PHOTOGRAPHIC SENSITOMETRY 195 



relatively rare cases is located aboye that axis. Assuming for the moment that a 

 common intersection point does exist, its coordinates may be represented by a and b as 

 shown in Fig. 26, and it has been proposed to define the speed of the material in terms 

 of the coordinates of this point. Under such conditions it is evident that the inertia is 

 a function of gamma, and hence speed based upon inertia value will become a function 

 of gamma. A speed value of this nature can only be significant provided the corre- 

 sponding gamma value is specified. For the purpose of certain theoretical investiga- 

 tions into the nature of exposure and development, a knowledge of the coordinates 

 of the intersection point, as shown in Fig. 26, may be of great value, but it does not 

 appear to be very significant for the purpose of determining the practical speeds. 



Another difficulty with this method of specifying emulsion speeds is that some 

 photographic materials do not have a common point of intersection for the various 

 D-logio E curves, and some materials — especially some positive printing papers^ — do 

 not have a very satisfactory straight-line relation between density and the logarithm 

 of the exposure. There is also a wide divergence in the relative shape of the curve 

 in the region of underexposure. 



Latitude-inertia Method of Speed Determination. — A modification of the inertia- 

 speed ratings, which is in reality another method of rating film speed, is the method 

 in which the speed is specified in terms of the inertia as well as the latitude of the 

 emulsion. 



In the Weston system of film-speed rating, which has found wide acceptance in the 

 United States, the speed is determined from the D-logio E characteristic of the film, 

 processed to the value of gamma most frequently encountered in practice for that 

 particular type of film. As shown in Fig. 24, the Weston film-speed number S is given 



by 



S = ^-^^ (45) 



where logio Ew, determined from the characteristic curve, is chosen to be numerically 

 equal to the gamma of the curve, i.e., logio E^. 



Minimum Useful Gradient Speed. — Another method of specifying speed or sensi- 

 tivity is based on some minimum useful gradient or slope of the D-logio E characteristic 

 curve. When it is considered that the chief functions of a photographic negative 

 material as used in practice is to reproduce as density differences the brightness differ- 

 ences existing in the object photographed, it seems logical to demand that the mini- 

 mum useful exposure be determined by some specified gradient of the Z)-logio E 

 characteristic. 



A system has been suggested that allows for the actual usefulness of the upper 

 part of the region of strict underexposure as the Weston system does not and 

 the H and D does only accidentally — but allowing for it in a manner that avoids the 

 dangers of the Scheiner and DIN systems. In this realistic approach to the problem 

 of speed rating, the measure of sufficient exposure would be that exposure for which 

 the rate of increase of density with increasing logio E first reaches a certain fraction 

 of the rate found in the linear portion. This fraction would be the fraction of the 

 proper contrast shown in the (strictly underexposed) deepest shadows, in an otherwise 

 perfect negative exposed to the predetermined minimum useful gradient. 



The difficulty with such a system is in the matter of deciding upon the value which 

 is to be taken as representing the minimum useful gradient. According to Sheppard, 

 the minimum useful gradient will in general depend not only upon the negative but 

 also upon the positive aspect of tone reproduction, so that its fixation is not expressible 

 by a unique function of the negative material itself. 



