1 8 THE ELECTRIC ARC 



rent flowing through the arc and the potential difference 

 at its terminal. The ordinates represent the voltage and 

 the abscissae the current. E' is the E.M.F of the dynamo. 

 This is partly used in maintaining the potential difference 

 at the terminals of the arc and partly in maintaining the 

 drop through the resistance. This latter we will call E". 

 As long as this resistance is constant, E" will be directly 

 proportional to 7, the current flowing through the arc. 

 The vertical distance from the line AB to any point on the 

 straight line AP represents the drop through this resistance, 

 while the abscissa of the point represents the correspond- 

 ing current. 



It is conceivable that with any given resistance there 

 should be two different currents corresponding to the 

 points P" and P, where the straight line cuts the curve 

 PP'P". For at both of these points the sum of the drop 

 in potential through the arc and that through the resist- 

 ance equals the E.M.F. of the dynamo. With other cur- 

 rents their sum would either be too small or too great. 



With the current corresponding to the point P there is 

 stable equilibrium. For if the current should be momen- 

 tarily increased, E will decrease by an amount dE, but at 

 the same time E" will increase by an amount dE" and 

 this is greater than dE, so that the two together would re- 

 quire an increase in the E.M.F. equal to dE" dE. In 

 other words this increase in current could not be main- 

 tained, if the E.M.F. of the dynamo remained constant. 



Similar reasoning will show that any momentary de- 

 crease in the current could not be maintained without a 

 decrease in the E.M.F. of the dynamo, so that P represents 

 a point of stable equilibrium. 



In a similar way it can be shown that the point P" 



