Theory of the Flicker Photometer, 111 



In the equation, if for (o be substituted the values derived 

 by experiment for the critical frequency, and for 8 be used 

 the value of the least perceptible difference of brightness, 



X 2 



about '01, then values of ^- are derived, which may at once 



be referred to the corresponding illuminations as read from 

 the critical frequency-illumination diagram. 

 Equation (5) reduces to 



K = cX 2 a>, • (6) 



so that a simple rectilinear relation exists between brightness 

 and K of the form 



K = X 2 [mlogI+ j p] (7) 



With K determined for each colour, it is now possible to 

 substitute back in equation (2) and plot the complete course 

 of the transmitted wave-form. For the present purpose, 

 however, it is sufficient merely to determine the range of 

 oscillation. If the ranges of the resultants of two alternated 

 stimuli are equal, then there will be no resultant fluctuation 

 (flicker), unless a considerable additional phase difference is 

 introduced. In the latter case the minimum of flicker is 

 given by equality of range, so that the question of phase 

 difference may for the present be neglected. _ x fm_ 



The range for any colour as given above is 2I e 2K . 



Now since the two colours must be compared at the same 

 frequency, and since the condition of equality does not depend 

 on choice of frequency (assumption 3), (o may be taken as 

 constant. 



Let the range for any colour at a brightness I x be 



— X / w 



2Ij e l 2K i , then the condition that another colour (L) 

 shall alternate with it to produce no flicker is 



-**«_«..-*•£ 



21, e l 2K 1= 2I 2 e 



(It is clearly seen from this equation why neither the 

 choice of lights equal on the equality of brightness scale nor 

 of lights equal on the critical frequency scale will give the 

 condition of no flicker in the flicker photometer.) 



logI ] -X 1 Y/2^ i loge=logI 2 -X 2 \/ 2 ^ h 



or 



loo- e. 



