Analytical Study of the Alternating Current Arc. 323 



angles of 45° in such a way as to reflect the ray coming from 

 focus at 1, and reverse its direction so as to bring it round 

 and make it fall on the left-hand side of the photometer-disk P. 

 It will thus be seen that, by moving the mirrors M 5 and M 6 , 

 the light falling on the left-hand side of the photometer-disk 

 P could be made to have any desired intensity within certain 

 limits, and could be gathered from any desired part of the 

 arc or craters ; and, moreover, this illumination was the mean 

 illumination, or proportional to the mean illuminative power 

 of any part of the arc selected for examination. It will thus 

 be clear that the arrangement enabled us to project on to the 

 right-hand side of the photometer disk P the rapidly inter- 

 mittent ray taken from any part of the arc, and always 

 gathered at one constant phase condition during the complete 

 period ; whilst on the left-hand side of the photometer disk 

 we could project a ray gathered from the same part of the arc, 

 but not interrupted. We could therefore compare the mean 

 value of the light proceeding from any part of the arc with 

 the instantaneous value of the light taken from the same part 

 of the arc and selected at any assigned instant during the 

 period. Thus the arc itself became its own standard, and 

 difficulties due to slow fluctuation of the mean light of the arc 

 disappeared. At the same time the contact-maker on the 

 motor enabled us to delineate in the usual manner the curves 

 of current and potential-difference of the arc, and thus to 

 record the variation in the arc of the arc current, the carbon 

 potential-difference, the power expended in the arc, the 

 resistance of the arc, and the luminous intensity of any part 

 of the arc. A long series of experiments was then made 

 with alternating current arcs of different lengths and powers, 

 the periodic electric quantities being delineated and the light 

 being taken, either from the centre of the true arc halfway 

 between the carbons or from one of the craters of the carbon 

 terminals, — generally the bottom carbon. The process of 

 taking measurements was as follows : — 



After setting the lenses and the mirrors so that the lens L x 

 and the mirrors M 1 and M 2 gave a sharp image of the arc on 

 the right-hand side of the photometer disk with the selected 

 area of the image covering the grease spot, the minors M 5 

 and M 6 were moved backwards and forwards until the balance 

 was obtained between the illumination falling on the right- 

 and on the left-hand side of the photometer disk. The right- 

 hand side of the photometer disk being illuminated by an 

 intermittent stream of light always selected in the same phase, 

 when considered as belonging to a periodically varying illu- 



