solvimj certain simple Electrical Problems* 375 



cut B in M. From A draw AE at right angles to A O to 

 represent the electromotive force e, and draw E M cutting C 

 in E' ; similarly, from B draw B F* to represent the electro- 

 motive force e u and draw F N cutting C (produced) in F'. 

 Then F' E' = F' + E ; represents the electromotive force which 

 is effective in the conductor of resistance r 2 represented by C, 

 and AE — FE' and FB-F'E' represent the electromotive 

 forces which are effective in the branches of resistance r and r x 

 respectively. 



III. Ordinates represent Strength of Current, and Abscissa 

 represent Resistances, 



With this system of coordinates, electromotive force is ex- 

 pressed by the area of a rectangle. Thus, if a given battery 

 produces a current whose strength is represented by the ordinate 

 M m of the point M (fig. 12), in a circuit the resistance of which 

 is represented by the abscissa m of the same point, its electro- 

 motive force must be proportional to the area of the rectangle 

 M ; and if the battery is " constant," the curreuts, repre- 

 sented by the ordinates Mj m lt M 2 ??i 2 , and corresponding to the 

 resistances denoted by the abscissa? m v m a , will be such that 

 the areas of the rectangles M, M x , and M 2 are all equal; 

 and hence the characteristic property of the battery will be ex- 

 pressed by the curve which is the locus of the points M, Mj, 

 j&c. — that is to say, by a rectangular hyperbola whose asym- 

 ptotes are the axes of no current and no resistance. When the 

 hyperbola characteristic of a given battery is drawn, it is of course 

 easy by measuring coordinates to find what current would flow 

 through a given resistance, or conversely to find what must be 

 the resistance of the circuit in order that the current may have 

 a given strength ; but the difficulty of tracing an hyperbola with 

 accuracy greatly lessens the practical utility of this method of 

 calculation. Since, however, the asymptotes are fixed, each 

 hyperbola is completely defined when one point of it is given ; 

 and, in like manner, when the corresponding values of current 

 and resistance are known in any one case for a given battery, 

 each is determined for any other case when the value of the 

 other is given. Accordingly the actual drawing of an hyperbola 

 is not necessary ; for when one point is assigned, any other points 

 corresponding to given problems can be easily found. 



For instance, let the coordinates of the point M (fig. 13), re- 

 ferred to the axes X and Y, represent respectively the 



* B F must be drawn in the opposite direction to A E if, as supposed 

 above, the batteries are so connected that the difference of potential be- 

 tween tiie points P and Q due to each battery separately is of the same 



; sign, : - - , . . . . ^ . 



