152 Mr. F. F. Renwick on tlie Fundamental Law 



called " deosities ; ') of tlie resulting photographic images 

 are the ordinates. 



Now since, in accordance with Beer's law, the density of a 

 neutral-tinted grainless medium is proportional to its thickness 

 or its pigment concentration per unit area, densities increase 

 in simple arithmetical progression from the light to the dark 

 end of an optical wedge. Moreover it is important to observe 

 that tlie gradation of such an optical wedge may be expressed 

 equally well either as a uniform rise in density per unit length 

 or as a uniform drop in log I of the same amount, if uniform 

 illumination of the wedge be assumed. Since a grainless 

 optical wedge affords a very convenient means of impressing 

 on a photographic material a known and continuous range 

 of exposures, changing in exactly tlie same manner as do the 

 values of log E along the exposure axis of a " characteristic " 

 curve, it is evident that the abscissa? values of any cha- 

 racteristic curve may be regarded as the logarithms of the 

 exposures given to the material by illumination received 

 through an optical wedge, while the uniformly illuminated 

 optical wedge thus becomes the subject whose photographic 

 rendering is under discussion. 



To every point on the exposure axis of the characteristic 

 curve there will then correspond a known logE and a known 

 density value, while a length between any two such values 

 will represent a known density difference or contrast and an 

 equal but opposite log E difference. 



For 



D^log}-; D,-log.5»; 



hence 



Di — D 2 = logI 2 — loglx 





= logE,-logE ] , 



where I = incident light intensity, I } and I 2 the transmitted 

 intensities, and D l and D 2 the corresponding density values 

 at any two points. 



Case 1. — In fig. 1 let the two continuous curves represent 

 the characteristic curves found for the negative and positive 

 materials to be used. It is desired to deduce from them the 

 gradation curve of a positive print made under the same 

 conditions (development etc.) as were employed when these 

 curves were obtained. 



Assume that it is intended just to preserve a pure white (or 

 clear glass) under the greatest density in the negative; then, 

 such an exposure must be given that the lower limit of th e 



