On the surface this would appear to be an easy task. Just give the film more exposure than the first excellent print exposure. In reality there’s more to it. In Jones and Nelson’s paper A Study of Various Sensitometric Criteria of Negative Film Speeds, they evaluate a number of different methods. They write, “after a careful examination of the sensitometric characteristics of the negative materials used, such a correlation was found. This correlation may be explained most conveniently by referring to Fig 1 (below). The negative from which the first excellent print was obtained was found to use a portion of this characteristic lying between the points M and O. Let the slope of the used portion of the curve be designated by G bar and the slope at point M by Gmin, this being the limiting gradient at the extreme shadow end of the object tonal scale.”
Study of Various Sensitometric criteria.jpg
Jones introduced the concept of the use of a minimum gradient in a 1935 paper, Minimum Useful Gradient as a Criterion of Photographic Speed. The paper makes no conclusions as to what the gradient would be. I believe this is what lead to the first excellent print test.
Nelson summarizes the different film speed methods, “The inertia speed criterion was found to give poor correlation. Speeds measured at a density of 0.20 above fog were also unsatisfactory. Speeds measured at a density of 0.10 above fog were better than inertia or 0.20 density speeds, but did not correlate with the print judgment speed as closely as was desired for a primary standard method.”
A good example of unsatisfactory correlation is the comparison of where the different methods would fall on curves of different shapes and with different gradients. In the example, S represents the print judgment speed. The tiny arrow represents the fractional gradient speed. S` represents the speed at 0.10 density above Fb+f, and the where the straight line extending down from the film curve intersect the line representing Fb+f is the inertia speed point.
Simple methods approx fractional gradient.jpg
What did Jones conclude? "From the standpoint of tone reproduction theory there seems to be no justification for the adoption of any value of density as a significant criterion of the speed of a photographic negative material. The primary function of the negative material is to record brightness (luminance) differences existing in the scene. Density, per se, has no significance as an indication of the ability of the photographic material to perform this function. The value of negative density by which any particular object brightness (luminance) is rendered, as, for instance, the deepest shadow, is of no consequence except insofar as it may have some bearing on the exposure time required to make a print from the negative."
"Tone reproduction theory indicates that there is only one characteristic of the negative curve that is significant in expressing the capacity of the material to reproduce brightness (luminance) differences, and it is upon the way in which brightness (luminance) differences are reproduced that the quality of the final positive must depend. This characteristic of the D-log E relationship is the gradient or slope, since this determines the magnitude of the density difference by which brightness (luminance) differences in the object will be rendered in the negative and eventually in the positive made therefrom."
As Nelson noted about the fractional gradient method in the introduction to Simple Methods, "This criteria was adopted because it gives speed values which correlate more closely with speeds obtained by picture tests than do the speeds obtained by any other known sensitometric speed criterion."