POTENTIAL OF A TRIANGULAR CURRENT. 



427 



within a function of the co-ordinates of the apex of the angle ; 

 a function whose sign depends on the sign of the surface turned 

 towards the point, and which, moreover, would disappear in 

 applications. 



448. POTENTIAL OF A TRIANGULAR CURRENT. Let us suppose 

 further that in the same plane there is a third current CC' (Fig. 98), 

 identical with the former, and forming with it a triangle abc. 



Fig. 98. 



The potential at P of the two former is proportional to the 

 apparent surface of the angle BrA', less that of the angle ArB'. 

 The potential of the current CC' is proportional to the apparent 

 surface of the plane CC'X taken with the - sign. If we add 

 together the effects of the three currents, the part in common 

 BtfM.' disappears, and finally there remain, in the expression of the 

 potential, the apparent surface of the triangle abc^ and that of the 

 external angles A^rB', C&A', and B#C', these latter being all taken 

 negatively. 



Let us add to the system three angular currents of the same 

 strength represented by bent arrows; they will introduce into the 

 potential the apparent surfaces of these same angles taken positively 

 this time, so that only the apparent surface of the triangle will 

 remain. Of all the currents only that circulating round the angle 

 will remain, for each of the external lines is traversed by equa 

 currents of opposite signs. 



