Candle* Power of Incandescent and Arc Lamps. 130 



A proof of this is given in Mr. Matthew's paper*; but an 

 interesting method is to deduce it from the well-known 

 Rousseau diagram, as follows : — 



Let n = number of pairs of mirrors used. 



I e = intensity of illumination in a direction making an 

 angle 8 with the horizontal. 

 Imax. = maximum intensity = OB. 



M.S.C.P. = mean spherical candle-power, 

 and M.H.C.P.^mean horizontal candle-power. 



Let OG1 (PL III. fig. 2) be the polar intensity curve of a 

 source symmetrical about the vertical AB. 



Let CDEF be the Rousseau diagram obtained in the usual 

 way from the polar curve. 



Divide the semi-circumference A IB into (n+l) parts at 

 the points 6, 5, 4, .... 7. 



Project these points horizontally on to CF, and through 

 the projections draw ordinates to the Rousseau curve, shown 

 dotted in the figure. 



Bisect the arcs A6, 6o, &c, and project the points of 

 bisection in a similar manner, obtaining the full-line ordinates 

 of the curve. 



Then, if a is sufficiently large, the whole area CDEF may 

 be considered to be made up of small strips, e. g., abed, cut 

 off by the full-line ordinates of the curve. 



Hence the area CDEF=2 (area abed) 



= 2 {adx^ (ab + c d)\. 

 Xow, with a sufficient degree of approximation, 



±(ab + cd)=l G , 



and 



a d— --=■ COS 6 I maX . 



/l+l 



Hence the area CDEF = -^- I max . 2 (I cos#). 



BntM.S.C.P.= area r ? h ] 5 )EF 



Cr 



_ area CDEF 



- x I max. 



Hence M.S.C.P. = , ". % (l,co<0). 



* "An Integrating Photometer for Glow-Lamps and Sources of like 

 Intensity/' by C. P. Matthews. Trans. Amer. Inst. Elec. Enfrin. vol. xix. 

 Nov. 1902. p. 1407. 



