ELECTRO-MAGNETISM. 



(196.) It follows, as a consequence of 

 the principles already laid down, that Ihe 

 action of a small portion of conducting 

 wire, bent into any number of flexures, 

 provided they extend to no considerable 

 distance, upon another current, any- 

 where situated, is equivalent to the 

 action of a similar wire proceeding in a 

 straight course between the two ex- 

 treme points of the contorted wire. 

 The action, for example, between a con- 

 ducting wire, A B, fig. 108, and an 

 elementary portion, C D, the one pur- 

 suing a sinuous course, the other recti- 



Fig. 108. 



lineal, is precisely the same as if the 

 former, instead of being contorted, had 

 passed in a straight line from the point 

 A to the point B ; that is, along the 

 dotted line A B. 



(197.) By an extension of the reason- 

 ing which led to the conclusion just 

 stated, it may be proved that the action 

 of a current traversing the contorted 

 line A B, fig. 109, (and which we have 

 seen is equivalent to that of a current 



Fig. 109. 



of equal intensity passing in a direct 

 line from A to B,) on any elementary 

 portion m of a distant current G D, will 

 be to the action of a similar current 

 E F, (comprehended within the angle 

 A m B, which A B subtends at the point 

 m, the middle of the elementary cur- 

 rent,) in the inverse proportion of their 

 mean distances from the point m ; that 

 is, drawing G H, making equal angles 



with A m and B m, through the middle 

 of E F, the action of A B is to the action 

 of E F, inversely as A m to G m. 



(198.) If the electric currents be con- 

 ceived as spread over a given surface, 

 A, Jig. 110, instead of being confined 

 to a single line ; then the action of this 

 superficial stratum of currents on the 

 elementary current m, which is a part of 



Fig. 110. 



the current CD, will be precisely equal to 

 that of B, or E ; or of any other super- 

 ficial stratum composed of similar cur- 

 rents, situated at any distance from m, 

 and inclined at any angle, provided it 

 be comprehended by the sides of the 

 same pyramidal or conical figure, hav- 

 ing the surface A for its base, and m 

 for its apex. This, indeed, follows as a 

 necessary consequence of the preceding 

 law : the diminished influence of the 

 currents in A, resulting from their 

 greater distance, being exactly compen- 

 sated by their greater number. It may 

 be derived still more directly, indeed, 

 from the general law of the action of 

 electric currents being inversely propor- 

 tional to the squares of the distances. 

 We shall have occasion hereafter to 

 make important applications of this 

 principle. 



3. Action of Terminated Currents. 



(199.) We have seen that the action 

 of a rectilineal current of infinite length 

 on a short portion of current at a dis- 

 tance, situated in the same plane, and 

 wholly on one side of the former, tends to 

 give it motion in a line perpendicular to 

 itself, and either in the same direction as 

 the extended current, or in the opposite 

 direction, according as it is receding from 

 or approaching to it. The same applies 

 to a current of any length, provided it be 

 situated wholly on one side of the cur- 

 F 



