710 LIGHT AND LIFE 



light intensity in arbitrary units. Now the properties of the cell are 

 such that the change in resistance is proportional to the change in 

 membrane potential, and this in turn is a linear function of the fre- 

 quency of impulses transmitted along the optic nerves in the steady 

 state. So the relation to light shown in Fig. 2 is fundamental to the 

 optic nerve message. It may be written: 



V - Vn = logf/-+ 1^ (^) 



where V is the membrane potential in suitable units. 



Vo is the value of V in the dark. 



Id is the "dark light" or intrinsic noise of the system. 

 Differentiation gives: 



AV = M/{I-\- Id) (2) 



Now Riggs and Graham (6) investigated the light increment A-^ 

 required for a constant discharge with various background lights /, 

 and found that l\I/ {I + In) was almost exactly constant over the 

 whole range of intensities. Hence the condition for a constant dis- 

 charge in these circumstances appears to be that A^ should have a 

 fixed value. From the careful and very extensive work of Hartline and 

 his colleagues (mostly unpublished) , it is clear that threshold re- 

 sponses in various changes of light are in general governed by a rela- 

 tion far more complex than A^' = constant. However, the simple 

 increment threshold results of Riggs and Graham (6) seem to obey 

 that relation, and so do the analogous measurements in man. 



In psychophysical experiments the constancy of l\I / (/ + /p) has 

 been known for a century as the Weber-Fechner Law. Stiles (9, 10) , 

 plotting upon log scales, has shown that the relation 



log ^ = log (/ + lo) 



(where A^ is constant) holds independently for rods and several 

 separate color mechanisms (upper dotted curve, Fig. 2) . Donner and 

 Rush ton (2) also were led to equation (/) in order to explain the 

 way in which the two receptors could replace each other in stinudation 

 by light substitution (lower dotted curve. Fig. 2) . 



If, then, we agree that equation (2) , derived in the first place from 

 Limiilus, is also the basis of intensity discrimination in vertebrates 

 and in particular in man, we may approach the question of dark adap- 

 tation from a somewhat different aspect. For, the threshold in the 



