418 Comparative Animal Physiology 



by the photochemical cycle but by some other process which is unaffected by 

 temperature. On this basis the phenomena of flicker fusion, brightness dis- 

 crimination, and visual acuity may be described as functions of intensit)r. 

 The same assumptions have also been applied to dark adaptation and, when 

 combined with equations for the kinetics of regeneration of visual purple, 

 offer a satisfactory explanation of the existing data on dark adaptation. The 

 statement is not meant to imply that factors other than the chemical cycle are 

 not involved or are not important. 



The equation for flicker fusion frequency is 



F = [ki I (a - x)]'^ (Fma.v - F)^ 



where F is the flicker fusion frequency, x the amount of P or A, (a— x) the 

 amount of S, 1 intensity, P the fraction of the flicker cycle during which 

 the light is on, k4 is the velocity constant of the LT reaction, q pertains to 

 the mechanism whereby the photoproduct E is utilized by the sense cells, 

 and r denotes a mathematical function of F.^^ 



The equation for brightness discrimination and visual acuity is 



A I Ci (C/k. 1)7" 1 



I ks x' t ka t 



where a denotes visual acuity, 1 denotes the concentration of L, K2 the veloc- 

 ity constant for E-^P -f A reaction, fes the velocity constant of the P -\- A-^S 

 reaction, and t the duration of the flash of light. '-'^ 



The validity of these equations for flicker fusion is shown in Figure 126. 

 In this figure the theoretical curves for flicker fusion for the turtle Pseud- 

 emys for two temperatures and for man under conditions of rod (on left) 

 and of cone (on right) vision are fitted to experimental data. The data are 

 well fitted, and the direction of the shift in the curve caused by the tem- 

 perature change is correctly predicted. 



N onphotochemical Theories of Vistial Phenomena. In the determina- 

 tion of the sensitivity of the eye to a small spot of light we considered a caten- 

 ary series of events. Let us call these events the series A to Z. If the stimulus 

 is a large spot of light or a geometrically complex light source, then there are 

 many parallel series of such events and a number of Z processes in the brain. 

 As such, the Z's are subject to statistical variation. This would also be true 

 if a single chain (A to Z) were repeated time after time; the sensation (event 

 Z) would not always, at least under experimental conditions, involve exact- 

 ly the same neurones in exactly the same way. This would be especially true 

 near the threshold intensity. 



However, the existence of a statistical variation in event Z has led to an alt- 

 ernative and nonphotochemical explanation of the above visual functions. 

 This alternative theory is based entirely on the existence of statistical varia- 

 tion, and its development was stimulated by the inadequacies of the early 

 photochemical theory. 



Acording to the statistical theory proposed by Crozier and his cowork- 

 (^.pj. -'H. .•{I,.?-', .{.!, .H, .{5, .{6, .{7 ^Y^^, siomoit} curves for flicker fusion, brightness 

 discrimination, and visual acuity as functions of intensity are probability in- 



