45 ELEMENTARY ACTIONS. 



proportional to the length of each element, to the intensity of the 

 current in each of them, and to a function, which remains to be 

 determined, of the distance of the elements as well as of their 

 relative distances. 



II. The action changes its direction when the direction of one of the 

 currents is changed ; it remains unaltered when the direction of the 

 two currents is simultaneously changed. This is a general property of 

 electrical currents. 



III. Principle of symmetry. It follows from this principle of 

 symmetry that the reciprocal action of two elements a and b (Fig. 

 1 08), one of which a is in the plane perpendicular to the other in its 

 middle, is null. 



X* 



Fig. 108. 



For consider a system a'V symmetrical with the first in reference 

 to a plane P parallel with the element a, and with the right line OC 

 joining the centres of the elements. 



The actions of a on , and of a' on b' are respectively along 

 OC and O'C, and in the same direction from symmetry. But 

 the second is none other than the first, in which the direction 

 of the current has been changed in the element b; the force 

 should have changed its direction owing to this inversion, hence 

 it is null. 



The force in particular is null, if the element a is perpendicular 

 to the right line OC, which joins the centres of the two elements, or 

 directed along this right line. These are two cases which will have 

 to be made use of. 



IV. Principle of sinuous currents. The principle of sinuous 

 currents may be applied as above (463) and with the same limi- 

 tations ; we can always replace a current element by its projections 

 on three rectangular axes. 



