and Flicker Photometer Speed. 101 



on a colour-mixture line c, in any convenient units, we then 

 have the speed given by 



iio -V 



M —*— ~T , • • • • (2) 

 V 0g F/ 



which may be simplified by the combination of constants to 



o, = M(log|) 2 , (3) 



where M is a function of the working intensity. From 

 inspection of this equation it is seen that the speed becomes 

 zero when the two compared colours are separated on the 

 mixture diagram by only the just distinguishable difference, 

 and that the speeds go up apparently without limit as the 

 colour difference increases. Actually, as experiment shows, 

 no hues exist sufficiently far apart to make the critical speed 

 of an equal luminosity mixture ever more than a fraction of 

 the speed necessary to eliminate flicker of the coloured light 

 against darkness. 



In order to plot this equation on such a scale as to 

 represent an actual case it is necessary to know the value 

 of S R . One method of obtaining this was developed in the 

 preceding paper. Another, bearing more directly on the 

 present problem, may be outlined. Suppose two coloured 

 lights of equal intensity to illuminate the two glasses of the 

 mixture photometer described in the previous paper. Let 

 these be represented as the end points of a straight line of 

 convenient length c. Suppose the critical speed determined. 

 Then let the two glasses be turned until each is illuminated 

 by two parts of one light and one part of the other. The 

 colour of each is then represented by a point one-third along 

 the line from the end, and the colour-mixture distance of 

 the two glasses is Jc. Suppose the critical speed deter- 

 mined for this condition. We then have two equations 

 from which 8 R can be found. 



In fig. 1 is shown a plot of equation (3), in terms of 



^> against .— . Direct experimental verification of this 



curve was not undertaken, since the curve shown by 

 Troland * for mixtures of red and white light is closely of 



* " Apparent Brightness, &c.," Ilium. Eng. Soc. Convention, Sept. 

 1916. 



