Electric Arc with Varying Power- Supply. 22 3 



bases; this being approximately the shape found by ex- 

 periment. 



Also let all the light in the case o£ the continuous-current 

 arc be supposed to come from the positive crater. 



Now, the expression for the mean spherical candle-power o£ 

 a source symmetrical about an axis is 



77 



M.S.C.P. = if 2 I 9 cos0d6, 



where I e is the luminous intensity in a direction making an 

 angle 6 with the horizontal. 



Now let I be the luminous intensity of the crater when 

 viewed normally. 



Then, as a rough approximation, assuming the crater to be 

 a flat circular disk, small compared with the arc length, 



l 9 = Isin0. 

 Bence for the arc 



M.S.C.P.= ill a *mdcos0d6 



J 2 



77 



= ilf/sin2 



J 2 



77 



= 11 [-cos 2^1 2 



26 cW 



Let a be the diameter of the lower carbon ( — ), and b the 

 diameter of the upper carbon ( + ) . 



Then, making the above assumptions, all the light, in the 

 continuous-current case, will be concentrated into the zone 

 between the horizontal and an angle « below the horizontal : 

 where 



, , a + x 

 a = tan -1 — — . 



i a 



Hence we get 



M.S.C.P.C.C. = lice. [- cos 20]* . 

 = ^ Ice. sin 2 «. 



Similarly for the alternating-current arc, considering each 



