A PERFECT NEGATIVE The authors defined "a technically perfect negative as one in which the opacities of its gradations are proportional to the light reflected by those parts of the original object which they represent," and their research showed that such a relation may exist but only when a plate has received correct exposure, and also a proper time of development. The reason for this def inition is clear when we remember that the neg ative is only a printing screen for use in making a positive picture and that the brightness of any spot on the print is directly proportional to the opacity of the corresponding area of the negative.
In the above definition the term "opacity" is assumed to be the reciprocal of this being the fraction of the incident light that a layer transmits. Thus the transparency of a film of reduced silver which transmits one third of the light incident upon it is and its opacity is 3. If the term density be applied to the actual quantity of silver deposited per unit area, it can be shown that density forms a convenient transition between opacity and the "exposure." In this discussion "exposure" will be understood to mean the product of the illumination ex pressed in proper units by the time during which the action lasts.
This is clear from the following discussion.
Suppose we have four areas a, b, c, d on some negative on which the silver deposit per sq. cm. occurs in the ratio of the numbers 0, 1, 2 and 3; these then may be taken as the several densities of the areas, and are in arithmetical progression.
Suppose now that the thickness of the area b be such that of the incident light is trans mitted. As area c has twice as dense a silver deposit as b, the light transmitted through it will be just as if c were made up of two superposed layers each like b. In this case the light incident on the under layer being < that incident on the upper, the two layers together will transmit only I of < or of the initial amount. So the
areas transmit respectively al, b!, cA, and d L of the quantity of light incident on each. As these numbers represent the transparencies, their reciprocals will denote the opacities or al, b4, c16 and d64.
Now we started with the densities in arith metical progression 0, 1, 2, 3, and have found the corresponding opacities to be in geometrical progression 1, 4, 16, 64, from which the follow ing relations are evident, viz. 4° = 1, 41= 4, = 16, 43 = 64. This is the same as saying that the density is proportional to the logarithm of the opacity, since 0 = log, 1, 1 = log, 4, 2 = log, 16 and 3 = log, 64, the base of the system depending on the scale of contrast chosen in the areas.
Had area b been so thin as to transmit 1 the incident light, the base of the system would have been 2 instead of 4; but still the opacities would have been in geometrical progression, the corresponding densities being in arithmet ical progression — a logarithmic relation.
It is clear then that the densities of a series of areas on a negative are always proportional to the logarithms of the corresponding opacities, but if the negative represent proper tone grada tions, the additional condition must hold, viz., the opacity must be proportional to the exposure. Therefore for a technically perfect negative the density should be proportional to the logarithm of the exposure. Thus we see that the law of true tone gradations is expressed by saying that the quantity of reduced silver per unit of time at any point in a negative is proportional to the logarithm of the light intensity incident at this point. Let us see under what conditions this is possible.