## Abstract

Further study is made of the statistical correlation between the *density scales* of negatives and the *sensitometric exposure scales* of photographic papers. A formula relating these two variables is proposed, for use as a guide in photographic printing, whereby the density scale of the negative can be used as a means of choosing the grade of paper to be used in making the print. The suggestions of Sanders regarding statistical methods of analyzing the data are discussed. The term *useful exposure scale* is abandoned and the terms *sensitometric exposure scale* and *transition point index* are proposed. It is suggested that the sensitometric exposure scale be adopted as the basis for grading photographic papers and that the new numbers be called *scale indices*. Reasons are given why the *contrast* of photographic paper is not suitable as a basis for deriving grade numbers. For specifying the shapes of the *D*−log*E* curves of photographic papers, the method proposed by Morrison is recommended. Data are presented on the frequency of occurrence of the various density scales of amateur negatives.

© 1948 Optical Society of America

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### Equations (20)

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(1)
$$\text{log}FCES=1.10\hspace{0.17em}\text{log}SE{S}_{y}-\mathrm{0.10.}$$
(2)
$$D{S}_{n}=1.35\hspace{0.17em}\text{log}SE{S}_{y}-\mathrm{0.40.}$$
(3)
$$TP(a,a+1)=1.35MP(a,a+1)-0.40,$$
(4)
$$MP(a,a+1)=[\text{log}SE{S}_{y}(a)+\text{log}SE{S}_{y}(a+1)]/2.$$
(5)
$$TP(a,b)=[{I}_{tp}\hspace{0.17em}(\text{for}\hspace{0.17em}a)+{I}_{tp}\hspace{0.17em}(\text{for}\hspace{0.17em}b)]/2.$$
(6)
$$\text{av.}\hspace{0.17em}D{S}_{n}=1.28\hspace{0.17em}\text{log}SE{S}_{y}-0.32,$$
(7)
$$D{S}_{n}=1.60\hspace{0.17em}\text{log}SE{S}_{y}-\mathrm{0.69.}$$
(8)
$$D{S}_{n}=1.75\hspace{0.17em}\text{log}SE{S}_{y}-\mathrm{0.90.}$$
(9)
$$\mathrm{\Omega}=f\hspace{0.17em}(\text{rate},\hspace{0.17em}\text{extent}).$$
(10)
$$\mathrm{\Omega}=k\overline{G}(D)\times ({D}_{\text{max}}-{D}_{\text{min}}),$$
(11)
$$V=[({D}_{v}-{D}_{h})/({D}_{s}-{D}_{h})]\xb7100.$$
(12)
$${D}_{n}=f(\text{log}{B}_{o}).$$
(13)
$$d{D}_{g}/d\hspace{0.17em}\text{log}{B}_{o}\xb7d{D}_{f}/d\hspace{0.17em}\text{log}{E}_{y}=1.$$
(14)
$${V}_{n}=[\text{log}{B}_{o}\hspace{0.17em}(\text{at}\hspace{0.17em}{v}_{n})-\text{log}{B}_{o}\hspace{0.17em}(\text{at}\hspace{0.17em}{h}_{n})]/\text{log}B{S}_{o}.$$
(15)
$${A}_{y}={A}_{n}(\text{cos}{\theta}_{n}/\text{sin}{\theta}_{y}),$$
(16)
$$D{S}_{n}={D}_{\text{max}}-{D}_{\text{min}}.$$
(17)
$$y={y}_{o}\hspace{0.17em}\text{exp}[-{({D}_{m}-{D}_{i})}^{2}/2\sigma ],$$
(18)
$$TP=1.35\left[\frac{\text{log}SES(a)+\text{log}SES(a+1)}{2}\right]-0.40,$$
(19)
$${I}_{tp}=1.35\hspace{0.17em}\text{log}SE{S}_{y}-\mathrm{0.40.}$$
(20)
$$\text{scale}\hspace{0.17em}\text{index}=100\hspace{0.17em}\text{log}SES,$$