370 Prof. G. C. Foster on Graphical Methods of 



tan Z A B 0. Also it is evident that, if the external resistance 

 is increased by equal amounts C C v C, C 2 , . . . each equal to 

 B C, the strength of the current, as denoted by the slope of the 

 line drawn from A to the points C, C v C 2 . . . , diminishes 

 by smaller and smaller amounts for each equal increment of 

 resistance, and that it would not vanish for any finite value of 

 the resistance. 



If any electromotive force acts in the part of the circuit ex- 

 ternal to the battery, its effect on the strength of the current 

 can be represented by drawing through C a line C C parallel to 

 O A, and of length proportional to the external electromotive 

 force, upwards if this electromotive force is inverse, downwards 

 if it is direct, — and drawing the straight line A C (fig. 2). If 

 c be the point where this line cuts C, tan Z Ac measures 

 the strength of the current. Of course the effect of any electro- 

 motive force outside the battery could also be represented by a 

 diagram such as fig. 1, if the line O A were there taken to repre- 

 sent, not the electromotive force of the battery, but the total 

 resultant electromotive force of the whole circuit. 



If a line be drawn from B (fig. 1) parallel to A, the length 

 BD, BD„ B D 2 . . . intercepted by the straight line through 

 A, whose slope gives the strength of the current, represents the 

 difference of potential between the terminals of the battery, or, 

 in other words, the electromotive force which is effective in 

 maintaining a current in the external conductor. The figure 

 shows that this varies between a maximum ( = A, the total 

 electromotive force of the battery) when the external resistance 

 is infinite (contact broken) and a minimum ( = 0) when the ex- 

 ternal resistance is nothing. If two values, B D and BD U of 

 the externally effective electromotive force are known, which 

 correspond respectively to two known values B C and B C x of 

 the external resistance, it is evident that the electromotive force 

 and internal resistance of the battery will be given by drawing 

 the straight lines C D and C l D ]f producing them till they meet 

 in A, and letting fall from A a perpendicular A on C B pro- 

 duced : A and B then represent respectively the values 

 required. Experimentally, the values to be given to B D and 

 B Dj could be found by direct measurement with an electro- 

 meter ; or they could be got from the relation e' = cr', where e' 

 is the externally effective electromotive force and c the current 

 as measured by a galvanometer in a circuit of external resistance 

 =r'. 



From the above relations it is easy to deduce a construction, 

 which may sometimes be of practical use, for folding the perma- 

 nent resistance and electromotive force of a constant battery 

 from two deflections of a galvanometer without using trignometri- 



