Analytical Study of the Alternating Current Arc. 325 



potential of which was determined by the same voltmeter, in 

 series with the voltmeter. In this way the series of obser- 

 vations were successively taken of the following quantities :— 

 First, the instantaneous value of the potential difference of 

 the carbons taken at equidistant intervals throughout a com- 

 plete period ; secondly, the instantaneous values of the 

 current through the arc taken throughout the complete 

 period ; and, thirdly, the instantaneous values of the luminous 

 intensity of a certain selected portion of the arc taken at 

 intervals throughout the complete period and expressed in 

 terms of the true mean luminous intensity of the same portion 

 of the arc at that time. These quantities having been obtained, 

 it was then possible to plot them down in a series of curves, 

 and to deduce therefrom curves representing the periodic 

 variation of power through the arc, and the periodic variation 

 of the resistance of the arc. Five sets of experiments were 

 made, taken for different frequencies and different lengths 

 of arc, each set comprising an observation taken with the 

 light proceeding from the centre of the true arc, and also 

 an observation taken with the light proceeding from the 

 centre of the crater of the lower carbon. The frequencies 

 employed were 83, 50, and 26. In all cases the current 

 was kept at 14 amperes (mean square value) ; the results 

 of these observations are embodied in the following 10 tables 

 arranged in 5 pairs. Table I. A, for instance, gives the 

 results of the observations taken with an arc having a fre- 

 quency of 83*3, the light being taken from the centre of 

 the true arc. Table I. B gives similar results of observations 

 for the same arc, the light being taken from the centre of the 

 lower crater. By holding a magnet at the back of the arc, 

 noticing which way the instantaneous image of the true 

 arc was projected by the magnet, and noting the pole of the 

 magnet presented to the arc, it was possible to determine 

 when the lower carbon was positive and when it was negative ; 

 and the diagrams corresponding to the above 10 tables are 

 marked so as to show the half of the wave when the lower 

 carbon is positive and when it is negative, in all those 

 diagrams which refer to the light coming from the crater. 

 The results of the observations given in the 10 tables are 

 delineated graphically in diagram in figs. 3 to 12 ; and on 

 referring to these diagrams a periodic line will be seen in 

 each, delineating the variation of the potential difference 

 of the carbons, and another periodic line indicating the varia- 

 tion of the current through the arc, whilst a third line indicates 

 the periodic variation of the luminous intensity of the selected 



