02 4 6 8 10 12 14 16 182022 2426 23 80 

 LENGTH IN MM, 



ARC IN AIR BETWEEN CARBON ELECTRODES 15 



where P is the power used. When this equation is plotted, 

 using power for ordinates and current for abscissae, we 

 have a straight line. 



When an arc is very long, the equations given by Mrs. 

 Ayrton do not hold, as has been shown by Duddell. 1 The 

 curve given by her equation 

 and that found experimen- 

 tally by Duddell are plotted 

 in Fig. 7. Duddell also found 

 a similar difficulty when the d 

 currents were less than 1.5 

 amperes, the voltage then 

 being less than that calcu- 

 lated from Mrs. Ayrton's 

 equations. 



The characteristic curves for arcs between solid carbons 

 in air and with currents as small as 0.6 ampere were 

 observed by Malcolm and Simon. 2 They give the equa- 

 tion El = 49 + 60 /, when the length is 8 mm., and 

 El = 31. 5+ 51.5 /, when it is 4 mm. 



We have here been giving the relation between the po- 

 tential difference and current for arcs that have been run- 

 ning sufficiently long to have reached a steady condition. 

 This is what one usually wishes to know. An engineer, 

 for example, wishes to know the power needed by a lamp 

 under certain constant conditions. But there are also 

 times when one wishes to know something about the rela- 

 tion between potential difference and current when they 

 are changing rapidly. Such knowledge, for example, is 

 desirable when using arcs hi wireless telephony. Curves 



FlG - 



1 Phil. Traas., 203, A, 338; 1904. 



2 Phys. ZS., 8, 471; 1907- 



