Theory of the Flicker Photometer. 299 



4. Critical Frequency-Illumination Relations with 

 Unequal Light and Dark Intervals. 



(a) Theoretical. 



Our theory o£ the flicker photometer is essentially a theory 

 o£ the action of the eye toward intermittent excitation by 

 light. The action of the flicker photometer follows on this 

 theory directly from the critical-frequency-illumination laws. 

 In undertaking an examination of the flicker photometer 

 for the case where the two lights are exposed for unequal 

 intervals — one of the principal objects of the study — it is 

 therefore necessary to test the sufficiency of our theory to 

 explain the critical frequency relations for unequal light and 

 dark intervals. 



The most extensive study of this case is that of T. C. 

 Porter *. He experimented with a series of disks, part 

 white, part black, and obtained results which he found well 

 represented by the equation 



?i = a + (6 + clog I) log it- (360 — iv), . . (7) 



where w is the size of the white sector in degrees, n = cycles 

 per second, I = illumination, a, b, and c constants. 



This equation, which has no theoretical basis, indicates 

 that the critical frequency should be a maximum for 

 w = 180 degrees; that the curves connecting critical fre- 

 quency with angle should be symmetrical about 180 degrees ; 

 that the log I critical frequency straight lines should have 

 a different inclination for each angle of opening (except 

 complementary angles, which have the same). His actual 

 numerical values call for a large negative frequency at and 

 360 degrees, instead of zero, and the equation is not satis- 

 factory for small angles at illuminations below the change 

 in slope of the straight critical speed-log I lines. 



While it is not necessary that our theory should yield the 

 same formula as that developed by Porter, we must be able 

 to explain the dominating phenomenon, namely the reduc- 

 tion of speed as the white opening is either increased or 

 decreased from 180 degrees. 



Let us consider two complementary disks, of white angles 

 less than and greater than 180 degrees respectively. Let 

 these be rotated at some finite speed. Suppose the diffusivity 

 of the receiving and transmitting medium of the eye to be 

 the same as either disk is observed. It is obvious that 

 (under this restricting condition) the two damped fluctuating 

 impressions which are transmitted to any given depth must 



* "Studies in Flicker," Porter. Proc. Itoy. Sec. vol. lxiii. p. 347 ; 

 vol. lxx. p*. 313 ; vol. lxxxvi. p. 445. 



