736 Lord Rayleigh on the General 



from fog — no photographic action where no light has fallen. 

 But the complementary relation t' — O when / = 1 is only 

 satisfied approximately. The relation between negative and 

 positive expressed in (4) admits of simple illustration. If 

 both be projected upon a screen from independent lanterns of 

 equal luminous intensity, so that the images fit, the pictures 

 obliterate one another, and there results a field of uniform 

 intensity. 



Another simple form, giving the same limiting values as 

 (4), is 



t>+t*=ll (5) 



and of course any number of others may be suggested. 



According to Fechner's law, which represents the facts 

 fairly well, the visibility of the difference between t and 

 t + dt is proportional to dtjt. The gradation in the negative, 

 constituted in agreement with (4), is thus quite different 

 from that of the positive. When t is small, large differences 

 in the positive may be invisible in the negative^ and vice versa 

 when t approaches unity. And the want of correspondence 

 in gradation is aggravated if we substitute (5) for (4). All 

 this is of course consistent with complete final reproduction, 

 the differences which are magnified in the first operation 

 being correspondingly attenuated in the second. 



If we impose the condition that the gradation in the 

 negative shall agree with that in the positive, we have 



dt/t=-dt'/t\ (6) 



whence 



U'=C, (7) 



where C is a constant. This relation does not fully meet the 

 other requirements of the case. Since t' cannot exceed unity, 

 t cannot be less than C. However, by taking C small enough, 

 a sufficient approximation may be attained. It will be re- 

 marked that according to (7) the negative and positive 

 obliterate one another when superposed in such a manner 

 that light passes through them in succession — a combination 

 of course entirely different from that considered in connexion 

 with (4). This equality of gradation (within certain limits) 

 may perhaps be considered a claim for (7) to represent the 

 ideal negative; on the other hand, the word accords better 

 with definition (4). 



It will be remembered that hitherto we have assumed the 

 exposure to be the same in the two operations, viz. in pro- 

 ducing the negative and in copying from it. The restriction 

 is somewhat arbitrary, and it is natural to inquire whether it 



