344 INTENSITY AND PHOTORECEPTION 



which means that the increase in intensity necessary to produce an 

 infinitely small increase in photochemical effect is directly propor- 

 tioned to the intensity itself. Let the intensity h produce the pho- 

 tochemical effect jEo, and the intensity h produce the photochemical 

 effect £i. Then if 



Ei-Eq= E (8) 



equations (6) and (7) tell us that 



h = h e^ (9) 

 and that 



^ = 4 log Y (10) 



k being a constant. In our data k = 0.43, which is the factor for 

 converting natural into common logarithms used in equation (10). If 

 natural logarithms are used, k becomes unity as we have previously 

 found. 



The significance of equations (5) , (6) , (7) , (9) , and (10) , particularly of 

 the latter two, is quite apparent. They are all different mathematical 

 forms of the law expressing the variation of a function at a rate pro- 

 portional to itself. This is a fundamental principle, which Lord Kel- 

 vin has called the "compound interest law in nature," and forms the 

 basis of such regularities as Wilhelmy's law for the velocity of chemi- 

 cal reactions, and Newton's law of cooHng. For our immediate in- 

 terest it is significant that this very principle applies to the absorption 

 of light passing through an absorbing medium (Lambert's law, and 

 Beer's law). 



Because of the basic similarity between the expressions for the ab- 

 sorption of light and for the photochemical action of light in photore- 

 ception it may possibly be that our results depend upon some con- 

 stant absorbing medium in the sense organ. In that event the photo- 

 chemical effect per se would be dir^tly proportional to the energy 

 transmitted by this absorbing layer to the photosensitive substance 

 behind it. 



Although a greenish black pigment is found scattered over the 

 photosensitive siphon of Mya it is hardly likely that this acts as such 

 an absorbing medium. The pigment is distributed thinly and irregu- 



