 

 dence with the perpendicular P Q. This 

 result may be verified by employing the 

 apparatus fig. 106, which, from its con- 

 struction, is, as we have seen, astatic, 

 and by which we may study the action 

 of a transverse current upon either of 

 the horizontal branches to which it is 

 presented. 



6. Mutual Action of Rectilineal and 



Curvilineal Currents. 

 (212.) If a terminated current, which 

 describes a curve line, be subjected to 

 the action of an unlimited rectilinear 

 current, its different portions will be 

 urged in different directions, each being 

 perpendicular to the respective portion 

 of the curve. Thus the different parts 

 of the circular conductors A B,/g-. 122, 



Fig. 122. 



A 

 A i 



