Analytical Study of the Alternating Current Arc. 327 



interesting facts : they show, for instance, that in the case 

 of the long arc the self-induction of the arc is more marked 

 than when the short arc is employed, and in that case there 

 is a very distinct lag of current behind the potential - 

 difference. 



It may also he noted in comparing the diagrams V. B and 

 IV. B in figs. 12 and 10, which represent the carves for arcs of 

 the same frequency but of lengths 1*2 centim. and '32 centim. 

 respectively, that in the case of the long arc there is no lag of 

 light behind power as far as regards the points of maximum 

 when the carbon is positive, but in the case of ihe short arc 

 there is a sensible lag. This might be expected to be the 

 case, because for a long arc the influence of the opposite 

 carbon in keeping up-tho temperature of its neighbour as ^his 

 last is cooling is less felt than in the case of a short -arc. 

 Broadly speaking, the facts may be summed up as follows : — 

 The purple light of the true arc undergoes a periodic varia- 

 tion, and, as far as the eye can judge, is completely extin- 

 guished during a certain interval during the phase ; it has 

 equal maxima values during the period, at instants slightly 

 lagging behind the instants of maximum power-expenditure 

 in the arc. On the other hand, the illuminating-power of the 

 carbon crater varies between a minimum value and two maxima 

 of unequal values ; the greatest maximum occurring when 

 the carbon is positive and at an instant slightly lagging behind 

 the instant of maximum power-expenditure in the arc. A 

 series of curves are also given (see figs. 18, 19, and 20) 

 in which the periodic variation of the current, potential- 

 difTerence, power, and apparent resistance of the arc for 

 various powers and frequencies are represented ; and it will 

 be seen from these curves that the resistance of the arc, 

 including in this any counter electromotive force which may 

 exist, varies periodically, the resistance being a minimum 

 when the current is a maximum, and vice versa. 



