G2 



ELECTRO-MAGNETISM. 



instance, the effective force of an oblique 

 current, in its action on another current, 

 is obtained by reducing: that force to a 

 direction at right angles to the medial 

 line. Let, us suppose this to be done 

 with regard to both the currents A and 

 B,//. 101, the former being; reduced to 

 the line a a, and the latter to the line b b, 

 situated respectively in planes perpendi- 

 cular to the medial line A B. The force 



Fig. 101. 



Fig. 102. 



a A, estimated in the direction A c, 

 drawn parallel to B b, or the force B b 

 estimated in the direction of B d, drawn 

 parallel to A a, will, in either case, be 

 reduced in the proportion of radius to 

 the cosine of the angle a A c, or d B d, 

 which is equal to it, and which may be 

 defined, the angle between two planes 

 passing through the medial line and each 

 of the currents respectively. Calling 

 this angle p, the formula, including all 

 possible relative positions of the cur- 

 rents, either in the same or in different 

 planes, becomes when the intensities and 

 distance between the currents are also 

 taken into account, 



/ = a b (sin. K. sin. /s.cos. ft.) 



~~d*~~ 



which should express the action of the 

 currents estimated in the direction of the 

 medial line, provided the hypothesis with 

 which we set out were correct. 



(185.) But experiment, the only cri- 

 terion of the soundness of physical theo- 

 ries, shows that an element is still want- 

 ing in this process for estimating the 

 value of the forces. It would follow 

 from the above formulae that when an 

 elementary portion of a current A, which 

 has the precise direction of the medial 

 line, that is, when it proceeds in a straight 

 line, either towards or from another ele- 

 mentary portion of a current H$,fg. 102, 

 no action can take place between them ; 

 for the angle being reduced to nothing, 

 its sine likewise vanishes : and the same 

 result should also obtain when the 

 planes in which two currents are situated 

 are at right angles to one another ; for 



B 



in that case the cosine of p. vanishes, 

 and the whole function expressing the 

 value of f is reduced to zero. This de- 

 struction of force ought to take place, 

 whatever be the position of the force B. 



(186.) This, however, is not found to 

 be the case, excepting only when the 

 current B is at right angles to the me- 

 dial line. If it be in any other position, 

 and more especially if it also coincide in 

 direction with the medial line, a repul- 

 sion is manifested. This will appear 

 from the result of the following experi- 

 ment : 



(187.) Let a flat oval dish of glass, or 

 porcelain,//^-. 103, be separated into two 

 divisions by a glass partition, fixed with 

 cement, and the divisions filled with 

 mercury. Insert into each of these 

 troughs, the sides of a copper wire, bent 

 in the manner shown in fg. 103, so that 

 they may be parallel to the partition, 



Fig. 103. 



over which the arc passes, joining the 

 two parts of the wire which float in the 

 mercury. Every part of this wire, ex- 

 cepting the steel points soldered to ifs 

 extremities, is to be covered with silk. 

 Two wires, forming connexions with the 

 two poles of a powerful voltaic battery, 

 being inserted in the cups P and N, 

 which communicate with the mercury in 

 the basin, in the diiections of the 

 straight branches of the wire produced, 

 the current from the one will pass 

 through the mercury in the adjoining par- 

 tition to the steel point belonging to one 

 ofthe extremities of the wire, and then, 

 circulating through the whole extent of 

 the wire, will pass out into the mercury of 

 the partition, and be carried off' by a third 

 wire. It is found that at the instant this 

 current is established, the wire moves in 



