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-« 



:»-•— T-"— • -• 



LIBRAIV/ 

UNIVERSITY OF 

CALIFORNIA 

SANTA CRUZ 



J 




C 



^mmmmmm 



•I 



Monographs on the Theory of Photography from the 
Research Laboratory of the Eastman Kodak Co. 

No. 2 



COPTBIQHT 1922 

Eastman Kodak Company 



The Theory of Development 



By A. H. Nietz 



ILLUSTRATED 



D. VAN NOSTRAND COMPANY 

NEW YORK 

EASTMAN KODAK COMPANY 

ROCHESTER, N. Y. 
1922 



15-^91 



Monographs on the Theory of Photography 

Edited by 

C. E. Kenneth Mees 

and 

Mildred Spargo Schramm 






Monographs on the Theory 
of Photography 

No. 1. The Silver Bromide Grain of Photographic 
Emulsions. By A. P. H. Trivelli and S. E. Sheppard* 

No. 2. The Theory of Development. By A. H. Nietz. 

No. 3. Gelatin in Photography. Volume I. By S. E. 
Sheppard, D. Sc. 

Price each $2.50 



Other volumes soon to appear: 

Aerial Haze and its Effect on Photography from the Air 

The Physics of the Developed Photographic Image. 
By F. E. Ross, Ph. D. 

Gelatin in Photography. Volume II. By S. E. Sheppard, 
D. Sc. 



Preface to the Series 

The Research Laboratory of the Eastman Kodak Company 
was founded in 1913 to carry out research on photography 
and on the processes of photographic manufacture. 

The scientific results obtained in the Laboratory are 
published in various scientific and technical journals, but the 
work on the theory of photography is of so general a nature 
and occupies so large a part of the field that it has been 
thought wise to prepare a series of monographs, of which this 
volume is the second. In the course of the series it is hoped 
to cover the entire field of scientific photography, and thus 
to make available to the general public material which at the 
present time is distributed throughout a wide range of journals. 
Each monograph is intended to be complete in itself and to 
cover not only the work done in the Laboratory, but also that 
available in the literature of the subject. 

A very large portion of the material in these monographs 
will naturally be original work which has not been published 
previously, and it does not necessarily follow that all the 
views expressed by each author of a monograph are shared 
by other scientific workers in the Laboratory. The mono- 
graphs are written by specialists qualified for the task, and 
they are given a wide discretion as to the expression of 
their own opinions, each monograph, however, being edited 
by the Director of the Laboratory and by Mrs. Schramm, who 
is the active editor of the series. 

Rochester, New York 
October, 1922 



Preface 

The present monograph presents the results of investigations 
undertaken to determine the reduction potentials of certain 
organic developers, and to establish the connection between 
these potentials and the developing characteristics of the 
various compounds. It was originally intended to use both 
electrometric and photographic methods, but since the results 
obtained by the latter method are complete, it has been de- 
cided to publish these at the present time. 

In the course of the work a large amount of sensitometric 
data has been accumulated, as well as much information rela- 
tive to various other aspects of the process of development. 
The inclusion of what may seem an unwarrantedly large 
amount of these data seems justified by the desire to render 
the information obtained as useful as possible for future work 
as well as to support the various conclusions reached. 

The results here presented should normally have been pub- 
lished in a series of papers, but this was prevented by the 
interruption caused by the war, and though completed in 1919 
most of the material is thus published here for the first time. 

The author is indebted especially to Dr. W. F. Colby of 
the University of Michigan, who, during the year in which 
he was associated with this laboratory, made many valuable 
suggestions as to some of the conceptions and methods of 
interpretation employed. Acknowledgment is due also to 
Mr. Kenneth Huse, who supervised the experimental work 
for a time. 



Rochester, New York 
October, 1922. 



i 



The Theory of Development 



CONTENTS 



Preface 
Chapter 



Chapter 



Chapter 



I. Developing Agents in Relation to their 
Relative Reduction Potentials and 

Photographic Properties 

General Introduction. — ^The Chemical 
Structure of Developing Agents and 
its Relation to Photographic Prop- 
erties. — Substances Investigated. — 
Chemical Theory of Reduction Potential 
Method. — Details of Experimental Work. 
— ^Sensitometric Theory. 

II. Developing Agents in Relation to their 
Relative Reduction Potentials and 
Photographic Properties (Continued) . . 
Normal Development and the General 
Effect of Bromide on Plate Curves. — 
Experimental Proof of the Existence of 
the Common Intersection. — Experiments 
Relating to the Effect of Bromide on the 
Intersection Point. — Method of Evalu- 
ating the Density Depression. — Relation 
of the Density Depression to Bromide 
Concentration; Depressions in Different 
Developers. 

III. Developing Agents in Relation to their 
Relative Reduction Potentials and 
Photographic Properties (Continued) . . 
The Relations for the Slope of the 
Density Depression Curves. — ^The Varia- 
tion of Cq with the Emulsion Used. — 
The Variation of Cq with the Developer ; 
Reduction Potential Values. — Previous 
Results on Reduction Potentials. — ^An 
Energy Scale of Developers. 



Page 

7 



13 



39 



52 



Chapter 



Chapter 



Chapter IV. A Method of Determining the Speed of 

Emulsions and Some Factors Influencing 

Speed 59 

Importance of the Method of Exposure. 
— Definitions and Sensitometric Concep- 
tions Involved. — ^A New View of the 
Matter. — Experimental Data. 

V. Velocity of Development, the Velocity 
Equation, and Methods of Evaluating 
the Velocity and Equilibrium Constants . 76 

Previous Work. — Experimental Methods. 
— Interpretation of Results; Various 
Velocity Equations and Experimental 
Data. — Conclusions as to the Form of 
Equation Best Expressing the Course 
of the Reaction. 

VI. Velocity of Development (Continued). 
Maximum Density and Maximum Con- 
trast and their Relation to Reduction 
Potential and to Other Properties of a 
Developer 97 

The Velocity Equation and its Character- 
istics. — Note on Experimental Details. 
— ^Variation of Maximum Density with 
Exposure. — Maximum Contrast (7 oo ) 
and a New Method for its Determination. 
— ^Variation of Doo and 7<x> with the 
Developer. — ^The Latent Image Curve. 

Chapter VII. Velocity of Development (Continued). 

The Effect of Soluble Bromides on 
Velocity Curves, and a Third Method 
of Estimating the Relative Reduction 

Potential 112 

The General Effect of Bromides on 
Velocity and on Velocity Curves. — 
Variation of Z)oo with Bromide Concen- 
tration. — ^A Third Method for Estimating 
the Relative Reduction Potential. — 
Effect of Bromide on Z)oo. — Proof that 
the Density Depression Measures the 
Shift of the Equilibrium. — Effect of 
Bromide on K. — ^Variation of t^ and 
/a with Bromide Concentration. — ^The 
Depression of the Velocity Curves. 



Chapter VIII. The Fogging Power of Developers and 

the Distribution of Fog over the Image . 134 

The Nature of Fog. — Fogging Power. — 

The Distribution of Fog over the Image. 

— ^The Fogging Action of Thiocarbamide 

« 
Chapter IX. Data Bearing on Chemical and Physical 

Phenomena Occurring in Development . 157 

The Effect of Neutral Salts. — The Effect 

of Changes in the Constitution of the 

Developing Solution. 

Chapter X. General Summary of the Investigation, 

with Notes on Reduction Potential in 
its Relation to Structure, etc 160 



The Theory of Development 



CHAPTER I 

Developing Agents in Relation to their Relative 
Reduction Potentials and Photographic 

Properties 

GENERAL INTRODUCTION 

Many of the principles relating to the chemistry of develop- 
ment and developers have been so well established that it is 
unnecessary to reiterate them, except in so far as they are 
required to make clear the purposes of the present work. In 
some cases, however, quantitative measurements have been 
urgently needed, as for instance in regard to the effect of 
soluble bromides on the development process, which repre- 
sents the principal portion of the subject matter here. 

Chemically, photographic development is now understood 
to be a reduction process. Many of the features of its mechan- 
ism, however, are relatively unknown, as, for example, the 
differentiation by certain reducing agents between the silver 
halide which has been affected by light and that which has not. 
To clear up these matters and to determine the nature of the 
latent image will require extensive experimental work on 
details which at first seem to have little bearing on the subject. 
Although it is impossible at present to rate the various phases 
of possible investigation according to their importance, it is 
evident that all effects of development must be eliminated one 
by one. The study of development characteristics land of the 
reduction potentials of developers is thus of the greatest 
importance. 

Photographic development may be divided into: (a) physic- 
al, where the silver forming the image is supplied by the 
developer, and on reduction is deposited on nuclei formed by 
light action; (b) chemical, where the silver is furnished en- 
tirely by the silver halide of the emulsion and largely by that 
portion affected by light; and (c) a combination of the two, in 
which some chemical development takes place, but, owing to 
the solvent action of the developer, some of the silver halide of 

13 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

the emulsion goes into solution from which it is deposited on 
nuclei or grains of silver already in the emulsion. It is prob- 
able that most cases of ordinary alkaline development rep- 
resent the third class, though the proportion of physical 
development is usually small, perhaps so small that the process 
may be considered as belonging to the second class. Physical 
development is not considered in the present work. 

The influence exerted by the developer in conditioning the 
character and extent of development has caused numerous 
controversies, most of which could have been avoided if data 
on developers which cover a wide range had been available. 
Many of the common developers are much alike, and fall 
within very narrow limits on a comparative scale; but it 
should be remembered that a wide range of characteristics is 
included in the term developer. 

Developing agents may be classified as follows : 

(a) Developers of too low reducing energy to be practically 
useful, — e. g., ferrous citrate; 

(b) Developers giving undesirable reaction products, — e. g., 
hydroxylamine, hydrazine; 

(c) Developers too powerful for practical use,— e. g., 
triaminophenol ; 

(d) Developers of practical utility, — e. g., paraminophenol, 
etc. 

Ederi divides developers into three groups: 

1. Those which develop a definite quantity of the latent 
image before fogging sets in. (Common developers) ; 

2. Those which develop quite energetically with a minimum 
of alkali, but at the same time cause fog; 

3. Those which with a maximum quantity of strong alkali 
scarcely develop the latent image, but develop fog vigor- 
ously, — e. g., phenylhydrazine, paraphenylenediamine sul- 
phonic acid. 

It is evident that the common developers occupy similar 
positions in these classifications, and are likely to have many 
properties in common, — i. e., those characteristics which make 
them good developers. Therefore, when investigating the 
effects of developers, it is necessary to go somewhat outside 
this range or to obtain a very high degree of precision in the 
measurements made. 

It is obvious also that a number of physical and chemical 
characteristics other than the relative energy of the compound 
determine whether or not it is a good developer. 

1 Eder. J. M., AusfQhrliches Handbuch fur Photographie. Fifth Edition. 1903. pp. 
288 et seq. 

14 



THE THEORY OF DEVELOPMENT 

Useful criteria for developers, apart from such practical 
considerations, are: 

1. Reducing power {valency); 

2. Reduction potential; 

3. Velocity (velocity function and magnitude); 

4. Temperature coefficient of velocity. 

All these are related to the photographic properties of the 
various substances and furnish not only a basis for quantita- 
tive chemical measurement but also the connecting link between 
such measurements and those of ordinary photographic 
properties. The second and third of these criteria were 
selected for investigation. 

The reduction potential of a developer, in the sense in which 
the term is used here, is a practical measure of the reducing 
energy of the developer, 

Bredig, Bancroft Nernst, and Ostwald (0 have pointed out 
the importance of the reduction potential in reactions in- 
volving chemical reduction, and its analogy to Ohm*s law; 

Velocity =1^^^. In accordance with this analogy, if we 

allow two developers to act against various additional chemical 
resistances, such as different concentrations of bromide, the 
resistances which cause the same change in the amount of 
work done by the developers should be a measure of their 
relative potentials. Whether the reduction potential thus 
measured is identical with the true electrochemical potential 
is a question which cannot be settled with the information 
now available; it is certainly related to it. 

When applied to photographic development, the analogy to 
Ohm's law given above may be written in the form. 

Velocity= ^^ + ^^ + ^' 



Ri+Ra+R, 



where tti represents the reduction potential of the developer 
and is no doubt the largest term of the numerator. The 
other terms in the numerator correspond to oxidation poten- 
tials for the latent image nuclei, a sufficiently high oxidation 
potential being required (under fixed conditions) to cause 
reduction, and it being conceivable that different groups of 
nuclei possess different oxidation potentials. Possibly other 
factors are included. Undoubtedly the reaction resistance 
represented by the denominator also consists of several factors 
or several terms. Thus it is difficult to connect the velocity 
of development with the reduction potential of the developer 

^ For Citations, see bibliography appended. 

IS 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

in all cases, as the other factors can not be measured by present 
methods. Only when some of these factors can reasonably 
be assumed to remain constant can two developers be com- 
pared by this method. The velocity of development is 
affected by diffusion processes to such an extent that any 
factor influencing the latter changes the velocity, although 
the potential may have undergone practically no change. 

THE STRUCTURE OF REDUCING AGENTS AND ITS RELATION TO 

PHOTOGRAPHIC PROPERTIES 

Before discussing the methods of measurement and the 
results obtained, it is desirable to review the structure of 
those organic compounds which have been found to develop, 
giving some attention to the photographic properties said to be 
associated with them. 

The brothers Lumifere with Seyewetz, and, independently, 
Andresen, are responsible for much of our knowledge of the 
developing properties of various organic reducing agents. 
While other authors have contributed to some extent, the 
many papers of Lumifere and Andresen during the past thirty 
years have established general rules for the structure of com- 
pounds which have developing properties. As is now well 
known, the presence of hydroxyl or amino groups or both is 
generally essential to developers. The following summary 
of their rules is taken from the various papers of Lumifere 
and Andresen. 1 

Compounds in which the developing function is contained 
but once, (Two active groups.) 

1. These comprise developing substances which contain in 
one benzene nucleus at least two —OH groups or two — NHj 
groups, or one -OH and one -NH2 group; 

2. These substances develop only if the groups are in the 
para- or ortho- positions. The meta- compounds have not 
been found to develop, so far as known; 

3. Developers having the two groups in the para- position 
are more powerful than those in which the groups are in the 
ortho- position; 

4. The dioxybenzenes are more powerful than the 
aminophenols, which in turn are more powerful than the 
diaminobenzenes ; 

5. The developing properties are not injured by the presence 
of more amino or hydroxyl groups ; 

* See Bibliography. 

16 



. 



\ 



THE THEORY OF DEVELOPMENT 

6. In the naphthalene series it is not necessary that both 
groups be attached to the same benzene nucleus. The general 
rules governing developing function do not apply to compounds 
of this series; 

7. Substitution in the amino or hydroxyl groups disturbs 
the developing properties when at least two such groups in the 
molecule do not remain intact. (Andresen disagrees with 
this, finding some cases where the developing properties are 
destroyed by such substitutions and others where they are 
unchanged or even increased.) 

It has been stated that alkyl substitution in the amino- 
group increases the developing energy. Apparently substi- 
tution for the hydrogen of the hydroxyl group lowers the 
developing energy or destroys the developing properties 
altogether ; 

8. Substitution of acid groups (COOH, SOjH, etc.) for 
hydrogen in the benzene nucleus lowers the energy; 

9. Substitution of chlorine or bromine for hydrogen in 
the benzene nucleus increases the developing energy; 

10. With two hydroxyl groups only, alkali is needed; 

11. With two amino groups only, or with one —OH and 
one — NH2 group the developer functions without alkali. 

Compounds in which the developing function is contained 
more than once (three or more active groups). 

12. Substances of the benzene series containing three active 
groups in symmetrical arrangement (1, 3, 5) have no develop- 
ing power. The other groupings differ in energy, no definite 
rule being established ; 

13. The hydroxy-phenols which contain the developing 
function twice (three —OH groups) can develop without alkali 
but are not practical when so used ; 

14. If the reducing agent contains a mixture of three or 
more —OH and -NH2 groups the developing energy is 
greater without alkali than it is with alkali when the developing 
function exists singly. 

Increasing the number of amino groups greatly increases 
the energy; 

15. In substances like substituted diphenyl the developing 
energy is not increased by the introduction of a third group 
in the second nucleus; 

16. In the naphthalene series the introduction of a third 
group raises the developing energy, regardless of the nucleus 
to which it is joined. 

• 17 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

General effects of subsHtuHon in a benzene compound already 
a developer,^ (Two active groups.) 

(a) Substitution of a halogen for hydrogen of the benzene 
nucleus in a para- or ortho- hydroxy- or amino-phenol raises 
the energy. (The same substitution in the meta- compounds 
has no effect on their inactivity) ; 

(b) Substitution of an alkyl group in the nucleus has no 
effect on the developing energy; 

(c) Substitution of acid groups in the nucleus lowers the 
energy; 

(d) Substitution of an alkyl group in the -OH group of 
hydroxy- or amino-phenols destroys the developing properties; 

(e) Substitution of an alkyl group in the -NHj group of an 
amino-phenol raises the reduction potential; 

(f) Any or all of the hydrogen atoms of the amino groups 
in an amine may be substituted by alkyl groups, thus increasing 
the reduction potential ; 

(g) If the -NH2 group of an amino-phenol or diamine 
be substituted to give a glycine the reduction potential is 
lowered ; 

(h) The reduction potential is increased by substituting a 
third active group in the nucleus. This substitution makes 
the meta compounds developers if the third group is not in 
the symmetrical position. 



The above summarizes those conclusions of Lumifere and 
Seyewetz and of Andresen, which apply to substances within 
the ordinary range. 

Valuable as these so-called "rules" have been, it is probable 
that some of them would be discredited could the necessary 
measurements be obtained. While in general they are 
correct as to the kind of substances which possess the develop- 
ing function to any degree, they are wrong in certain respects 
as to the relative energies possessed by the substances in 
question, especially as to the effect of certain substitutions 
on the developing energy. We know of no accurate quantita- 
tive experimental work in photography except the limited 
results of Sheppard, and of Sheppard and Mees, which could 
possibly justify and support these conclusions as to the effects 
of structure. While admittedly correct in many cases, the 
conclusions must have been reached mainly by a priori 
chemical reasoning, as they were evidently submitted to only 
rough qualitative tests, which are by no means conclusive. 

1 Compiled from the above rules. 

18 



THE THEORY OF DEVELOPMENT 

The molecular structure of the reducing agent undoubtedly 
has a considerable effect on the developing properties in so far 
as it influences or conditions the several specific properties of 
the reducer, but a classification of developers on the basis 
of free molecular energy alone would not agree, strictly at 
least, with a classification made according to developing 
properties. At present there is no method for determining 
the true chemical affinity or reduction potential of the devel- 
oping agent per se, and therefore the classification* of organic 
reducers given is made according to apparent developing 
properties; and what is referred to as reduction potential is 
relative energy from the standpoint of practical development. 

To furnish evidence on the question of structure especially 
it was proposed to study the reduction potentials and devel- 
oping characteristics of a large number of compounds. 
Although this plan has not yet been completed, much work 
has been done on many of the substances. 

Table 1 shows part of the original plan. The compounds 
marked "X" in Table 1 and those listed in Table 2 have been 
examined. 

This investigation has been limited by the very great 
difficulties encountered in the course of the work. In the 
first place, it was found practically impossible to prepare 
some of the compounds required in a sufficiently pure state. 
From the experience of the Organic Chemical Department of 
this laboratory in the preparation of substances of this char- 
acter, it is doubtful ^ivhether some of the photographic devel- 
oping agents mentioned by previous investigators have ever 
been prepared in such a form that their real photographic 
properties could be determined. Other difficulties arose in 
working out suitable experimental methods and in securing 
sufficiently accurate and reliable data. However, the results 
of the experimental work here presented are given with a very 
reasonable assurance that they are the best obtainable under 
the most favorable conditions. Photographic research of 
this kind is an especially slow, tedious, and expensive process, 
a fact which is not always fully appreciated. 

CHEMICAL THEORY OF THE METHOD EMPLOYED IN DETERMINING 

REDUCTION POTENTIAL 

The principal method employed in determining relative 
reduction potentials depends on the restraining action of 
soluble bromides when used with the reducers in question, 
a method first applied by Sheppard^ A soluble bromide, 

» Sheppard, S. E., Theory of alkaline development. J. Chem. Soc. 39: 530. 1906. 

19 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



Table I 



SYSTEMATIC STUDY OF DEVELOPING PROPERTIES 



iraol«*r arttirlAtlaa 



SM*-«taftln-a*ttorI*»lM. 




Tkivd fmtif 



CM^ftMtUa 



01 

- Cr 



«telflnMtt]rUtl«i 





o.ou 



Cbuic* to Gljrolas 



•tVk 



•ffh* 



0-0" O-Q- $"$> 







(eia)i 



i(au)i 







0" 
Cr 




01 









•ClaOOOl 



The reduction potentials and developing characteristics of 
the compounds marked **X" have been studied. 



20 



THE THEORY OF DEVELOPMENT 



Table II 



ADDITIONAL COMPOUNDS WHICH HAVE BEEN EXAMINED FOR 
REDUCTION POTENTIAL AND DEVELOPING CHARACTERISTICS 

Ferrous oxalate 




OH 



FTTOgaUoI 



I^W 



KH« 



?ta«Bgrl IqrAfasliM 



.^ 




^^ 



Slciaor l9droq>iiiiioat 



Broa hjnlroquiaont 



BlteOB XqrAroquiaoM 



Bdinol 



80tB 




Soratol 



IlkMOgMI 



CH*/^^ 



SBa 



CHt 
CH« 



NH2.OH.HCI. Hydroxylamine hydrochloride. 



21 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

such as potassium bromide, may affect development (i. e., may 
exert restraining action) in two and possibly three ways. 
(It is understood that the development of a silver bromide 
emulsion is under consideration.) 

1. Soluble bromides, being reaction products of a reversible 
reaction, such as 

ONa O 

I + 2Ag Br ^ f I + 2Ag + 2Na Br 

\y \^ met. 

ONa O 

- + 
lower the driving force of the reaction in the forward direction. 
This view was first presented by H. E. Armstrong, and later 
adopted by Hurter and Driffield and by Luther. » 

2. The bromide depresses the concentration of silver ions 
by the action of the common anion, Br, — a theory first due 
to Abegg.2 

3. The bromide may have a specific action on the silver 
halide other than that mentioned in 2. Concerning such a 
possibility we have little knowledge, but various phenomena 
occurring at high concentrations of bromide indicate effects 
quite different from those described in 1 and 2. (Chapter IX.) 

Abegg, applying physico-chemical laws, considered develop- 
ment as consisting of two simultaneous processes — oxidation 

of the developer R — > R, and reduction of the silver 

+ 
ion Ag — > Agmet. each tending to reach equilibrium as defined 

+ 

[Rl [Ag"] 

by fixed values of the ratios -^ and 



[R] [Agmet.] 

For a '^strong" developer the value of the equilibrium ratio 

+ 
for the reaction Ag — > Agmet. is greater than for a "weak" 
one — i. e., the stronger developer can reduce silver from a 
solution weaker in silver ions (richer in bromine ions). The 
bromide susceptibility is therefore a measure of the developing 
potential of the reducing ion. 

Further, for the reaction above,* the potential of the reducing 

ion R in the process of losing one electron at equilibrium is 

f Rl 
RT log -^ and this must be equal (but opposite in sign) to 

[R] 

1 For citations, see bibliography appended. 
* Sheppard — for citation, see bibliography. 

22 



THE THEORY OF DEVELOPMENT 

+ 

+ . [Agl 

that of Ag in acquiring one electron — RT log rr — --' 

lAgmet.] 

., [Ag] [Br] 

Also, [AgBr] = ^- 

And since [AgBr] is in excess and may be considered constant, 

[Ag] [Br] = K and [Ag] = j^- 

Hence, the potential of the ion R in passing to the higher 
oxidation stage R may be written 

-A = RT (log [Ag] - log [Agmet.]) 

= RT (log k - log [Br] - log [Ag„,et.]) 
where k is the dissociation constant of the silver bromide and 

log [Agmet.] is a constant (for fixed exposure), log [Br] being 
the only variable in the right-hand member. ^ Hence the 

reduction potential varies with log [Br], or the logarithm of 
the concentration of bromine ions corresponding to the 

equilibrium value ofr-r , 

^ [Agmet.1 

The above is based on the assumption that the bromide 
acts chiefly by depressing the dissociation of the silver bro- 
mide, which is probably the case. However, taking all the 
evidence into account, it is not justifiable to assume that it is 
ever the only effect, or always the chief one. The form of 
the function relating reduction potential to bromide concen- 
tration is therefore unknown, and no assumptions will be 
made regarding it. For simplicity the results interpreted as 
relative reduction potentials are considered as measured by 
the concentrations of bromide involved. 

It should be especially noted also that in the present 
investigation the relations are not expressed in terms of the 
concentrations of the bromine ion, but in terms of potassium 
bromide concentrations, this being a logical procedure until 
the true relations are established. The reduction potentials 
as measured by the methods employed will be in the proper 
order, if not of the right magnitude, and all the results may 
be converted when further information warrants. 

In accordance with the deduction made above Abegg 
suggested as a measure of the potential the amount of bromide 

1 The author is indebted for this suggestion to Dr. S. E. Sheppard. 

23 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

against which a reducing agent can just develop. But, as 
Sheppard points out, this method fails with most organic 
developers because the oxidation products are not stable and 
their concentrations are indeterminate. Hence the equilibrium 

fRl 
condition is not maintained by -^=- and the energy is a 

function of the time. [R] 

Sheppard 's method was to compare the concentrations of 
bromide required by different developers to produce the 
same depression in density at the same degree of development. 
But Sheppard did not give any clear quantitative relation as 
the basis of his method, and certain of the conclusions reached 
were erroneous through lack of sufficient data. By use of 
experimental results now available, however, the method, 
with modifications, can be justified. Its bearing, in terms of 
well established chemical theories of reduction potential, is 
still somewhat obscure. It is believed that when certain 
electrochemical data are secured the relationship will be 
established. At any rate, the photographic action 'of bromide 
has been thoroughly investigated and some definite concep- 
tions have resulted. 

It may be assumed from data given below that: 

1 . The presence of bromide causes an increase in the reaction 
resistance ; 

2. The more powerful the developer, the greater the concen- 
tration of bromide against which it can force the ratio 

+ 

^} ^ , past the value at which metallic silver is precipitated. 

[Agmet.] ^ 

That is (as stated above), a powerful developer can develop 
in the presence of a higher concentration of its reaction 
products than a weak one, or it can reduce silver from a 
solution weaker in silver ions. Also, the more powerful the 
developer, the greater the concentration of bromide required 
to produce a given change in the amount of work done ; 

3. The bromide susceptibility is a measure of the potential 
of the reducing ion, though the quantitative relations are not 
definitely known at present; 

4. The bromide susceptibility may be measured by the 
concentration of bromide required to produce a given change 
in the amount of work done; 

5. The change in the total amount of work which can be 
done may be found photographically by determining the shift 
of the equilibrium — i. e., the lowering of the maximum or 
equilibrium value of the density for a fixed exposure. The 

24 



THE THEORY OF DEVELOPMENT 

reduction potentials will then be related as the concentrations 
of bromide required to produce the same amount of change, 
or more probably as the logarithms of these concentrations. 

The last is essentially the principle of Sheppard*s method, 
although it could not be shown at the time that the quantity 
measured was the shift of the equilibrium. 

It will be shown that several methods place developers in 
the same order, and much indirect evidence indicates that the 
fundamental conceptions of the theory are correct or nearly so. 

DETAILS OF THE EXPERIMENTAL WORK 

It now becomes necessary to consider some of the basic 
principles of those quantitative photographic methods which 
are often incorrectly grouped under the term sensitometry. 
Various details of the experimental work are presented first, 
as leading up to the interpretation of the data. 

The methods adopted are similar to those of Hurter and 
Driffield and of Sheppard and Mees. For the convenience 
of readers not familiar with the work of these investigators, 
it is reviewed below in so far as is necessary to an understand- 
ing of the principles involved. 

To obtain quantitative measurements of the character of a 
photographic plate, or to determine the effect of any factor on 
the development process, it is necessary to carry out the 
following steps : 

(a) Exposure of the plate in a definite manner, for a definite 
time; 

(b) Development under known conditions; 

(c) Measurement of the resulting deposit of silver; 

(d) Interpretation of the data obtained. 

The extent to which this plan is followed depends of course 
on the information desired. For the present purpose certain 
phases of the work are necessarily quite extensive. For 
example, while the effect of a wide range of exposures is not 
studied, the development of the plates is carried out for a long 
time under varied conditions, and the data are carefully 
studied. The physical side of the photographic process may 
be ignored so long as the necessary conditions are constant 
throughout. Thus photographic methods are turned to 
the uses of chemistry, and the present investigation is there- 
fore as much a chemical as a photographic one. 

(a) Exposure of the Sensitive Material. 

The plates were exposed in a sensitometer, or exposing 
machine, which by means of an electrically controlled sliding 
metal plate placed immediately in front of the sensitive 

25 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

material exposes the latter in a series of steps for known 
times to a standard light source. This type of sensitometer 
has been described by Jones. ^ The light source used was the 
acetylene burner described by Mees and Sheppard,* screened 
to average daylight quality with a Wratten No. 79 filter. 
The times of exposure represent a logarithmic exposure scale, 
or a series of times in£reasing by consecutive powers of some 
number, usually 2, \/2~, or 1.58 (of which logio = 0.2). This 
scale is used because it is found that the blackening produced 
upon development increases with the increase of exposure 

(exposure = product of light 
flux multiplied by the time) 
in such a way that the darken- 
ing, expressed in terms of density 
plotted against the logarithm of 
the exposure, gives a curve which 
shows the character of the emul- 
sion. Such a curve is generally 
— referred to as an H. and D. 



p. . ' curve. (See Fig. 1.) The den- 

sity is defined as follows: 

T = transmission of the deposit on the developed plate ; 
=r = opacity of the deposit =0; 

logio = density = D, 
Using a logarithmic scale of exposures as abscissae and D as 
ordinates, it is evident that the successive pairs of exposure 
steps will be separated by equal distances on the horizontal 
axis. 

D is proportional to the amount of metallic silver present in 
a given area of the deposit under average conditions. The 
H. and D. curve therefore shows the relation between the 
amount of silver deposited and the exposure for a fixed degree 
of development. 

(b) Method of Development. 

To insure standard conditions during the development of 
the plates it is necessary to provide for efficient stirring of the 
developer, to maintain a constant temperature, and to see that 
the times of development are accurate. The question of 
stirring during development is a rather troublesome one, as 
some developers require much more vigorous stirring than 
others to ensure uniform development. This of course means 

1 For citation see bibliography. 

< Mees, C. E. K., and Sheppard, S. E., New investigations of light sources. Phot. J. 
5): 287. 1910. 

26 



THE THEORY OF DEVELOPMENT 

that it is more necessary to keep the oxidation products 
thoroughly washed out of the emulsion in some cases than in 
others. 

There are two disadvantages in the use of a tray for devel- 
oping. First, the mechanical rocking of a tray (motion in a 
vertical plane) is very likely to produce streaks, though when 
this is done by hand the motion is more irregular and the 
results are better. Secondly, a large surface of the developer 
is exposed to the air. The use of a water-jacketed tube as 
shown in Fig, 2 does away with these objectionable features. 




rnx 




Fig. 2 

This apparatus consists of a heavy glass tube T, seven inches 
long and one and one-quarter inches in diameter, within a 
stoppered glass jar. The space surrounding the inner tube 
is filled with water at 20° C. from a centrifugal pump in a 
thermostat. Concentric rubber tubes, A and B, with a metal 
connector C, connect with the pump so that the water from 
the pump is thermally shielded by the water returning to the 
thermostat. A' and B' are flexible rubber tubes connecting 
with the water-jacket. The plates used were one inch wide 
by four and one-quarter inches long and were developed two 
at a time in the silver-plated holder H, shown at the side. 
The prongs at the bottom of the holder were fitted with soft 
rubber to prevent breakage of the inner tube. About 60 cc. 
of developer were poured into the tube T, the plate holder 
and stopper inserted, and the whole was shaken by hand. 

27 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

This quantity of developer left an air space large enough to 
assure thorough shaking, which was aided by the movement 
of the plate holder. 

Sufficient skill was acquired in the use of this device to 
make possible a time of development of fifteen seconds with 
an accuracy of ten per cent. For longer times greater accuracy 
was obtained. Various timing devices were used. Fresh 
developer was used for each pair of plates. In some cases it 
was necessary to economize on developer because of the small 
quantity of developing agent obtainable compared with the 
large amount of experimental work for which it was to be 
used. The water- jacketed tube described was especially 
advantageous in this respect. 

A silver-plated metal water- jacketed tray provided with a 
cover was used for some of the work, and for very long times 
of development a silver-plated cylindrical water- jacketed 
tank, fitted with a revolving shaft with fan stirrer at the 
bottom and holders for the two plates mounted above the 
stirrer was useful. The shaft was revolved slowly by means 
of an electric motor. 

The three developing apparatus were compared on numerous 
occasions. No definite conclusions were reached as to which 
gave most uniform results, but for constant use it was found 
that glass vessels like the developing tube first described are 
rather more satisfactory than the metal containers as the silver 
plating wears off and the exposed metal is apt to cause trouble. 

Developers Used. In all comparisons of developing agents 
the same concentrations of the necessary ingredients were 
used. The formula adopted is: 

Developing agent M/20; 

Sodium sulphite 50 gms. ; 

Sodium" carbonate 50 gms. ; 

Water to 1000 cc. 

In some cases the sodium carbonate was omitted, and in some 
cases caustic soda was used. These exceptions are noted in 
the tables. The concentration M/20 was used except in 
those cases where the developing agent was not soluble in this 
proportion. Exceptions are noted in the tables. On the 
whole, the concentrations in the above formula give satis- 
factory developers, though not necessarily as good as could 
be made in individual cases by careful adjustment of the 
concentrations of the various constituents. 

28 



THE THEORY OF DEVELOPMENT 

As previously shown by Sheppard and Mees,i Luther and 
Leubner,* and Frary and Nietz,» a developer like that indicated 
by the above formula represents a very complex chemical 
system. Apparently the developing agent and the sodium 
carbonate react to form phenolates to an extent depending on 
equilibrium conditions, and probably there is a reaction 
between the sulphite and the developing agent or its pheno- 
lates. The various reaction products then hydrolyze and 
dissociate, so that the developing properties depend on a very 
complicated adjustment. It is obvious that in the absence 
of definite knowledge of these reactions a comparison of two 
developing agents under identical chemical conditions is 
impossible. Even with standard concentrations of alkali 
and sulphite there is no assurance that hydroquinone used 
in the above formula is under chemical conditions identical 
with those under which paraminophenol would be. The 
hydroquinone probably forms a mixture of the two phenolates 
which reacts to a certain extent with the sulphite. These 
reactions would be different or proceed to a different equili- 
brium point with paraminophenol, and the state of the two 
systems would be different also because of variations in the 
degrees of hydrolysis and dissociation. 

The best that can be done at present, therefore, is to use 
a standard method of comparison by employing always the 
same concentrations. This will give the right order as to 
the reducing energy of most developers, though not properly 
distinguishing between those nearly alike. It should be 
pointed out that for these reasons (as well as for others pre- 
viously mentioned), the photographic method cannot be used 
for determining the true relative affinities of the reducing 
agents themselves, but it is valuable in giving a classification 
of these substances as developers when used in the ordinary 
way. From the standpoint of photographic theory the latter 
is more important. 

Emulsions used. Seed 23 and Seed 30 emulsions were used 
for most of the experiments, though a number of special 
emulsions (noted below) were prepared. Eastman Portrait 
film was also used. Though much of the work was done 
with plates, film is more satisfactory in many ways. 

^ Sheppard, S.E., and Mees, C. E.K., Investigations on the theory of the photographic 
process. 

' Luther, R., and Leubner, A., The chemistry of hydroquinone development. Brit. J. 
Phot. 59: 632, 653, 673, 692, 710, 729, 749. 1912. 

« Frary, F. C, and Nietz, A.H., The reaction between alkalies and metol and hydro- 
quinone in photographic developers. J. Amer. Chem. Soc. 37: 2273. 1915. 

29 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

(c) Measuring the Silver Deposits. 

The density (silver deposit) was determined by measuring 
the amount of light transmitted, using the Martens pho- 
tometer. Special precautions were taken to minimize the 
effects of stray light in and around the instrument. Measure- 
ments were made with the emulsion side of the negative in 
contact with a diffusing surface, a piece of ground pot opal 
glass being used. For the high densities a powerful light, 
housed in, with a pair of condensers, was used, and a compen- 
sating photographic density was placed in the comparison 
field to increase the accuracy of reading. The densities as 
read and used represent the total deposit, no subtraction of 
the fog reading being made. Reasons for this will be given 
in the chapter on the distribution of fog. 

(d) Interpretation of the Data. 

In order to understand fully the results obtained in the 
experiments, it is necessary to interpret them according to 
certain fundamental principles which are reviewed in the next 
section. 

SENSITOMETRIC THEORY 
I. PRINCIPLES ESTABLISHED BY OTHER INVESTIGATORS. 

The results obtained by Sheppard and Mees confirmed and 
amplified those of Hurter and Driffield in the field of quantita- 
tive photographic research. The significance of the H. and 
D. curve, the general character of which was shown in Fig. 1, 
has been mentioned. Although in the figure the curve is 
drawn as having a considerable straight line portion any 
equation representing it must indicate that it has a point of 
inflection and with certain emulsions precise measurements 
show this to be the case. However, under most conditions 
(within the errors of observation), a considerable portion of 
the curve is a straight line. In the present work emulsions 
giving a rather long straight line region were used, and in 
the later discussion the ''toe" and "shoulder*' of the curve 
are not considered. 

The straight line portion of the curve has the equation 

Z> = Y (log E - log i) 

where y is the slope, and log i is the intercept on the log E 
axis, y is termed the development factor, log i the inertia 
point, and i the inertia (expressed in the proper exposure 
units) . 

If a number of plates which have been given the same ex- 
posure in the sensitometer are developed under constant 

30 



THE THEORY OF DEVELOPMENT 

conditions for varying times, the densities plotted against log 
E as before give a series of curves for the dilTerent times of 
development of the kind shown in Fig. 3. 

The density increases with 
development until a limit is 
reached, and on infinite develop- 
i( ment (for a non- fogging de- 

veloper and emulsion) the up- 
permost curve is obtained. The 
laws relating to the growth of 
density with time are discussed 
in a later chapter. For the 
■»■ present it is sufficient to note 

Fig. 3 that the development factor, y, 

increases with time of develop- 
ment to a limiting value, but that, for the case shown, 
the inertia point (log i) does not change with time. Also, 
T is independent of the exposure. 

The so-called "law of constant density ratios" of Hurter and 
Driffield is a necessary consequence of the above results. 
This is illustrated for the two exposures represented by 
log E = 0.9 and log E = 1.2. 

£.' = R^* 
D, D'," 

That is, for the straight line region, the density increases 
proportionately with time of development. 

More meaning may be attached to the constant t- Over 

the straight line region the slope tan a = —j-j p- = y- 

The rate of growth of density with exposure is interpreted 
photographically as the "contrast", y may therefore be 
termed the contrast of the negative. 

Although in the above case (Fig. 3) the inertia is constant 
with increasing time of develop- 
ment, this is not true when 
soluble bromides are present 
in the developer. Moreover, 
at the same degre of develop- 
ment (same development factor, 
t) the plate curve is "shifted" 
from its normal position. These 
results are illustrated in Fig.' 4. 
The straight line portions only 
are considered. Fig. 4 

31 




MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Curves for the unbromided and bromided developers at 
three degrees of development are shown. This result was 
referred to by Hurter and Driffield and by Sheppard and 
Mees as a lateral shift of the plate curve, though the latter 
spoke of the "density depression" (AD in the figure), as the 
lowering of density produced by the bromide in plates at the 
same y. They stated that the effect of inertia change or 
density depression wears off with time, so that finally the same 
inertia (same D) is reached as if no bromide were present. 
This conclusion has not been confirmed in the present work, 
the result being in some cases, however, obscured by the 
growth of fog. 

Further, the amount of the shift of the curve (or the 
depression) produced by a given amount of bromide varies 
with the developer, it being greater for hydroquinone than 
for paraminophenol, for instance. Also, bromide is found 
to have a marked effect on the time required before develop- 
ment begins — the "time of appearance." This also varies 
noticeably with the developer. It is more or less evident, 
therefore, that developers differ in their "susceptibility" to 
bromide, and that their bromide sensitiveness is connected 
with their developing energies, as discussed above. 

Sheppard 's method of determining the relative reduction 
potentials of developers by means of the density depression 
with bromide may now be briefly outlined, though the calcu- 
lation employed will not be clear until the velocity of develop- 
ment and the velocity constant have been considered. How- 
ever, neglecting these for the time being, the method in general 
was to determine the depression for a definite degree of 
development with the developers to be studied, the depression- 
bromide concentration relation having been established for 
ferrous oxalate. The concentration of bromide necessary 
to produce the same depression at the same degree of 
development was then calculated for each developer. By 
comparing the concentrations of bromide thus found necessary 
to produce the same depression, the following values were 
obtained : 

Relative 
Reduction Potential 

Ferrous oxalate 1.0 

Hydroxylamine 1.13 

Hydroquinone . 5-0 . 7 

Paraminophenol 3.4 

Sheppard worked only over the range of bromide concentra- 
tions where practically the same y is obtained in a given 

32 



THE THEORY OF DEVELOPMENT 

time as if no bromide were used. The depressions under 
these conditions are small and the errors are proportionately 
large. Furthermore, this method cannot be used for all 
developers, as concentrations of bromide sufficient to cause 
much depression, require a much longer time to reach the 
same development factor with some developers than with 
others. 

Though the fundamental basis for the method, as stated 
above, was not well established, the nieasurements undoubt- 
edly show the relative shifts of the equilibrium points, and 
accordingly place the developers in the right order. 



II. NEW CONCEPTIONS INTRODUCED IN THE PRESENT 
INVESTIGATION. 

In the present work the effect of bromide on development 
was investigated and as a result some modifications in the 
above theory have been made. A new method of interpreting 
the depression data has been adopted. This revised theory 
is based on a study of about 25,000 sensitometric strips, 
representing all types of emulsions and a much wider range 
in developers, bromide concentrations, etc., than previously 
used. The general conclusions reached, relative to the 
bromide depression method, are explained below. The 
experimental results supporting the method, and obtained 
by means of it, constitute the second and third chapters of 
this monograph, and the effects of bromide on the velocity 
are considered in later chapters. 

It was found that with all normal plates and normal 
unbromided developers the straight line portions of the H. 
and D. curves for varying times meet in a point on the log E 
axis for the entire range of times where fog is not produced 
to any great extent. (Excessive fog is usually considered as 
being greater in density than 0.5 or more.) This is the 
condition represented by Fig. 3. Consequently log i or the 
inertia point is independent of the time of development. 
Hurter and Driffield and also Sheppard and Mees found this 
to be true and stated it as a rule, though with scarcely sufficient 
proof. 

It will be easier to ascertain whether or not the curves 
meet in a point by applying the theory about to be described 
than by actually extending the lines of all the curves. More- 
over, the personal error is greatly lessened, because at low 
gammas the intersection point, or log i value, can be varied 

33 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

greatly for only a small change in gamma. Also the new 
method is of more value in studying the whole subject of 
development. 

The equation for the straight line portion of the curve, as 
previously stated is 

D ^-t (log E - log i) (1) 

If for a fixed value of log E (log E = constant) we plot D 
against y for each separate time of development (different 
values of y) we shall obtain a straight line through the origin 
{D = O, Y = O) if log i is a constant, because the equation 
for each curve is 

D = T^, 
where = log E — log i = constant. (2) 

That is, the rate of variation of density with gamma, -=— is 

at 

and the density-gamma . function is one of constant slope — 
i. e., a straight line. 

The results of several hundred examinations were plotted 
(D against y for a given exposure) and in many cases the 
data were least-squared to make sure of the lines passing 
through the origin. In this way the method was well estab- 
lished for the normal case. 

Next, data for bromided development were examined and 
plotted in the same manner to determine the character of 
the D-y curves. These were straight lines also, but gener- 
ally they did not pass through the origin, having a positive 
intercept on the y axis. This fact led to the formulation of 
more general conceptions. 

Let us assume any system of straight lines (representing the 
H. and D. curves) of varying slope, intersecting in any point 
on the log E axis or below it, which correspond to plates 
developed for different times and therefore to different 
gammas. The ccordinates of the point of intersection are 
a and 6, where a is the abscissa expressed in units of log E, 
and b the ordinate expressed in units of density. It is con- 
venient to use a log E scale of relative values so that a is 
always positive, b is always negative or zero. From the 
system of curves the following equation can be written to 
express density at fixed exposure in terms of the coordinates 
of the point of intersection: 

D-h 



\ogE-a 
^^ D = Y (log E - a) +b, (See Fig. 5.) (3) 

34 



THE THEORY OF DEVELOPMENT 



It is obvious from this general 
equation (and from g^eometric 
considerations) that so long as 
the straight lines meet in a 
point the relation between 
density and gamma is expres- 
sed by the equation of astraight 
line, which can be written in 
another form — 

D = e{-(-A} = er-Ae. w 

where & is the slope of the line 
{D, t) and A the intercept on the gamma axis. By com- 
paring equations 3 and 4 

= \og E - a, and (5) 




b A0. 



(6) 



Equation 4 describes a density-gamma straight line of slope 
and intercept A on the -j axis. This is exactly what was 
observed in cases of bromided development. It is clear from 
mathematical considerations that when this condition obtains, 
the straight lines of the H. and D. curves must meet in a 
point. The coordinates of this point are derived from experi- 
mental data by the relations above. D is plotted against y, 
giving a straight line of slope and intercept A. 

Log E, the standard or fixed exposure chosen, is known. 
Hence a, from equation 5, is known, since 

a =iogE -0. (7) 

b is determined by equation 6. 

Other relations may be determined from those now available. 
For example, the gamma-log i relation was studied prior to 
the adoption of the present method and found to be in most 
cases a hyperbola, but errors in the measurement of gamma 
at high and low values obscured the result. The present 
interpretation clears up the matter. It can be shown graphic- 
ally that 



iogt — o 



(8) 



This is a rectangular hyperbola referred to the axes y - 
and log t = a, a fact which Is significant in connection with 
bromided development, where log i exhibits considerable 
variation. 

35 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

To illustrate further: from equation 4t, D ^ 6 ^ — A 0, 
Then \l A = 0, D = ^ y, or Z> = y (log E - a) 
and -A ^==6=0. Hence if the D-y straight line passes 
through the origin {A = 0), 6 =0, and the lines meet in a 
point on the log E axis. Then a = log i and D = 
Y (log E — logi), (the original H. and D. equation), and again 
we have a description of the family of curves in Fig. 3. 

The usefulness of the density-gamma curve as a criterion 
for this characteristic of the H. and D. curves cannot be 
questioned. By this means it has been established that not 
only do the curves for unbromided developers meet in a point 
and on the log E axis, but also that the curves for the bromided 
developer meet in a point of coordinates a and h. 

Now let us consider the effect of bromide on the location of 
the intersection point. The experimental data examined 
show that over the range of bromide concentrations employed, 
the D-Y lines meet in a point which moves downward with 
increasing bromide concentration. It is thus seen that 
Sheppard's ''density depression*' may be interpreted as a 
downward shift of the intersection point. There is no logical 
reason for assuming that the H. and D. curve is shifted 
laterally. 

A constancy of a and increase (negatively) of h indicate 
that the intersection points move directly downward with 
increase of bromide concentration. This can be seen by 
comparing the D-y curves for the different concentrations 
of bromide. From equation 7, a is constant if the slope is 
constant, and, from equation 6, the growth of h (negatively) 
is shown by the growth of Ay the intercept. This is corrob- 
orated by the experimental work, as will be shown. 

Therefore we may proceed to formulate the relations for 
the density depression, d, as measured by the downward 
shift of the intersection points. This will be generalized in 
order to include possible variations. The various steps are 
shown to make the deduction clear. From Fig. 6, 

J = WN = WT + TN; 

^ = Y ; WT = (TM) Y = {a. -a,) y; 

TN = -h^ -f&i. 

Hence, d = -6j H- fti H- {a^ — a^ y- 

If /be the standard (for zero concentration of potassium 
bromide) and the a and h values for zero concentration are 
called Qq and h^ , the density depression, d, is given by 

d ^ - b -{-b^ + (a- ao). (9) , 

36 ' 



THE THEORY OF DEVELOPMENT 

But for the normal case b^ = and a = a^. Hence the 
depression caused by the concentration of potassium bromide, 
C, is 

d = -6, (10) 

and this is independent of y . 




LM.E 



Fig. 6 

This relation is supported by ample proof that for the 
average case a is independent of the bromide concentration 
(i. e., a = Gq) and that b^ = 0. There are, of course, experi- 
mental deviations from this, but they represent relatively 
small accidental errors. Equation 10 is contradictory to 
numerous statements made by other investigators that "the 
effect of bromide wears off with time,** and that the same 
inertia is obtained on prolonged development with bromide 
as without it. It will be shown that such statements are 
erroneous in so far as complete regression is concerned, and 
that although such results may be obtained at times, they are 
due mainly to the fog produced on prolonged development. 
These cases may be analyzed by the methods described here. 

Having established a means of obtaining the density 
depressions produced in different developers by varying 
concentrations of bromide, it will be possible to inquire 
further into their meaning and to study the relation between 
the density depression and the concentration of bromide 
producing it. 

37 




MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Summarizing briefly, it is found 
that if the density depression, 
dy for any developer is plotted 
against the logarithms of the 
corresponding bromide concen- 
trations, a straight line is ob- 
tained, like those shown in 
Fig. 7. 

The equation for this curve is 

^^^•^ J=m(logC-logCo), (11) 

where m is the slope, and log C^ is the intercept on the log C 
axis. Co corresponds to the concentration of bromide which 
is just sufficient to cause a depression of density. 

It is shown also that the d-log C lines for different developers 
have different intercepts (different values for log C©) but 
have practically the same slope, w. Thus two developers 
yield parallel lines, as shown in Fig. 7. Whether or not m is 
constant for all plates and all developers used could not be 
conclusively proved, but it was evident that in practically 
all cases tested it has very nearly the same value. 

These facts are of importance in connection with the 
reduction-potential method. As stated above, C^ is the 
concentration of bromide required to cause a perceptible 
shift of the intersection point. The comparison of the values 
of Co for two developers, therefore, gives a comparison of the 
reduction potentials if we assume that the change in the loca- 
tion of the intersection point measures the change in the 
amount of work done. Also, if m is constant, the rate of 
change of density depression with bromide concentration, 

, f^ ^ , is constant and independent of the emulsion, of 
a log C 

the developer, and of the bromide concentration. The 
constant m may therefore be connected with fundamental 
laws relating to the development process. 

These matters will be taken up again in connection with 
the experimental evidence, and in addition other relations 
of the bromide effect will be developed. The plan of outlining 
the propositions to be proved, or of stating many of the 
conclusions first, has been adopted because a large mass of 
photographic data presented without very clear aims would be 
quite confusing, and it is felt that in an investigation of this 
scope it would be equally unsatisfactory to develop all the 
steps of the theory along with the experimental evidence. 

38 



CHAPTER II 



Developing Agents in Relation to their Relative 

Reduction Potentials and Photographic 

Properties {Continued) 

EXPERIMENTAL DATA 

The following terminology has been adopted in presenting 
the experimental data : 

D Density (proportional to mass of silver in given area); 

Opacity; 

T Transmission ; 

E Exposure; 

F Fog (density of fog under any conditions) ; 

t Time of development; 

ta Observed time of appearance of a visible image during develop- 
ment (for standard exposure); 

a Log E coordinate of the point of intersection of straight line por- 
tions of the H. and D. curves; 

h Density coordinate for the same; 

Gq Value of a when no bromide is used (concentration of potassium 
bromide = 0); 

^o Value of 6 when no bromide is used; 

C Concentration of bromide; 

Co Concentration of bromide which causes the first perceptible de- 
pression of density (log C intercept of dAog C straight line) ; 

a Angle of inclination of H. and D. straight line with log E axis; 

Y Tan a development factor or contrast; 

Q Slope of density-gamma straight line; 

A Intercept of density — ^gamma straight line on Y axis; 

d Density depression = A — i?2 (standard log E) at same y for 

general case, 

Di — Dj (independent of y) — —h for normal case of 

development in the presence of bromide; 
m Slope of d-\og C straight line; . 

TTBr Inverse bromide sensitiveness, or relative reduction potential by 

^C ) X 
bromide depression method = (cj standard' 

THE GENERAL EFFECT OF BROMIDE ON PLATE CURVES 

The normal effect of increasing the concentration of bromide 
is shown in Fig. 8. Plates are developed with and without 
bromide, for varying times, producing different values of y, 
and a complete series is obtained for no bromide and for each 
concentration of bromide used. After plotting the H. and D. 

39 



UONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



Fig. 8 

curves, values of D at the standard exposure are plotted against 
the corresponding values of t- This gives a D-y straight 
line for each concentration, indicating that the straight 
lines of each set of plate curves meet in a point. The co- 
ordinates of the point of intersection, a and b, are determined 
as outlined above. The effect of bromide is then found to be 
that indicated by the figure, the intersection point undergoing 
a displacement downward along a vertical line. There may be 
deviations right and left in the value of a, but these are usually 
small. The general relations are as follows: 

At C - and b^ = 0, for the unbromided developer the 
H. and D. curves intersect on the log £ axis; 

At the critical concentration, C^, the intersection point 
begins to move downward; 

40 



THE THEORY OF DEVELOPMENT 



d, the density depression (for any concentration of potassium 
bromide) = ~b, or the lowering of the intersection point; 

b is therefore a function of the bromide concentration 
-b - m (log C - log Co). 
Consequently, over a range of concentrations, b increases 
(negatively) by the constant Ai if the concentration is 
increased by the same proportion each time; that is, 

ft, = A. 4- A 6 
b,=b,+ Ab 
bA = b,+ Aft, etc., if 
c, _C,^C. , 

EXPERIMENTAL PROOF OF THE COHHON INTERSECTION 

So much of the data can be clearly presented only by 
reproducing the curves obtained (tables of data would convey 
little meaning) that it is impossible to give as much as desired. 
An attempt has been made to avoid choosing, consciously or 
otherwise, only those cases giving nearly ideal results. By 
no means all the results obtained are as good as those shown, 
but the conclusions throughout are based on the general 
average of many examinations. 



. ^gi==i 1 




Fig. 9 Fig, 10 

Fig. 9 shows a set of H. and D. straight lines copied from 
the original curves. The times of development vary from 
20 seconds to 20 minutes. Seed 23 emulsion on patent plate 
glass was used. The developer was M/20 pa rapheny I glycine. 
(For concentration of sulphite and alkali and other experi- 
mental details see Chapter I.) Development was carried 
out without bromide at 20° C. These curves illustrate the 
intersection point for unbromided development. 

41 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



Fig. 10 gives the results for the same emulsion under similar 
conditions, but with M/20 paraminophenol hydrochloride 
and 0.04 M. potassium bromide. This result is not so good as 
many obtained. 

It is unnecessary to consider the H. and D. curves them- 
selves, for it has been shown that the best criterion for the 
existence of the common intersection point is the relation 
between density and gamma. If the latter represents a 
straight line function the curves meet in a point. Accordingly 
we shall examine some representative D-y curves. 

If the D-r curve for the results shown in Fig. 9 is plotted, 
we get the straight line in Fig. 11. The fact that this is a 



• 

« 
• 

m 






/ 






/ 






/ 












r 

Fig. 


11 









•/ 




1 


Z 




/ 


/ 

-y ■ 







Fig. 12 



straight line indicates that the lines meet in a point, and the 
fact that it passes through the origin shows that the lines meet 
on the log E axis. That is, in accordance with what has been 
said, if the intercept A on the y axis is equal to zero, h = [0. 

Plotting the data from Fig. 10 in the same way gives the 
line of Fig. 12. Here the points of the D-y relation are 
not in so straight a line. Least-squaring the data for both 
slope and intercept gives the line shown. A has a positive 
value. Since 6 = —AQ (equation 4), h has a real value, 
indicating, as shown in Fig. 10, that the H. and D. straight 
lines meet in a point below the log E axis. 



y 

3x: 



^^^ 



Fig. 13-A 



Fig. 13-B 



42 



THE THEORY OF DEVELOPMENT 



■ i^B^ia^^^ a^aaB^-^B ■^■^•«aa» 
• ^ 

« ^^^^^^^^ ^^—jgT ^^m^mmi^-mm, 
^^— 1 iy 



H 










• 








^ 




^ 












■ « 



Fig. 13-C 



Fig. 13-D 



Other examples are shown in Figs. 13 and 14. 

Fig. 13 represents cases of normal development with no 
bromide present. Fig. 13a gives results of M/20 paramin- 
ophenol on Pure Bromide Emulsion Is Fig. 136, of M/20 
chlorhydroquinone on Pure Bromide Emulsion I; Fig. 13(;^ 
of M/20 paraphenylglycine on Pure Bromide Emulsion lis 
Fig. 13d, of M/20 paraminophenol on Seed Process Emulsion. 

AH examples shown in Fig. 14 have the same log E. 



yd 



y 

Fig. 14-A 




41 




















^•^ 


X 








^ 


> 









y 














^ y ' 







«• 








/ 


/ 








/ 


/ 




1* 
• 




/ 


/ 






/ 














^ y ' 







Fig. 14-C 



Fig. 14-D 



I Special experimental emulsions made in the laboratory and containing only bromide 
of silver as the sensitive salt. 

43 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



Fig. 14o, M/20 paraminophenol on Special Emulsion XII, 
no bromide in developer; Fig. 146, M/20 paraminophenol on 
Special Emulsion X, no bromide in developer; Fig. 14c, M/20 
paraminophenol on Special Emulsion XIII, no bromide in 
developer; Fig. 14dy M/20 paraminophenol on Special Emul- 
sion XI, no bromide in developer. 

Fig. 14a illustrates a special case in which, because of an 
emulsion effect which can be explained in accordance with 
present conceptions, the D-y line usually does not pass through 
the origin. That is, the H. and D. curves meet below the log 
E axis when no bromide is used in the developer. 

Many other illustrations could be given, but the above are 
sufficient. Though some experiments were not conclusive, 
there were no cases of normal development in which any other 
systematic condition existed. 

DATA ON THE EFFECT OF BROMIDE ON THE 
INTERSECTION POINT 

Density-gamma curves were plotted for many developers 
used on different emulsions with varying concentrations of 
bromide. In general, these results were in accord with those 
illustrated here. As required by the theory outlined, ^, 
the slope of the D-y line, is constant, and independent of 
the bromide concentration. From equation 3, a = log E — 0, 
Since log E is constant (unless otherwise stated), a constancy 
of 6 indicates a constancy of a. That is, the intersection 
point moves directly downward as h increases. 

To prove this, the data from the D-y relation were least- 
squared for slope and intercept where the straight lines could 
not be drawn by inspection. 

Fig. 15 shows the curves for M/20 paraminophenol on Special 
Pure Bromide Emulsion I, with various concentrations of 
bromide. The slope of the straight lines is nearly the same, 
even at the highest concentration. 





'D-'^ curves for KBr concentrations 
0, .01, .04, .08 and .32 M. 

Fig. 15 



44 



D-T Curves for KBr concentrations 
0, .01, .02, .04, .08, .16 and .32 M. 

Fig. 16 



_^ 



Fig. 17 



THE THEORY OF DEVELOPMENT 

Fig. 16 gives the D-y straight lines (obtained by least- 
squaring the data), for M/25 bromhydroquinone on Special 
Pure Bromide Emulsion II. The various points are not 
indicated because the curves are so close together that the 
many points would be confusing. 

The curves in Fig. l7,forM/20 
chlorhydroquinone on Special 
Pure Bromide Emulsion II, are 
not so good as those generally 
obtained. The curves for .01 
and .02 M potassium bromide, 
and for 0.16 and 0.32 M, lie 
nearer each other than they 
should. 

Space does not permit detail- 
ing more of these individual 
cases. However, one very complete experiment is described 
to illustrate the method, which fulfills all present requirements. 
This experiment was performed with M/20 dimethylparamino- 
phenol sulphate on Seed 30 emulsion coated on patent plate 
glass. The range of concentrations of bromide was from 0.01 
to 0.64 M. The data were interpreted as follows: The 
Z>-Y data were plotted for each concentration, and the 
observations least-squared for slope and intercept. The 
average slope for all the curves was then obtained, and the 
observations again least-squared to the average slope for the 
value of the intercept A, This is justifiable since a great 
deal of experimental data has indicated that the slope is 
practically constant. The curves in Fig. 18 show how well 
the observations bear out the conclusions, and what deviations 
there are from the common slope. As may be seen, deviations 
are relatively small. The standard value of log E used was 
3.00 (logs to base 10 of relative exposures). The average 
slope, Q, was 2.78. Hence a = log E - ^, or a = 3.00 — 
2.78 = 0.22 for all cases. The value of A may be seen from 
the curves for each concentration ; and it will be remembered 
that 6 = —A0, 

Analysis of all available data has shown that the normal 
effect of bromide on the plate curves (H. and p. curves) is a 
downward displacement of the intersection point. 

Having now proved the existence of the common intersection 
and its behavior with bromide, we may proceed to a study of 
the bromide depression and its applications. 



45 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 




• 






/ ■ 


• 


y 


/ 






/ 






/ 








L y ■ II 



C=.01 

Fig. 18-B 



Jif 






/ 




• 




/ 


/ 




m 


9 


0/ 
/o 






/ 


• 










1 


1 


\ 



y 

O=.02 

Fig. 18-C 



41 






/ 


• 




/ 


/ 


M 




/ 






/ 










y ' 





C=.04 

Fig. 18-D 



46 



THE THEORY OF DEVELOPMENT 




u 






/ 




D 




^ 


/ 








O /& 








/ 










I -. ■ n 



y 

C=.16 

Fig. 18-F 




C=.32 

Fig. 18-G 




47 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 
THE EVALUATION OF THE DENSITY DEPRESSION 

The density depression, d, may be expressed most conven- 
iently in terms of the coordinates of the points of intersection 
and their relative shift due to the bromide (equation 9, 
Chapter I) 

(/ == — 6 + 60 -f (a — flo) T » 

where a and h are the coordinates for the bromide concentra- 
tion C, and ao and ft© their values when no bromide is used. 
This is the general equation which includes corrections for 
deviations from the ideal case in which a = a©, ^o =='0, the 
depression d = —6, and d is therefore independent of y. 

Table 3 gives an analysis of least-squared density-gamma 
data from earlier experiments on Seed 23 emulsion (patent 
plate). These data are much less perfect than those from 

TABLE 3 

Seed 23 Emulsion of May, 1917 

Analysis of Least-squared Density-gamma Data 

KBr 



Developer 


C 


\ogE 


A 


a 


h 


d 


2Q Chlorhydroquinone 





2.30 


1.82 





.48 










.OlM 




2.30 


.21 


.00 


- .48 


00 


Experiment 14 


.02 




2.25 


.29 


.05 


- .68 


.22 




.04 




2.15 


.30 


.15 


- .65 


.32 




.08 




2.64 


.52 


-.34 


-1.37 


.55 




.16 




2.20 


.48 


.10 


-1.05 


.67 




.32 




2.06 


.50 


.24 


-1.03 


.79 


M Monomethyl par- 





2.10 


1.62 


.05 


.48 


-.08 





20 aminophenol sulphate 


.01 




1.53 


.09 


.57 


-.14 


.15 


Experiment 45 


.04 




1.82 


.16 


.28 


-.29 


.00 




.08 




1.42 


.14 


.68 


-.20 


.32 




.16 




1.36 


.15 


.74 


-.20 


.38 




.32 




1.23 


.15 


.87 


-.19 


.50 




.64 




1.33 


.20 


.77 


-.27 


.48 


M Paraminophenol hy- 





2.40 


1.98 


.06 


.42 


-.12 





20 drochloride 


.01 




1.74 


.06 


.66 


-.10 


.20 


Experiment 37 


.02 




2.00 


.13 


.40 


-.26 


.12 




.04 




2.00 


.20 


.40 


-.40 


.26 




.07 




2.08 


.29 


.32 


-.60 


.38 


» 


.10 




1.67 


.23 


.73 


-.38 


.57 




.20 




3.10 


.43 


-.70 


-1.33 


.09 




.40 




data of 


insufficient range. 




M Hydroquinone 





2.40 


2.24 


.06 


-.16 


-.12 





20 


.005 




2.36 


.15 


.04 


-.35 


.11 


Experiment 11 


.01 




2.45 


.28 


-.05 


-.69 


.36 




.02 




2.42 


.34 


-.02 


-.81 


.51 




.04 




2.04 


.32 


.36 


-.65 


.73 




.10 




2.50 


.60 


-.10 


-1.50 


1.12 



48 



THE THEORY OF DEVELOPMENT 





■ ■ei* 





tn 



=9= 



later more complete work. Different values of log E were 
used because the straight line range of the plate-curve was not 
great enough to provide for the varying conditions which 
were obtained, and it was desirable to use values of D which 
lay within the straight line portion in all cases. 

The deviations in 0y and consequently in a, are greater 
than desirable, and irregular. The density depression, J, 
in the last column is computed from equation 9, the formula 
repeated above, where the value 1.0 is taken for y. Although 
b^ is not equal to in each of these cases, a general trend in 
that direction is indicated. 

" " * * ** Before proceeding with the de- 

termination of the density de- 
pression, let us examine more 
closely the relations for the con- 
stant a. In Fig. 19, a (as meas- 
ured from the D-y curves) is 
plotted against the logarithm of 
the bromide concentration for 
several average cases These 
and other results show that the 
total deviation of a is relatively 
small. It is not necessary to 
discuss here at greater length 
the fact that over a wide range 
a is independent of the bromide 
concentration and a constant 
for the given plate and devel- 
oper. Accordingly the density 
depression is found by means of 
the simple relation d ^ —b (b 
is considered negative, d positive) . The use of the constant a 
and the method outlined in determining plate speeds will be 
discussed in the next chapter. 

RELATION OF THE DENSITY DEPRESSION TO THE BROMIDE 
CONCENTRATION AND THE DEPRESSIONS WITH DIFFERENT 

DEVELOPERS 

If the density depression, d, is plotted against the logarithms 
of the corresponding bromide concentrations, a straight line 
is obtained, as indicated in Chapter I. The equation for 
this line may be written 

d = m (log C - log Co), 
m being the slope and log C^ the intercept on the log C axis, 
as explained above. (See Fig. 14.) 

49 



Fig. 19 



MONOGRAPHS ON THE THEOEY OF PHOTOGRAPHY 

Typical experimental results are given in the following 
figures. Fig. 20A gives the results obtained with M/10 ferrous 
oxalate on Seed 23 emulsion. Fig. 20B represents the depres- 
sions for M/20 paraphenylglycine on Seed 30 emulsion. 



lMjc 



if 



*• 



t4 



SI. 



~2P^ 




Jt 



n 




Figs. 20-A and B 

Not only these, but practically all the curves obtained have 
very nearly the same slope, m. The general method of 
treatment of the data is therefore like that of the D-y curves. 
The (/-log C curves were obtained for each emulsion with all 
the developers used on that emulsion, and least-squared 
(where necessary) for slope and intercept. The slopes, which 
were very similar, were averaged, and the data again least- 
squared to the common slope for the intercept log Co. It 
will be seen that in some cases there are not many observations, 
but it must be remembered that each point on the curves 
represents much experimental work, sometimes as many as 
fifty or sixty plates, and it was impossible at the time when 
some of this work was begun to foresee that so much material 
would be necessary. In some cases, therefore, we ran short 
of the particular batch of emulsion or developer needed. The 
deviation of observations based on so many plates can scarcely 
be explained, but they are in accord with general experience 
in photographic work. Fig. 21 gives data for different 
developers on Seed 23 emulsion. The lines represent the 
result of least-squaring to the common slope, m = 0.43. 

Fig. 22 illustrates similar results with Pure Bromide 
Emulsion I. 



50 



THE THEORY OF DEVELOPMENT 




Fig. 23 

In Fig. 23 are shown the depressions for four developers 
used on Seed 30 emulsion. In the second of these experiments, 
at high concentrations of bromide, represented by Fig. 236, 
there is a departure from the relations thus far described. 
This is also shown, though to a less extent, by dimethylpar- 
aminophenol, in Fig. 23c, and was noticed in other cases. 
The phenomena may be due to a change in the photometric 
constant, (ratio between density and mass of silver per unit 
area) or to some specific action of the bromide, a possibility 
discussed later, or, more probably, to both. 

51 



CHAPTER III 

Developing Agents in Relation to their Relative 

Reduction Potentials and Photographic 

Properties {Continued) 

THE RELATIONS FOR THE SLOPE OF THE DENSITY 

DEPRESSION CURVES 

The comparison of the values of C^ for diflferent developers 
will be a logical method only if the slope m of the density- 
depression curves is constant. The evidence we have for this 
is shown in Table 4. Some later work has shown the rate of 
change of depression of the maximum density or equilibrium 
value with bromide concentration to be the same (i. e., the 
depression in maximum density expressed as a function of the 
bromide concentration has the same slope), so that very 
probably it is correct to assume the slope constant. 

The data in Table 4 were least-squared for slope and 
intercept except where otherwise noted. 

TABLE 4 

BMULSION DEVELOPER m 

Seed 23 of May, 1917 . . Bromhydroquinone 20 

Monomethylparaminophenol sulphate 28 

Toluhydroquinone 52 

Paraminophenol hydrochloride 36 

Chlorhydroquinone 50 

Hydroquinone .80 

Average 44 

Pure Bromide I Hydroquinone 64 

Paraminophenol hydrochloride 54 

Chlorhydroquinone .56 

Average 58 

Pure Bromide II Bromhydroquinone 28 

Chlorhydroquinone 38 

Paraphenylglycine .70 

Average 45 

Seed 23 of June, 1919 . .Ferrous oxalate 54 

Hydroquinone 98 

Paraphenylglycine 87^ 

Seed 30 of July, 1919*. . Paraphenylglycine 54 

Pyrogallol 42 

Dimethylparaminophenol sulphate 46 

Paraminophenol hydrochloride .40 

Average 46 

1 Only four depression values were obtained here, therefore the data were not least 
squared. 

> Most complete data secured. 

52 



THE THEORY OF DEVELOPMENT 

The values in Table 4 are of wide range for averaging. The 
conclusion that the slope is practically constant was reached 
by weighing this and later analogous data, the relative values 
of which cannot be indicated in the present table. In the 
earlier work the deviations were large because but few dif- 
ferent concentrations of bromide were employed. For the 
most complete data (widest range and greatest number of bro- 
mide concentrations, and data therefore of most weight) such 
as the last series of table 4, the values were much more consist- 
ent. The averages for the other series of the table are partly 
accidental. 

There is a possibility, however, that hydroquinone is an 
exception to the rule, as it persistently shows a higher 
slope. This developer was found to be somewhat unusual in 
other respects, possibly because of the easy regeneration of 
the developing agent from its oxidation products by the 
action of the other constituents — a question to be discussed 
later. But until there is proof to the contrary, it will be 
assumed that the slope of the density depression-bromide 
concentration function is constant. 

It is found also that the slope m is independent of the 
emulsion and of the developer used. This is, therefore, one 
of the more fundamental constants, and probably indicates 
an important fact which will be used as a general law, for the 
present at least. 

Since m is constant — that is, the rate of change of de- 
pression with bromide concentration is independent of 
emulsion, developer, and bromide concentration — a, method 
for determining the relative bromide sensitiveness of any 
developer may be formulated. For any two developers, 
a comparison of the log C values at which the same depression 
is produced will yield the same results as a comparison of the 
intercepts (log Cq). Hence, the concentrations of bromide 
required to produce the same depression or the same change 
in the amount of work done by any two reducing agents, 
used under conditions described above, may be computed. 
As stated above, this method is analogous to comparisons of 
physical forces, since the resistances required to cause the 
same change in the amount of work done have been measured. 
It may be assumed that these give a measure of the relative 
chemical potentials of any two developers, though, as pre- 
viously stated, this is not necessarily a true indicator of the 
relative chemical potentials of the isolated reducing agents. 
Also, further work will be required to establish the quantitative 
relations connecting this method with the chemical theory. 

53 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

However, as already stated, additional evidence in favor of 
this method (see Chapter VI) shows that the rate of displace- 
ment of the equilibrium is the same as that measured here, 
and comparisons made on that basis place developers in the 
same order. Consequently it is felt that this method will 
eventually be established as fundamentally correct. 

THE VARIATION OF Cq WITH THE EMULSION USED 

Although m has been found to be independent of the emul- 
sion employed, this is apparently not true of Cq, the value of 
the concentration of bromide required for initial depression. 
This is unfortunate, as it necessitates the use of one developer 
as a standard each time a different emulsion is used, which 
means a laborious re-determination of the density-depression 
curve for a developer with which other comparisons have been 
made. The values of C^ for a given developer on different' 
emulsions are usually of the same order, but the deviations are 
so great that we must conclude for the present that the emul- 
sion influences the result. Table 5 gives the data available. 

TABLE 5 
Values of Co (in units of 4th decimal place, i. e. X 10*) 

DEVELOPER EMULSIONS USED 

Seed 23 Pure AgBr Pure AgBr Seed 23 Seed 30 
May. 1917 I II June, 1919 July, 1919 

Hydroquinone 10 4.4 .... 20 .... 

Paraminophenol hydro- 
chloride 69 72 . 5 25 

Paraphenylglycine 3.4 .... 11.8 42 10 

Chlorhydroquinone 59 35.5 40 . 8 .... .... 

Bromhydroquinone 155 .... 186.0 .... .... 

If the values of C^ vary with the emulsion, this constant 
may be of some importance in expressing the characteristics 
of the plate. However, the difficulty of determining it 
would prohibit its practical use. 

THE VARIATION OF Cq WITH THE DEVELOPER. RELATIVE 

REDUCTION POTENTIAL, TT^^ 

The greater the value of C^, the lower the bromide sensitive- 
ness of the developer. Hence, we may say that 

Bromide sensitiveness « — . 

But the greater the value of C^ the greater the reduction 
potential. Therefore, 

''''Br = / (Co), which is possibly 'f^r = k log Q. 

54 



THE THEORY OF DEVELOPMENT 

But for the time being we arbitrarily define this as 

TT Br = ^ Cq. 

At present there is no means for determining this 
constant k. As stated above, it is impossible with our 
present knowledge to measure the absolute chemical 
potential. The reduction potential of a developer X will 
be (tt Br) X = k (Cq) X ; that for a given standard developer 
will be (tt Br) std. = k (Cq) std. Consequently the relative 
reduction potential, '"'Bn for any developer X referred to a 
given standard is 

(■^Br) std. k (Co) std. (Co) std. 

This relation has been used for obtaining the new data by 
this method. The results are given in Table 6. Values of 
Co are expressed in units of the fourth decimal place (molar 
concentrations of potassium bromide). TTBr is relative to 
the standard developer indicated. All values of "WBr are 
referred to M/20 hydroquinone as having a reduction potential 
of unity. It should be remembered that all the developers 
(except bromhydroquinone and ferrous oxalate, which were 
used in concentrations of M/25 and M/10, respectively), 
are twentieth molar, with 50 gm. sodium sulphite + SO gm. 
sodium carbonate, per liter. 

TABLE 6 
Values Co and TTBr 

C -X io« (C)x 

EMULSION "' (^o)Std. 

Seed 23 of May, 1917— 

Paraphenylglycine 3 0.3 

Hydroquinone 10 1.0 Std. 

Toluhydroquinone 25 2.5 

Chlorhydroquinone 60 6.0 

Paraminophenol hydrochloride 70 7.0 

M/25 Bromhydroquinone 160 16.0 

M /20 Monomethylparaminophenol 

sulphate 200 20.0 

Pure Bromide I — 

Hydroquinone 4.4 1.0 Std. 

Paraminophenol hydrochloride 73 16. 5. Small amount 

of data 
Chlorhydroquinone 36 8.1 

55 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Pure Bromide II — 

Paraphenylglycine 12 1.7 

Chiorhydroquinone 41 6.0 (Assumed Std. 

and = 6.0 
as on Seed 
23) 

M/2S Bromhydroquinone 186 26.8 

Seed 23 of June, 1919— 

M/10 Ferrous oxalate 8 0.3 

M/20 Hydroquinone 25 1.0 Std. 

M/20 Paraphenylglycine 40 1.6 

Seed 30 of July, 1919 — Most complete data — 

Paraphenylglycine 10 1.6 Std. 

Paraminophenol hydrochloride 25 5 

Dimethylparaminophenol sulphate 60 10 

Pyrogallol 100 16 

A Study of Table 6 shows that it is extremely difficult to 
reproduce actual numerical values of 'rr^r. For example, 
the following were obtained for paraminophenol used on three 
emulsions : 

Seed 23 of May, 1917 7 

Pure Bromide 16.5 

Seed 30 5 

Values for paraphenylglycine vary as follows: 

Seed 23 of May, 1917 0.3 

Pure Bromide II 1.7 

Seed 23 June, 1919 1.6 

Seed 30 July, 1919 16 

However, with the one exception of paraphenylglycine on 
Seed 23 emulsion of May, 1917, the developers always fall in 
the same order. We, therefore, weigh the data as fairly 
as possible, and adopt the result as the best we can, with 
no great claims for accuracy. With paraphenylglycine, for 
instance, the value 0.3 is obtained with only three concentra- 
tions. The data for the other emulsions, especially for the 
last, are more complete. The evidence in any case is three to 
one in favor of the higher value. Proceeding in this manner 
we can construct a table of what we consider to be the fairest 
approximations to the relative reduction potentials. This 
table, including some of the results of previous work, is given 
below. 

TABLE 7 "^Br 

Hydroquinone 1.0 

Paraphenylglycine 1.6 

Toluhydroquinone 2.2 

Paraminophenol 6 

Chiorhydroquinone 7 

Dimethylparaminophenol 10 

Pyrogallol 16 

Monomethyl paraminophenol 20 

Bromhydroquinone 21 

Methylparamino-orthocresol 23 

56 



THE THEORY OF DEVELOPMENT 



PREVIOUS RESULTS 



Measurements of reduction potentials made prior to those 
recorded above are given in Table 8. 

TABLE 8 

REDUC?riON POTENTIAL VALUES 

From Work done Prior to 1917 

Sheppard (Photographic Method) — ^Br 

M/IO Hydroquinone (caustic) 1.0 

M/10 Ferrous oxalate 1.8 

M/10 Hydroxylamine hydrochloride 2.0 

M/10 Paraminophenol hydrochloride (caustic) 5.4 

Frary and Nietz (Electrometric Method) — 

Hydroquinone (Sod. carb.) 1.0 

Mixture of hydroquinone and monomethylparaminophenol sul- 
phate 2.7 

Diamidophenol 36.0 

Thiocarbamide 53.0 

Nietz (Preliminary work, this laboratory) (Photographic Method)* — 

M/20 Paraphenylglycine 0.7 

M/20 Hydroquinone 1.0 

M/20 Chlorhydroquinone 1.4 

M/20 Toluhydroquinone 1.8 

M/20 Paraminophenol 2.7 

M/20 Monomethylparaminophenol 7 to 16 

M/20 Paraphenylene diamine — no alkali 0.3 

M/20 Paraphenylene diamine — ^with alkali 0.4 

M/20 Methylparaphenylene diamine — no alkali 0.7 

M/20 Methylparaphenylene diamine — with alkali 3.5 

M/20 M ethyl paramino-orthocresol 23 

M/20 Paramino-orthocresol 7 

Sheppard's results, recomputed to a basis of hydroquinone 
= 1.0, were corrected for the reduction equivalent, or 
reducing power." Sheppard found, as did also the writer, 
that hydroquinone had certain marked characteristics, not 
yielding, by the former's method, a constant value for the 
relative reduction potential. The joint work of Frary and 
the writer was of a preliminary nature, and was unfortunately 
not carried out with standard concentrations of the developers. 
But the values obtained are apparently in the proper order 
and useful as an indication of the relations. 
||^ The values given in the third section of the table were 
obtained by the writer by the use of Sheppard's method. 
These are not as accurate as later work, but again the results 
are in the same order. 

57 



it 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 
AN ENERGY SCALE OF DEVELOPERS 

As a result of the measurements recorded here, we may 
now state the general order, on a scale of developing energy, 
of a number of developers. Including the averaged and 
weighted results obtained from Table 6, and the general results 
from Table 7, we may write this * 'scale of developers'* as 
in Table 9. 

TABLE 9 

M/10 Ferrous oxalate 0.3 

M/20 Paraphenylene diamine hydrochloride, no alkali 0.3 

M/20 Paraphenylene diamine hydrochloride, plus alkali 0.4 

M/20 Methylparaphenylene diamine hydrochloride, no alkali 0.7 

M/20 Hydroquinone 1.0 

M/20 Paraphenylglycine 1.6 

M/10 Hydroxylamine hydrochloride 2.0 

M/20 Toluhydroquinone 2.2 

M/20 Methylparaphenylene diamine hydrochloride, plus alkali. ... 3.5 

M/20 Paraminophenol hydrochloride 6.0 

M/20 Chlorhydroquinone 7.0 

M/20 Paramino-orthocresol 7.0 

M/20 Dimethylparaminophenol sulphate 10.0 

M/20 Pyrogallol 16.0 

M/20 Monomethylparaminophenol sulphate 20.0 

M/25 Bromhydroquinone 21.0 

M/20 Methylparamino-orthocresol 23 .0 

M/20 Diaminophenol 30to40 

M/20 Thiocarbamide 50.0 

Further information on reduction potentials is obtained 
by the application, made later, of the study of the velocity 
curves and the final or equilibrium value for the density. 
A discussion of reduction potential and its relation to photo- 
graphic properties and to the chemical constitution of the 
developing agent is necessarily deferred until the collected 
results are given. 



58 



CHAPTER IV 

A Method of Determining the Speed of 

Emulsions and Some Factors 

Influencing Speed 

The so-called "speed" of a photographic emulsion is a 
subject which has played a most important part in the history 
of photography. In fact we may almost say that it has been 
largely responsible for the scientific development of photog- 
raphy, since, some of the most important researches in which 
the principles of chemistry, physics and mathematics have 
been applied grew out of an endeavor to obtain measurements 
of plate speeds. This is particularly true of the well-known 
work of Hurter and Driffield. Many controversies arose 
following the appearance of Hurter and Driffield's first paper, 
many of the discussions centering around the determination of 
emulsion speed. Investigation of the subject is still being 
actively pursued by workers in the field of sensitometry. 

Special mention is made of the subject here because of its 
historical importance and because it is hoped that the data 
made available by the present work may be of use in studying 
the many unsolved questions related to emulsion speed. 

IMPORTANCE OF THE METHOD OF EXPOSURE 

It is to be noted especially that while most of the principles 
already stated may be applied to a study of photographic 
development irrespective of how the exposures are made 
(so long as they are made always in the same way), it now 
becomes necessary to take into account the method of expo- 
sure. Because of the failure of the plate to integrate properly 
intermittent exposures, and the failure of the so-called 
''reciprocity law" (E = //), both of which may be different for 
different emulsions, and even for different batches of the same 
emulsion, the comparison of two emulsions for the exposures 
required to give a definite result involves considerable care 
and knowledge. The questions of intermittency effect and 
reciprocity failure are under investigation. The general 
results have shown that a non-intermittent exposure on a time 
scale with proper adjustment between intensity and time, or, 
better still, exposure on an intensity scale with a proper value 
for the intensity, is required. An intermittent (rotating 
sector-wheel) sensitometer will give results approaching those 

59 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

of the non-intermittent instrument as the speed of revolution 
falls below a certain value and is gradually decreased to one 
revolution for the entire exposure. This fact should be borne 
in mind in comparing the relative speeds shown by two emul- 
sions where the exposures are on an intensity scale and the 
time is relatively short. 



DEFINITIONS AND SENSITOMETRIC CONCEPTIONS INVOLVED 

It is obvious that according to any conception of speed, 
the shorter the exposure required to give a definite result, 
the greater the speed. If we term H the speed 

^ oc A or jy = -It. 
E E 

It is evident that this ''definite result" should be standard- 
ized as regards the method for obtaining the speed, the value 
of kj and the units in which to express E, 

A clear conception of the meaning of emulsion speed was 
first presented by Hurter and Driffield. If any two plates 
are always developed (with any developer) to a normal con- 
trast (as is often done in practice) — that is, to a standard value 
of Y — the relative speeds of the two plates are to each other 
inversely as the exposures corresponding to their inertia 
points. (Reference to the contrast is necessary if all cases are 
to be covered.) This is made somewhat clearer by considera- 
tion of Fig. 24 and the explanation following. 

If plates I and II are exposed 
in a sensitometer, developed to 
the same degree, and their 
densities measured and plotted 
against the logarithms of the 
corresponding exposures, curves 
having certain straight line por- 
tions, like I and II in Fig. 24, 
are obtained. If the straight 
lines are extended they cut the 
log E axis at log ii and log i%^ 
which are termed the inertia 
points. Speed is interpreted as the measure obtained from 
values of the exposure required to give a definite density. 
Accordingly, choose any ordinary value of density lying in the 
''region of correct exposure" or straight line of the plate, such 
as Z^std. in the figure. Projecting a line parallel to the log E 
axis from Dstd. to curves I and II and from the intersections 




Fig. 24 



60 



THE THEORY OF DEVELOPMENT 

vertically downward to the log E axis gives the points log Ei 

and log Ei, Logs Ei and Et are, therefore, the exposures 

required to give the same density on plates I and II under 

these conditions. Therefore, according to the equation 

k 
H = ^=ry the speed of one emulsion compared with the other 
lit 

is given by 

Hi ^ Ei 

Hi El 

But since I and II are parallel lines (plates at the same degree 
of development) the ratio =^ is the same as -r; or, the speed 

iil ti 

relations can be obtained from the values for the inertias. 

Hence we may write W = ^- Further, if log ii and log it 

Hi ii 

remain constant with increasing development, then the ratio 

T is not affected by development; that is, the speed is inde- 

pendent of y. 

Unfortunately, the inertia is not always independent of the 
degree of development, especially if bromide is used in the 
developer; and it is here that the* results described in the pre- 
ceding chapters may be applied. 

We may get rid of comparisons and relative speed values 
by deciding in what units to express i and what value to 
assign to the constant k in the equation 

k 
H ^ — (by definition of absolute speed). (12) 

Although E and i have always been measured in visual units, 
there is obviously no logic in such a procedure, since the 
visual measurement of light intensity is affected by limitations 
of the human eye quite different from those affecting the 
photographic emulsion. In other words, the photographic 
plate does not necessarily see two intensities in the same 
relation as does the human eye. However, until there has 
been put forward a satisfactory photographic light unit, we 
must continue to use the visual unit, E and i being expressed 
in candle-meter-seconds (or, as commonly written, c. m. s.). 

Usually ^ is so evaluated as to give values of H in convenient 
numbers. The value ife = 34 was selected by Hurter and Drif- 
field, adjusted for use with their "Actinograph** or exposure 
calculating scale. 

61 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

All further considerations in this monograph avoid the 
use of absolute speed values in arbitrary units. We may 
proceed very satisfactorily by employing a relative exposure 
scale, this being convertible at any time by knowing the rela- 
tion between the scale and the actual intensity-time measure- 
ments. For example, all exposures made during the course 
of this work, beginning in February, 1919, were such that 
log E = 2.4 represents 1.4 candle -meter-seconds (visual) of 
acetylene screened with Wratten No. 79 filter to daylight 
quality. This fact furnishes the connecting link between the 
relative and absolute exposure values. 



A NEW METHOD 

The details of a somewhat different method for the 
determination of definite sensitometric constants expressing 
the speed of an emulsion have already been described. It 
is for the purpose of emphasizing this method in its affiliation 
to the whole subject of speed that it is taken up again. The 
writer also wishes to point out that the older method, as 
presented in the foregoing section, serves very well in ordinary 
cases where a good standard developer can be used on emul- 
sions of the usual type. But in order to obtain a fair estimate 
of speed in practically every case, no matter what the emulsion 
or the developer, other conceptions are most emphatically 
necessary. Much of the controversy on the question has 
arisen from the erratic results obtained in certain cases. 

It has been shown that the straight lines of the H. and D. 
curves for any case of normal development always have a 
common intersection. The coordinates of this point of in- 
tersection were termed a and 6, and these are the sensitom- 
etric constants with which we are principally concerned here. 
a is the log E coordinate of this point and h the density coor- 
dinate. If 6 = 0, the curves intersect on the log E axis. This 
is the case for nearly every ordinary emulsion and every 
developer of the 'usual type which contains no bromide. 
But if emulsion or developer contain bromide, h has a real 
value and the intersection point lies below the log E axis. In 
consequence, log i changes with time of development and with 
contrast. Now a is not affected by bromide, and therefore can 
be determined with any concentration of bromide (over a 
wide range) in the developer. It has been assumed that for 
no bromide h will be zero. Exceptions to these rules are rare 
in the case of ordinary materials and can be explained either 
by the fog error or by a progressive secondary reaction 

62 



THE THEORY OF DEVELOPMENT 



during development, which produces a shifting equilibrium 
point. Any case of general deposition of silver over the plate 
of course upsets the relations. 

The application of the method to the most general case is 
illustrated in Fig. 25. 




-L0«^ 



Fig. 25 



Consider first a comparison in speed of two emulsions, I and 
II. Different times of development (under constant 
conditions) yield for emulsion I a family of H. and D. curves 
whose straight lines intersect in the point Q, Q has coordin- 
ates fli and 61, as shown. Similarly emulsion II gives curves 
intersecting in iV, of which the coordinates are at and bt. 
Compare the two emulsions at any value for the contrast, y. 

63 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

The curves under consideration will be, for example, those 
marked I and II, both at the same r- for this particular 
value of y the exposures required to give a standard density 
(Ostd.) are E, and £„ which will be in the same ratio as »i 
and it. But if another value for the y of the two emulsions 
is chosen, the ratio will change; and if the two plates are 
not at the same f the relative speeds can not be determined 
at all except under the particular conditions chosen. In 
either case the value obtained is not constant and does not 
express any characteristic of the plates. This is precisely 
where the old method fails, and on such points much time and 
discussion have been wasted. 

The constants a and b are fundamental characteristics of 
the two emulsions for the given developer, and the speed 
relations may be expressed in terms of them, as detailed below. 



H, 


= 


r.1 

a 






(from 


above) 


■-!: = 


log 




a-iog£, 


-log< 


- log i, 


- MN 


- Bfl-SM 


BN 


= a. 


BM . 


a, -MR 




-.^ 


= tan a = Y- 


Hence, MR 




'JJI*-. (positive) 


Hence, log 


H, 


= '-^1 


= a,- a,— 


6. - fi 




(13) 



This expression holds for any value of r- It shows that in 
such cases the relative speeds of the emulsion depend on y , 
and the relations are such tl 
the speed of II compared witi 
when 6, < bi the speed of II 
increase of r . If either 6i ■ 
simplifies. If both 6i and b 
plate speeds are defined by a. 



a, being identical with log i 
have the original Hurter an 
the latter holds only if the 
families of curves lie on the lo 
pointed out. In this case o 
pendent of the contrast. 



THE THEORY OF DEVELOPMENT 

Now in the case of a single emulsion, say emulsion I in 
the figure, if b has any considerable value the absolute speed 
of the plate increases with y. In the case of curves I and la, 
for example, the inertia decreases from ii to ti, and the speed 

k k. , , 

increases from H = —rto H = t— This is better shown 

by the following: ^ 

log H = log —r- = log k — log ii. 

From the figure f : = r , and log /i «= a (14) 

log ti —a Y 

Consequently log H = log k — a -\ . (IS) 

Hence, the lower the value of a, the greater the speed; the 

greater the absolute value of 6, the less the speed; and the 

greater the value of y, the greater the speed (for a given 

value of h), \i h = 0, we have log H = log k - a, and the 

speed is independent of gamma. 

We may define the absolute speed, in a purely arbitrary 

but general way, as inversely proportional to that exposure 

in visual meter-candle-seconds (of light from a definite source, 

such as screened acetylene) which is required to initiate the 

deposition of silver, assuming that the emulsion is developed 

to a gamma of unity and that the H. and D. curve consists 

entirely of a straight line. Practically, this is not so complex 

as it sounds. Referring to the figure, curve for emulsion I, 

k 
for example, we simply state that H = ^— where i is the value 

at Y = unity and expressed preferably in terms of a and 6, 
and in the proper units. From the figure it may be seen that 
at y =1.0, log f = a — b. This is evident also from equation 
14. Consequently, to fit the definition 

log ZT = log ife -a -f- b. (16) 

On this basis the relations for speeds between emulsions 
will be the same as if we chose densities actually on the 
straight line portions of the plate curves (so long as both the 
emulsions are at a gamma of unity). The arbitrary selection 
of the speed ratio at a particular value of y is necessary if 
any definite speed number is to be assigned to an emulsion 
having a real value of b (and there are such emulsions). It 
should be clear from the above that for this case the speed 
value obtained varies with the contrast. To eliminate 
contrast, therefore, the constants a and b are determined and 

65 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

the speed number expressed by the use of equation 16. When 
b is zero the method is as simple as the older one, and it may 
be made more precise. 

Therefore, our conclusions are that a and b are the 
sensitometric constants desired, and that the use of i as a 
characteristic constant should be abandoned. Further, we 
find it possible to express the correct relations for the speed 
in terms of a and ft, whether or not the speed is independent of 
the contrast. 

For the experimental method of determining the constants 
a and b the reader is referred to Chapter I. In practice, 
for the purpose of speed measurements, it is sufficient to 
develop five pairs of plates for varying times and to plot the 
H. and D. and the D- y curves for the standard exposure. 
a and b are computed from the latter. 

DATA ON EMULSION SPEEDS AND THE VARIATION OF SPEED 
1. VARIATION OF SPEED WITH EMULSION 

The above conclusions were reached from examination of 
data from thousands of plates, about thirty different develop- 
ing agents and fifteen different emulsions being used. The 
following typical cases are sufficient for illustration. Table 
10 gives results for eight emulsions, each developed in three 
developers. Values of a, ft, and H are given. H is found 
from equation 16 by assigning the value 100 to ^ and expressing 
a in units of the logarithms of relative exposures. Hence 
equation 16 becomes log H = 2 — a -\- b. This expresses 
speed values (on an arbitrary scale) which are independent of 
Y when ft = 0, and apply only for y =1.0 when ft has a real 
value. Since in most cases ft = 0, they may be considered to 
be parallel to the H. and D. speed numbers. 

A great deal of data like those in Table 10 was obtained 
incidentally to other work. Owing to occasional difficulties 
in' obtaining consistent and uniform results with certain 
developer and emulsion combinations no great precision could 
be obtained. However, it was demonstrated that, by the use 
of a suitable standard developer, a very satisfactory degree of 
precision and reproducibility in comparing emulsion speeds 
may be obtained by this method. The personal error is 
eliminated to a great extent, and the information obtained, 
especially if the emulsion under consideration does not behave 
in the normal way, is of more value than that obtained by 
the Hurter and Driffield method, where, as a rule, the inertia 
point is obtained from two plates. 

66 



THE THEORY OF DEVELOPMENT 



TABLE 10 

SPEED OF PLATES 



Emulsion Used 


M/20Paramino- 
phenol hydro- 
chloride 
(R 340.15) 


M/20 Dimethyl 
paraminophe- 
nol sulphate 
(R 354.1) 


M/20 Pyrogallol 
(R 43.25) 




a 


h 


H 


a 


h 


H 


a 


h 


H 


Special Emulsion IX. . 
Special Emulsion VIII. 
Special Emulsion XI . . 
Special Emulsion XII . 

Pure Bromide III 

Special Emulsion XIII. 

Special Bromide XIV. . 

Film Special Emulsion 

XV 


.14 
1.34 
1.18 

.58 
1.99 
1.74 
1.24 

1.10 
.12 


-.17 



-.22 


-.21 

-.25 





49 
4.6 
6.6 

16 
1 

1.1 
2.1 

8 
76 


.50 
1.66 






32 
2.2 


.14 
1.42 


.04 



80 
3.8 


0.73 
2.00 
1.68 


-.14 


-.25 


13.5 
1 
1.2 


.50 
1.72 
1.65 
1.54 




-.24 
-.12 


32 
1.9 
1.3 
2.2 


.88 
-.32 






13 
210 




Emulsion 3533 


-.88 





760 



Table 10 shows that there is an increase in speed when 
pyrogallol is used, and that paraminophenol increases the 
speed to a somewhat greater extent than dimethylparamin- 
ophenol. Tlie effect of the developer is considered below. 
The Special Bromide Emulsion XIV, which contains some 
free bromide, persistently shows a real value for 6. This 
may be interpreted in the light of what was said in the second 
chapter concerning the effect of bromide on the intersection 
point, — i. e., on the values of a and h. It was shown that 
normally, when no bromide is present, 6=0, but with increas- 
ing concentration of bromide b assumes a real value and 
increases, or the intersection point moves downward, a is 
not affected. Consequently we may infer that if an emulsion 
shows a real value of &, it contains some free bromide, as we 
do not know of any other explanation of this result. The 
bromide may be held by adsorption or inclusion but must be 
present when development takes place. Further, according 
to earlier theories, the depression of the intersection point 
(the value of 6), for a given concentration of bromide in the 
emulsion is less the greater the reduction potential of the 
developer. Pyrogallol has the highest reduction potential 
of the three developers, and in three out of four cases showing 
a real value of h, the latter is smallest with pyrogallol; that is, 
in these three experiments the free bromide in the emulsion 
has the least effect when pyrogallol is used. The presence 
of free bromide in the emulsion can not be considered detri- 
mental, provided the depression produced is not too large. 

67 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

The above explanation may account for various effects 
observed with certain developers and emulsions. Hydro- 
quinone without bromide, for example, often shows a shift or 
* 'regression" of the inertia point. Hydroquinone, having a 
low reduction potential, and being therefore very sensitive to 
bromide, may be affected by an amount of free bromide in 
the emulsion so small that it has no effect on other developers. 
The foregoing facts may also account for the successful use of 
pyrogallol in speed determinations. This does not imply 
that other developing agents will not do as well, but it is true 
that many developers whose reduction potential is as great or 
greater than that of pyrogallol give much more fog, thereby 
vitiating the results. 

That some slow emulsions show a considerable value for b 
also partially accounts for the fact that these emulsions are 
relatively faster when developed to high gammas. However, 
this phenomenon may be explained partly by other sensi to- 
metric considerations. 

2. EFFECT OF BROMIDE ON SPEED 

If certain developers (of low reduction potential) containing 
an appreciable amount of bromide are used, the actual effective 
speed of the plate is reduced because of the depression in 
density produced by the free bromide in the developer. The 
extent of this effect is, of course, measured by the effect on b, 
as shown by equation 16 — 

log H = log k - a -\- b. 

Although the question of the advantages and disadvantages of 
the use of bromide has been debated again and again, we may 
now state with a reasonable degree of certainty that there is a 
real advantage in the intelligent use of bromide in the 
developer. To present this point properly would require a 
separate paper and the use of results not yet explained. 
However, the following facts may be presented: 

As a rule, the fogging propensity of a developer is not 
connected with its reduction potential, many developers of 
exceptionally low potential giving much fog; 

With most developers the growth of fog is affected to a 
very much greater extent by bromide than is the growth of 
image density; 

For a developer of relatively high reduction potential 
(monomethylparaminophenol, pyrogallol, etc.), an amount 
of bromide sufficient practically to inhibit fog even with 

68 



THE THEORY OF DEVELOPMENT 

relatively prolonged development does not greatly affect the 
density (i. e., the depression is small) provided the concentra- 
tion of the developing agent is great enough. 

In other words, for the preceding conditions, bromide cuts 
down the fog but does not lower the effective speed of the 
plate. 

As a general rule, therefore (other conditions being equal), 
there is an advantage in the use of a high reduction potential 
developer of suitable character with enough bromide to 
minimize chemical fog. 

In speed determinations on ordinary emulsions, especially 
if developers or emulsions apt to fog are used, it is a distinct 
advantage to use bromide. If no bromide is used, b is assumed 
0, which is true for nearly all ordinary plates, a is not affected 
by bromide. The speed may therefore be determined with 
sufficient bromide to eliminate the fog error. (See Chapter 
VIII on distribution of fog over the image.) 

3. EFFECT OF THE DEVELOPING AGENT 

This is another question which has been the subject of 
much discussion. While the determination of emulsion 
speeds for different ordinary emulsions may be made easily, 
the same measurements with many different developing 
agents on a plate of sufficient latitude (usually a moderately 
fast plate), will be attended by many difficulties. This is 
especially true for developers such as those employed in the 
present work, where the concentrations are always the same, 
and no attempt is made to obtain good practicable formulae. 
This series of developers represents similar conditions chem- 
ically, and we believe that on the whole the results are of 
value from the theoretical point of view. It is emphasized 
here and later that little practical importance is attached to 
the data (given below), on the effect of the developing agent, 
as they would not be duplicated by the use of commercial 
developers. A similar application of the method with the 
latter, however, could not fail to be of value. 

The greatest error in the present problem is that due to fog. 
It has been quite conclusively demonstrated that fog does not 
lie uniformly distributed over the image, but is greatest over 
the low densities. Hence it is seen that as fog increases it 
can change the character of the plate curve, giving a false 
result. This leads to false values of log i, of a, and of ^, or in 
some cases renders their determination impossible except over 
the narrow range where no fog is produced. In such cases 
there is great advantage in the use of bromide. 

69 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

In Table 11 are given results, obtained with seven developers 
used on a Seed 23 emulsion. These were obtained from 
bromide depression data, so that the value of a is the average 
from determinations at several concentrations of bromide, 
and may therefore be considered quite reliable, h was 
zero. The speed numbers {H) are found, as above, from 
log H = log k — a + ft, where k is 100 and a is expressed in 
units of log E Relative. The reduction potentials of the de- 
velopers are recorded also. 

TABLE 11 

INFLUENCE OF THE DEVELOPING AGENT ON PLATE SPEED 

(ft-0) 

Developer '''"Br a H 

M/20 Hydroquinone 1.0 .07 85 

Paraphenylglycine 1.6 .12 76 

Toluhydroquinone 2.2 — . 24 174 

Paraminophenol hydrochloride 6 .49 32 

Chlorhydroquinone 7 .10 80 

Bromhydroquinone 21 .49 32 

Monomethylparaminophenol sulphate 23 .63 23 

There is no regularity in these results. On another and 
faster emulsion the following were obtained : 

TABLE 12 

Developer ''''Br a H 

Paraphenylglycine 1.6 — .17 148 

Paraminophenol hydrochloride 6 4-12 76 

Dimethylparaminophenol sulphate 10 -j- .28 53 

Pyrogallol 16 - .05 112 

Again no connection between reduction potential and plate 
speed is apparent. However, pyrogallol, paraminophenol, 
and dimethylparaminophenol stand in the same order as to 
speed as in Table 10. 

Table 13 gives results less reliable than those above, as the 
data were obtained incidentally to other work for which no 
bromide was used. The range of developing agents is much 
greater and the same general trend is indicated as in Tables 
11 and 12, though the results are somewhat erratic and some of 
them no doubt are erroneous. Each value of a is the result of 
but one determination, and that without bromide. The 
Z)-Y curve for each case is based on from ten to twenty pairs 
of plates, plates showing bad fog being included. The 
determinations marked with an X are from the most consistent 
data. A Seed 30 emulsion was used throughout and all the 
conditions were as previously described. 

70 



THE THEORY OF DEVELOPMENT 
TABLE 13 

INFLUENCE OF THE DEVELOPING AGENT ON PLATE SPEED 

Experiment 

Number ^Br a b H 

131 M/10 Ferrous oxalate 0.3 X 100 

132 M/20 Paraphenylenediamine hydrochlor- 
ide, no alkali 0.3 -".52 330 

126 M/20 Hydroquinone 1.0 - .66 X 460 

136 M/20 Toluhydroquinone 2.2 -.24 0X175 

123-140 M/20 Paraminophenol hydrochloride... 6 .12 OX 76 

165-167 M/20' Chlorhydroquinone 7 .20 OX 63 

127 M/20 Paramino-orthocresol sulphate... 7 —.54 X 350 
125 M/20 Dimethylparaminophenol sulphate 10 -.32 X 210 

124 M/20 Pyrogallol 16 - .88 X 760 

135 M/20 Monomethylparaminophenol sul- 
phate 20 X 100 

144 M/25 Bromhydroquinone 21 .20 OX 63 

130 M/20 Methylparamino-orthocresol 23 -.78 600 

145 M/20 Diamidophenol hydrochloride, no 
alkali 30-40 .20 63 

129 M/20 Dichlorhydroquinone -.48 X 300 

133 M/20 Dibromhydroquinone -.60 X 400 

137 M/20 Paraminomethylcresol hydrochlo- 
ride -1.00 XlOOO 

146 M/20 Diamidophenol, 4- alkali - . 60 X 400 

154 M/20 Pyrocatechin +26 OX 55 

172 M/20 Phenylparaminophenol -.06 0X115 

184 M/20 Edinol +.46 35 

195 M/20 Eikonogen -.26 180 

193 M/20 Hydroxylamine hydrochloride + 

0.25M,NaOH +.12 76 

194 Commercial Pyro Developer (containing 

bromide) +.20 .63 

Log E — 2A (relative scale) 
Seed 30 Emulsion 

We doubt that such wide deviations occur. Indeed, this 
conclusion is upheld by the fact that if a certain fixed exposure 
which gives densities lying well up on the plate curves, out of 
the region of fog, is selected, the densities (on prolonged 
development, at least), vary with the developer, showing a 
general tendency to increase with reduction potential. But 
the variation is not so great as these speed values would indi- 
cate. Consequently we must attribute some of this deviation 
to fog, which, as indicated, can change the contrast and inertia 
values. 

It is clear from the above and from many other experiments 
that variations of emulsion speed with developing agents are 
far from orderly, and that the speed obtained in a given case 

71 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



depends on several factors, among which are, undoubtedly, 
the reduction potential of the developer, the general balance 
of the ingredients of the solution (which conditions hydrolysis 
and the character of secondary reactions), the physical action 
of the developer on the gelatine and on the silver halide, and 
the fogging propensity of the developer. From data on 
velocity and maximum density, to be presented later, it is 
concluded that, other conditions being equal, the speed 
increases somewhat with increasing reduction potential. At 
any rate, it should not be concluded that the deviations found 
(especially those in Table 13) necessarily obtain for any condi- 
tions other than those described. It will be found that the 
results with commercial developing formulae are much more 
nearly balanced. 

4. INFLUENCE OF THE CONCENTRATIONS OF THE 
OTHER INGREDIENTS OF THE DEVELOPER 

These complex effects are not capable of ready interpreta- 
tion. As the state of balance among the various ingredients 
of the developers is changed the degree of hydrolysis and 
dissociation of the developing substance varies. The physical 
action of the developing solution probably changes to some 
extent also. To these and to the other factors mentioned 
above we may attribute the results, but without definite 
knowledge that it is correct to do so. 

The changes in the constant a for the hydroquinone devel- 
oper are shown in Fig. 26. The concentrations of sulphite. 







Figs. 26-A, B and C 

72 



THE THEORY OF DEVELOPMENT 

carbonate, and hydroquinone were varied as indicated. Vari- 
ation in bromide concentration produces no change in a, as 
previously shown. 

The lower the value of a here, the higher the speed. In all 
cases 6=0. 

There is practically no change in speed with changing 
sulphite concentration over a wide range (Fig. 26x^). 

There is, however, a marked increase of speed as the alkali 
concentration is increased until a maximum is reached, after 
which the speed decreases (a increases). (Fig. 26B). This 
may be accounted for by the hydrolysis relations and also by 
the physical effect of the alkali on the gelatine, excess of alkali 
causing a hardening of the gelatine, while over the lower 
range a gradual softening takes place. 

Insufficient data were obtained on variations of hydro- 
quinone concentration, but such results as are available are 
shown in Fig. 26C. 

It is to be understood that these relations may be quite 
different with other developing agents. 

5. PRECISION OF THE METHOD. RESULTS WITH COMMERCIAL 

EMULSION AND DEVELOPER 

The data in Table 14 illustrate the precision which can be 
attained by the use of the method described above. Under 
favorable conditions the original Hurter and Driffield method 
was found to give slightly greater deviations from a mean. 
Under less favorable conditions the Hurter and Driffield 
method would require modification to approach the reproduci- 
bility and consistency of the method described here. 

A panchromatic plate was used with a commercial pyrogallol 
developer. Exposures were made under varying conditions 
which need not be described at present. Five pairs of plates 
were used for each determination of a. Three separate deter- 
minations were made, numbered 1, 2, and 3. A 5 is the 
deviation from average speed. 

TABLE 14 

I II III IV 

Speed A5 Speed AS Speed A5 Speed A5 

1 85.0 +4.8 66.0 +1.5 54.0 -0.9 33.9 -0.9 

2 77.5 -2.7 59.2 -5.2 52.8 -2.1 31.7 -3.1 

3 79.3 -1.9 68.2 +3.7 57.9 +3.0 38.9 +4.1 

Mean 80.2 64.5 54.9 3^.% 

Average 

deviation 2.8% 5.4% 3.6% 7.8% 

73 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

The deviations for sixteen such cases averaged 2.3 per cent. 
The old (H. and D.) method carried out in exactly the same 
way for sixteen cases gave 3.3 per cent deviation. For the 
latter the inertia points of five pairs of plates were averaged. 
In the usual routine application of this method but two pairs 
are used. 

CONCLUSIONS 

The inertia point is not a fixed characteristic of an emulsion » 
and it is better to avoid the use of i or log i as constants 
wherever possible. 

More fundamental sensitometric constants for given condi- 
tions are a and b, the coordinates of the point of intersection 
of the H. and D. straight lines obtained by varying the times 
of development. 

a and b are determined from the relations 

- a = log £ - tf 
b A0 

by the use of the D-y function, for which is the slope 
and A the intercept on the y axis. Log E is the standard 
exposure for which the D-y curve is plotted. 

When 6=0 the H. and D. straight lines intersect on the 
log E axis. This is true for nearly all ordinary emulsions and 
for developers containing no bromide. 

If sufficient bromide is present b differs from zero and 
increases (negatively) with increasing bromide concentration. 
In such cases the new method is of advantage in interpreting 
the results. 

A few of the slower emulsions contain free bromide, so that 
they exhibit a regression of inertia with increasing develop- 
ment — i. e., have a non-vanishing b. This effect is less for an 
emulsion of this kind when a developer of high reduction 
potential is used than with one of low reduction potential. 

If bromide is present in the developer, the relations are the 
same as in the preceding. A developer of high reduction 
potential may be used with more bromide without lowering 
the effective speed. 

There is considerable advantage in the use of a suitable 
developer of high reduction potential with enough bromide 
to cut down fog. 

In many cases, speed determinations are made more easily 
if bromide is used judiciously. 

74 



THE THEORY OF DEVELOPMENT 

The emulsion speed does not vary consistently with any 
known characteristic of a developer, but is probably affected 
by the factors noted above. Others of these factors being 
the same, it is believed that the speed increases with increasing 
reduction potential. 

The method of speed determination described can be made 
sufficiently accurate for all ordinary emulsions and developers. 

The conclusions reached apply only to the conditions stated 
— i. e., for the region of correct exposure (the straight line 
portion of the plate curve) — ^just as in the original speed 
determinations by Hurter and Driffield. A separate investiga- 
tion will be required to measure relative speeds for the region 
of under-exposure. However, so far as the effect of the 
developer is concerned (as studied here), the relations would 
not be different. 



75 



CHAPTER V 

Velocity of Development, the Velocity Equation, 

and Methods of Evaluating the Velocity 

and Equilibrium Constants 

In preceding chapters an attempt has been made to study 
the affinities of certain organic reducing agents, and to correlate 
their photographic properties on this basis. However careful 
such work may be it cannot be entirely successful because the 
reduction potential of a developer is not always the chief 
property in conditioning the nature of its photographic 
action. Moreover, other properties important in this respect 
are relatively unknown, which makes a fair quantitative 
comparison of developing agents extremely difficult. Among 
factors influencing the results of such comparisons we may 
mention those contributing to differences in reaction resist- 
ance, in physical action (adsorption, penetration, effect of 
tanning, etc.), and in the chemical system affecting the entire 
reaction. The reaction resistance is influenced by factors of 
which we know little. The solvent action of the developer 
on silver bromide, the nature of the chemical reactions among 
the ingredients of the solution (developing agent, alkali, and 
sulphite), the degrees of dissociation and hydrolysis of the 
resultant compounds, and the effects of relatively high concen- 
trations of other ions — all these influence reaction resistance 
and determine the chemical state of the system. 

It was felt that a study of reaction velocities might lead 
to a better understanding of these questions, and the work 
about to be described was undertaken. 

In working out methods for the study of the velocity of 
development, it was decided not to make use of the relation 
between the contrast (gamma) of the plate and the time of 
development, as has been done to some extent by other 
investigators, but to use the chemically more logical quantity 
density (D), which has been defined as being proportional to 
the mass of silver. The problem thus becomes a physico- 
chemical one, dealing with familiar relations and quantities. 
It is evident that here we are dealing with a heterogeneous 
reaction very probably susceptible to disturbing influences, 
as such reactions often are. A rough preliminary analysis of 
one case will show the method of examining the velocity and 

76 



THE THEORY OF DEVELOPMENT 

acceleration curves. The data were obtained by developing 
a pure silver bromide emulsion in M/20 paraphenylglycine 
(with 50 grams of sulphite and 50 grams of carbonate per liter) 
which contained M/lOO potassium bromide. In Fig. 27A 
density {D) is plotted against the time of development for a 
fixed exposure, as will be explained directly. The slope of the 
curve at any time (/) is the velocity of development at that 
instant. By plotting the velocity against the time the 
so-called acceleration curve, Fig. 27B, is obtained. The 
velocity is expressed in terms of density developed per minute. 



D 



Velocity 








of Dev. ' 


A 








A 








/ 







5 min. T 10 15 

Fig. 2 7- A 



20 



5 min. T 10 

Fig. 27-B 



15 



The example chosen shows a well defined period of induction, 
or period of increasing velocity — a characteristic of photo- 
graphic development, but not always so well shown. In 
fact, in many cases it fe practically absent, and unless the 
experimental work is exceptionally accurate it is best ignored. 
However, the existence of this period of induction has been 
generally recognized as a feature of the kind of reaction we 
are investigating here. It is evident from the figures that 
more or less time elapses before there is measurable develop- 
ment, and that the velocity then rapidly rises to a maximum, 
after which it decreases in the usual way as the amount of 
material remaining to be acted upon decreases. 

A period of acceleration or induction is usually accounted 
for by inherent reaction resistance or by the reaction taking 
place in a series of intermediate steps, or by both. The 
factors generally considered important in producing a period 
of induction in photographic development are (1) the time 
required for the invasion of the developer, and (2) the time 
required to saturate the solution in the emulsion with silver 
after reduction begins. Neither seems to the writer to 
account sufficiently well for the long periods of delay observed 
with some developers.^ 

1 See Sheppard. S. E. and Meyer G., Chemical induction in photographic develop- 
ment. J. Amer. Chem. Soc. 42 : 689. 1920. 

77 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

It should be understood that the period of acceleration, 
or what is termed the period of induction, is ignored in the 
present discussion, as it is generally of short duration. The 
term refers to the delay before the reaction begins. 

It may be seen from a first analysis that velocity curves 
of the usual kind are obtained, and that these should be 
capable of interpretation by ordinary methods. The imme- 
diate problem, therefore, is to investigate the possibility of 
fitting a mathematical expression to the experimental data on 
velocity of development — that is, an equation which properly 
describes the course of reaction with time. Having found 
methods for doing this, it becomes possible to compare devel- 
opers and to discover what effect various conditions have on 
both the velocity and the end-point. 

PREVIOUS WORK ON VELOCITY EQUATIONS 

Hurter and Driffield first formulated the relation between 
the density produced for a given exposure and the time for 
which the plate had been developed, using the expression 

D ^ D^ (1-a*), (17) 

where D is the density at time /, Z> » the ultimate density, and 
a a constant. This equation was based on certain assumptions 
as to the arrangement of the silver bromide particles affected 
by light and as to the mechanism of penetration and reduction 
by the developer. These assumptions were later questioned 
and are now practically discredited. 

However, Sheppard developed in a different way an equa- 
tion resembling that of Hurter and Driffield. He found that 
the velocity of development was obtainable by the expression 

^ = if (I>„ - D), (18) 

where as usual D signifies the density at time ^, Z> » the ulti- 
mate density, a quantity proportional to the mass of latent 
image, and K a constant. Sheppard deduces that K is equal to 

A 

-^ , A being the diffusion constant for the developer, a the 

concentration of the developer, and S the ''diffusion path." 
This simple expression (equation 18) for a heterogeneous 
reaction is obtained by assuming that the velocity of develop- 
ment depends chiefly on diffusion processes. There is much 
experimental evidence to support this view. Nernst developed 
a theory for reaction velocities in heterogeneous systems, 

78 



THE THEORY OF DEVELOPMENT 

assuming that diffusion is predominant. But this theory 
evidently does not take into account all the phenomena 
encountered. 

Basing his reasoning on Wilderman's theory, Sheppard 
formulates for the case of ferrous oxalate a more complete 
expression for the velocity, which includes the view that 
development is a reversible reaction. Omitting the inter- 
mediate steps we may write this equation 

^-^=K{D^-D) , ,^^~^f!^^ (19) 

dt ^ ^ h {Dcx> — D) + d ^ ^ 

Here, a, 6, h, and d are constants which include such factors 
as equilibrium constants for the various reactions considered, 
equilibrium concentrations, and surfaces of the developable 
halide and of silver. 

By replacing b and a in such a way that b/a = />f , where 
f represents the equilibrium constant of development, the 
above equation becomes, on integration (as suggested by 
Colby), 

Upon closer examination, this relation is seen to resemble 
the integrated form of equation 18, which is 

In equation 20, p f represents the equilibrium value of the 
density developed, or the maximum density corresponding to 
-Dooin (21). i^ooas used in (20) indicates the density or mass 
of latent image which can be developed in the given case on 
infinite development, p f therefore tends to approach D » , 
depending on a number of conditions which will be enumerated 
elsewhere. Equation 20 differs from (21) in that there is a 
correction term in the former which, as Sheppard states, 
expresses the effect of reversibility, but is of importance 
only when there is a high concentration of bromide or of the 
oxidized developer. 

In ordinary alkaline development there are disturbing 
factors which are not included in equation 20, so that this is 
probably only an approximation. In fact, it has been 
obtained by a rather free use of assumptions as to the state of 
balance among the various reactions. Other reactions which 
disturb this balance may occur. Even if we could determine 

79 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

these disturbing influences and their effect the velocity func- 
tion would probably be so complicated that it could not be 
integrated to any useful form. Because of the very great 
difficulties of enumerating the constants p, f, d, and A, 
especially in alkaline development, and because of our present 
lack of knowledge of the mass of the latent image, it is impos- 
sible to test this equation. This matter will be discussed 
more fully after more experimental evidence has been 
presented. 

EXPERIMENTAL METHODS 

The genera! methods used by Hurter and Driflield and by 
Sheppard and Mees were followed in the present work, with 
such modifications as seemed necessary. Although in general 
the entire procedure resembles very closely that used in other 
chemical kinetic investigations, the reader who has but 
little occasion to interpret sensitometric data may find it 
somewhat confusing. For this reason the methods will be 
described in some detail. 

It is our purpose, first, to construct for a given constant 
exposure a curve showing the growth of density with time of 
development. Since (under usual conditions), density is 
proportional to mass of silver, there results a velocity curve 
of the usual type, showing the amount of silver produced at 
any time of development t. To obtain this it is sufficient 
to illuminate a plate uniformly, cut it up into strips, and 
develop the strips under constant conditions for different 
lengths of time. After fixing, washing, and drying, the 
densities of the various strips may be determined and plotted 
against the time of development corresponding to each 
density. But lack of sufficient uniformity in exposure and 
in sensitiveness of large plates, as well as a rather high per- 
centage of accidental errors, make this procedure less reliable 
than is required in the present investigation. 

Better results are obtained 
from the type of data menti- 
oned in previous chapters, and 
much of the same material can 
be used here. It has been 
shown that a series of plates, 
exposed in the sensitometer 
in a definite way, and devel- 
oped for varying times, gives 
_- a series of H. and D. curves 

Fig 28 the straight line portions of 



#. 



THE THEORY OF DEVELOPMENT 



which meet in a point (for practically all cases where emul- 
sion or developer do not contain soluble bromides). Fig. 28 
shows this for the normal unbromided developer. 

The toe and shoulder of the H. and D. curve are drawn 
for the upper and lower curves only. The lines represent the 
straight line portions of the H. and D. curves for plates 
developed for the times /i, etc., up to too • Similar data were 
obtained in the study of reduction potential by exposing plates 
in a sensitometer and developing them in pairs for varying 
times at a constant temperature in a thermostat, as previously 
described. 

If, now, we take a cross section of this series of curves at 
AB — i. e., use a standard value of log E, we have the informa- 
tion desired — the growth of density with time of development, 
the exposure being fixed. This method is somewhat more 
accurate than that of using a single flaghed plate, as first 
described, because if we use the value A, for example, as the 
intersection of the H. and D. smoothed curve, and ABj its 
value is influenced by the values obtained for the other densi- 
ties on the plate. That is, D^ represents an average of several 
values. Any one attempting sensitometric work on a large 
scale will appreciate some of the difficulties encountered as 
well as the desirability of these methods. 

As stated above, it has been found that with many of the 
developers used commercially and with good plates and care, 
uniform and consistent results may be obtained. But when a 
large number of different developers in which the equivalent 
concentrations of all the ingredients are always the same are 
used on a large number of different emulsions, many and wide 
variations are likely to occur, probably because some of the 
developers so made are not practically useful. But for 
purposes of comparison it is important to use developing 
agents at the same equivalent concentration, and this almost 
no previous workers (except Sheppard and Mees) have done. 

Returning to the discussion 
of the curves, the value for the 
density coordinates of the inter- 
sections ofAB with the straight 
lines plotted against the cor- 
responding times of develop- 
ment give a curve similar to 
that shown in Fig. 29, in 

which the period of induction 

' •«••«•) is disregarded, as explained 

Fig. 29 above. The curve, which is 



81 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

at least roughly exponential, has coordinates in terms of mass 
of silver and time of development. 

Experimental evidence of this kind has made it possible to 
study the properties of the curves, thereby explaining some 
of the relations between the photographic and the chemical 
properties of the developing agents used. In studying the 
velocity curves about 15,000 plates, exposed to acetylene 
screened to daylight quality in a sliding-plate (non- 
intermittent) electrically operated sensitometer, and developed 
in various water- jacketed tubes and tanks supplied by water 
at 20® C. from a thermostat, were examined. A constant 
value of the exposure was used in plotting the data. This 
exposure (log E = 2.4) represented 1.4 candle meter-seconds 
of screened acetylene. 

As stated in a previous chapter, all developers were made 
up to standard concentration and, unless otherwise specified, 
every developer contains in one liter 1/20 of the gram- 
molecular weight of the developing agent with 50 grams per 
liter each of sodium sulphite and sodium carbonate. No 
bromide or other substances are present unless so stated. 

A number of different emulsions and developing agents were 
examined, of which a few will be described. It is obviously 
impossible to record the results of many of the experiments. 

INTERPRETATION OF RESULTS 

Taking up first an analysis of the curves, the experimental 
results of previous workers as well as theoretical deduction 
have indicated that the relation between density and time of 
development at constant exposure may be expressed by an 
equation of the general type 

Kt = log J^"^ -, or D = Do. (1-e-^O. (22) 

U CO U 

This form would indicate that photographic development 
proceeds approximately in accordance with the law for a 
unimolecular homogeneous reaction, and that the concentra- 
tion of only one substance, the silver halide forming the latent 
image, is changing. Hurter and Driffield gave very meager 
data in support of their equation. The results obtained by 
Sheppard and by Sheppard and Mees, who investigated the 
relation much more thoroughly, especially for ferrous salts, 
indicate that the ferrous salts as developers (acid developers) 
follow this law rather closely. The results obtained with 
alkaline developers did not fit the equation so well, though 
the range of times used was too small for conclusive evidence. 

82 



THE THEORY OF DEVELOPMENT 

The writer, working over a much greater territory, finds many 
cases where the expression under consideration does not fit the 
results at all. The general conclusions reached, however, are 
capable of interpretation in harmony with Sheppard and 
Mees* results. 

It is hardly to be expected that the course of so complicated 
a process as photographic development in the presence of 
alkali could be described by so simple a law, since we know of 
changes which take place at various stages. Even if the law 
formulated in equation 22 held approximately over a consid- 
erable range, there are possibilities of several complications 
which might increase in importance as time went on, or be of 
more importance in the early stages of the process, thereby 
giving rise to departures from this law. For example, it is 
unlikely that diffusion of the developer into the gelatine emul- 
sion and of the reaction products out of it is the simple process 
assumed. Through absorption and various other physical 
phenomena, relatively large local changes in the concentration 
of the developer may occur. In such a case, development 
might approximate a second order reaction, the velocity being 
proportional both to the mass of latent image remaining to be 
reduced and to the concentration of the developer. That is, 
the quasi-bimolecular form, 

^ = K{Doo- D) {A - D). (23) 

may be a more nearly correct expression. A is the concen- 
tration of the developer at the beginning and D equivalents 
have been used at the time t. The integrated form of (23) is 

1 Do, {A - D) . 

^ = T '^^ (Do.-D)A' (^^) 

If over a range of times D is small compared with A (and 
this is often the case, a very small amount of silver being 
formed compared with the amount of developing agent 

A — D 
present), then ^ — is nearly equal to unity, and equation 24 

becomes practically the first order form. But if because of 
the tanning of gelatine, or by other mechanical means, inclu- 
sion of the developer occurs, so that its local concentration 
changes as time goes on, then a gradual departure from the 
first order law takes place. Something like this does occur, 
but the phenomena are undoubtedly more complex than the 
above explanation suggests. 

S3 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

It is not impossible that two successive reactions of the 
first order take place, giving rise to disturbing influences at 
the beginning. As Mellor points out, if ki and ki for two 
such reactions are widely different, the general trend of the 
reaction is a close approximation to a single first order reaction 
after ''initial disturbances," and the sooner they take place 
the greater the ratio ki/kt. 

It is not intended to advocate the view that photographic 
development proceeds through a well defined intermediate 
stage, but it has become evident that many complex 
phenomena are involved in the failure of the reaction to follow 
any definite law throughout its course, and so little is known 
of the mechanism of the oxidation of the reducing agents 
themselves that an intermediate reaction is a possibility. 

Whatever views may be held on the matter, the best previous 
work indicates that as a first approximation the velocity of 
development is expressed by the ordinary law of mass action 
for a first order reaction as given above — 

^ ^K{Do,-D) or, integrated, Ki « log tt^^Ss- (^1) 
at iy 00 — V 

Equation 21 may be applied to the density- time data as a 
beginning. From it or its exponential form Z> = Z>oo (1 — «~^0i 
it is evident that when / = 0, Z> = 0; and thus this equation 
represents a family of exponential curves through the origin. 
The density-time curve shown in Fig. 29 is certainly not well 
fitted by this form if the curve intersects the horizontal axis 
very far from the origin — that is, if the time of appearance is 
long. The method of applying equation 21 to the data is as 

follows : If the correct value of Z> oo is inserted and log jz — ^^-^ 

X/ 00 A^ 

plotted against the times corresponding to the observed values 
of D used in log^r — ^-^, a straight line of slope K is obtained. 

JJ CO JJ 

Since it is necessary, as shown above, that Z> = when ^ = 0, 
it is also a condition for this graphical solution that the origin 
be used as a point on the line — i. e., that the straight line pass 

Do, 



through the origin. When / = and Z) = 0, log ^ _ ^ 
also = 0. The equation D = Z?oo (1 - «-"^0 will fit the 

observed data over the range of times where log -=5 jz 

JJ CD JJ 

plotted against i gives a straight line. Bloch used this method 
incidentally to other work, but not enough data are given in 

84 



THE THEORY OF DEVEXOPMENT 

his account to throw light on the velocity equation. In the 
present application Z) oo is enumerated by trial and error, that 
value being taken which gives a straight line over the maximum 
range. However, in instances where equation 21 fits at all 
over any range, the value of Z> oo can be approximated from 
the experimental results, or may even be obtained by long 
development. The method of choosing the value of £>oo to 
be used and its experimental verification will be; given in 
greater detail later. 

It should be noted that logarithms to the base e aije used 
unless otherwise indicated. 

It was found that equation 21 fitted the data for only 
those cases where the time of appearance was exceedingly 
short, and then only for the early stages, usually for not more 
than three or at the most five minutes' 46velopment. Many 
cases could be presented b.ut space does not permit. All the 
experiments show that the development reaction follows the 
usual first order law for a time but that, on the whole, the 
latter law does not completely describe the process. This 
fact, observed repeatedly, makes it appear probable that new 
phenomena predominate as development proceeds. 



D 



-rr 



Fig. 30-A 















r 






— o 


\ 












" 














D 


^ 


^ 





















i 


T 






















■ 4 


f 






T ' 


1 


T- 






\ 1 




1 

























Fig. 30-B 
85 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



I I I f 1 

D 

' * *ss =— — « H X i - 



Fig. 30-C 



*^ u 1 



T 
Fig. 30-D 



In Fig. 30 A, B, C, and D the 
experimental results and the den- 
sities computed from the equa- 
tion D = Doo (1 - e—Kt) are 
given. For experiments A , B , and 
C an ordinary fast emulsion was 
used . The developers used were : 



A. M/20 Paraminophenol hydrochloride (pure); 

B. M/20 Pyrogaliol (pure); 

C. Same as a + 0.16 M potassium bromide; 

D. M/20 Monomethyl paraminophenol sulphate of high purity. 

Experiment D was carried out on a slow emulsion. 

The constants to be used in computing the densities were 
determined by the method described. The attempt was made 
in each case to fit the data over the maximum range from the 
beginning. A, B, and D are cases where the time of appearance 
is very short and the equation might be expected to apply. 
With each a value of Doo is necessary (in order to give 

log -j: — °° against / as a straight line through the origin) 

which is exceeded on longer development, as may be clearly 
seen from the figures. Fig. 30C is a case in which we could 
not expect the equation to apply. The time of appearance is 
very long. Therefore, the computed and experimental curves 
do not agree at the beginning, since the equation necessitates 
a curve through the origin, although no density is obtained 
for three or four minutes* development. For longer times 
insufficient data were secured, so that the usual departure in 
the later stages of development is not evident. 

Fig. 30D shows more markedly what was often found to be 
the case — that the equation under discussion fits the data 
at the beginning and usually can not be applied at any other 

86 



THE THEORY OF DEVELOPMENT 



stage of the reaction. The method of evaluating the constants 
for this experiment will be given later, and then the limited 
application of the simple first order equation will be evident. 
In this case neither a higher nor a lower value of Z^oo gives 
better agreement. 

In case the time of appearance is long — i. e., there is a 
considerable delay — the velocity equation can be corrected 
to a certain extent by allowing for the initial period of apparent 
inactivity. In equation 21 the correction is: 



^('-'o) =^°^P^' 



(25) 



where t^ is the induction period. In its exponential form 
(25) becomes D == Do, {I - e -^it-to) ). (26) 

The velocity of the reaction is the same as before, i. e.. 



dD 
dt 



= KiDoo - D). 



Equation 25 is the basis for applying the data. Log 



D 



00 



Doo-D 



is plotted against the time as before, such a value of Z> oo being 
chosen as will give a straight line when observed values of 
density are inserted, and the function is plotted against the 
corresponding times. The slope of the straight line is K 
and the intercept on the time axis gives /q, or the induction 
period. K is defined here in the usual sense, as the velocity 
when unit density remains to be developed. 

This equation is quite applicable, however great the period 
of induction, but very often the curves are fitted for the 
beginning of the reaction only. 

The curve in Fig. 31 illustrates the use of equation 26 on 
the data used with equation 21 in Fig. 30, curve C. The 
densities indicated by the circles are computed from equation 
26, and agree well with results obtained. 

Many results were computed 
for this equation. The general 
results tend to show that the 
corrected equation represents; 
the facts over a considerable 
range from the beginning of the 
reaction. The time range for 
which it fits varies widely, in 
some cases being for only a minute, while for others an ob- 
served range of fifteen minutes is satisfactorily fitted. From 

87 




Fig. 31 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

results which will be discussed later it is concluded that photo- 
graphic development represents a series of phenomena which 
change with time; that because of this fact it is impossible 
or at best very difficult to describe the entire process by one 
mathematical expression; and that, since the principal 
information desired is the value of Z> oo (the equilibrium point 
for given conditions), it is justifiable and of more value to 
turn our attention to better means of determining this import- 
ant constant, and accordingly to neglect the early stages of 
the reaction. 

The use of equation 25 often necessitates values of D oo 
which are obtained in a short time and which are greatly 
exceeded on longer development. Experiments show that 
in the average case the density continues to increase for a 
long time, and that the ultimate density is very likely to have 
a higher value than any reached within the usual limits. 

It was found in the great majority of cases that with a fairly 

reasonable estimate of Doo in the function log =r ^~- the 

U CO J^ 

latter would give a straight line over a considerable range 
when plotted against the logarithm of the time instead of 
against the time itself. It was evident that this method 
would be quite satisfactory as giving an empirical expression 
describing the reaction beyond the initial period, as the data 
were usually well fitted beyond two or three minutes' develop- 
ment. In other words, here the discrepancies between obser- 
vation and theory were at the beginning. This fact was very 
carefully examined in many cases, but in none of them could 
the early stage be represented by the expression used for the 
curve as a whole. 

When log =. — °°y^ is plotted against log t as just described, 
the equation for the straight line is 

K (log t - log Q = log -pf^F ' (^^^ 

the slope being K as before, and the intercept on the log i 
axis log Iq, In the exponential form this is 

Z? = Deo (1 - e-^»°8'/'o), (28) 

which, differentiated for the velocity, becomes 

^=-f {Da.-D), (29) 

88 



THE THEORY OF DEVELOPMENT 



So far as the writer is aware this is different from other 
^'corrected" forms for the velocity equation, many of which 
have been published. Equation 29 indicates that the velocity 
is inversely proportional to the time, a fact for which there is 
no satisfactory explanation at present. There may be some 
poisoning influence from oxidation products or the like, but 
experimental evidence for this is lacking. It seems possible 
that the velocity equation describes a complex effect from 
stored up oxidation products, tanning, and, in general, 
defective diffusion. Quantitatively, this effect is probably 
not the simple function of time required by the above relation, 
but the various factors are taken up in such a way that K/i 
gives a close approximation over a considerable range. Here 
^L is a constant, as before, but its significance must be different 
since it undoubtedly contains new factors. From equation 
29, K may be defined as the product of the velocity and the 
time of development when unit density remains to be 
developed. 

Fig. 32 illustrates quite com- 
pletely the entire process of 
fitting an equation to the 
data. The experiment was 
carried out with M/20 monome- 
thylparaminophenol sulphate 
on a Seed 23 emulsion. This 
developer (among others) in- 

variablyshowed wide departure 
^ Fig. 32-A f j.^j^ ^^ l^j.g^ order relation 

-J- = K {Dcxi — D), The open circles in Fig. 32A show 
at 

the observed densities. Using data from the smoothed curve 

Poo 

through these points, values of log jz =r- were computed 

for several estimates of Z? oo , and these were plotted against 
the corresponding times of development in Fig. 32B. The 
value of Z^oo used is indicated on each curve. It is evident 
that a value still lower than Doo = 2.00 is required to produce 
a straight line over any range. Referring to the data obtained 
it is seen that this value for the density is reached after about 
three minutes' development, and is much exceeded later. 
The value 2.00 or less is therefore wrong, and when examined 
in detail the method is found not to apply. On plotting 




values of log 



cx> 



D 
Dco-D 



against log t, a very reasonable value, 



89 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



Doo = 2.80, gives a straight line over the entire range observed. 
Fig. 32C shows this and the effect of using too high or too low 
values of D 00 . For the value Z> oo = 2.80, therefore, the relation 



is: 




Fig. 32-B 




K (log t - log Q = log 



D 



00 



Dc-D' 



in which the constants are as follows: 

K = 0.58; 
Da> = 2.80; 

log/o 1.05; 

t^ = .35. 

Putting the equation above in the exponential form 
D = Doo (1 - e ~*^°*! '/'»), and computing densities by 
means of it, with the constants indicated, the points in Fig. 
32a shown by black dots are obtained. This agrees very well 
with the results obtained. Obviously, it is unnecessary to go 
to the additional labor of computing densities, since the curve 

Deo 

^^ ^^^ ~n — ITn plotted against log t indicates the nature of the 

JJ CO -L/ 

agreement. 

Several experiments, detailed in Table 15 show the possi- 
bilities of the values of Doo as computed being reached on 
longer development. 

90 



THE THEORY OF DEVELOPMENT 



TABLE 15» 



dev. 



Min. 



0.5 
1 

2 
4 

6 

8 

10 
15 

20 

25 

30 
Computed 



Special 
Emulsion 



Experiment 

108 

Paramino- 

phenol 

D 




0.52 

1.12 
1.66 

1.97 
2.12 



2 
2 



27 
54 



2.72 
2.82 

2.86 

3.00 



See 30 



Experiment 

124 
Pyrogallol 


Experiment 

126 

Hydroqui- 

none 


D 


D 


0.52 
1.00 



0.26 


1.66 
2.38 


1.12 
2.00 


2.77 
2.96 


2.52 
2.85 

* 


3.06 
3.26 


3.06 
3.32 


3.36 
3.43 


3.40 
3.48 


.... 


3.60 


4.00 


3.80 



Experiment 

135 

Monomethyl 

paramino- 

phenol 

D 



0.60 
1.06 

1.66 
2.24 



2 
2 



52 
67 



2.79 
3.00 

3.10 
3.21 



3.60 



Experiment 

136 

Toluhydro- 

quinone 

D 



0.24 
0.77 

1.42 
2.20 

2.66 
2.98 

3.20 
3.48 

3.62 
3.76 



4.40 



Experiment 

140 
Paramino- 
phenol 



0.25 
1.58 

1.04 
1.53 

1.80 
1.98 

2.12 
2.43 

2.67 
2.87 

3.02 

4.20 



The values oi Dm appear very reasonable in all cases except 
perhaps the last two. However, the densities are still, after 
thirty minutes' development, increasing at a fair rate. In 
the last case (Experiment 140) the increase from the beginning 
is very gradual. There were isolated cases in which the 
difference between the highest observed density (usually after 
thirty minutes* development) and the computed Doo was 
rather large. In general, the evidence is so strong that the 
few experiments giving such differences are thought to be 
either erroneous or exceptions due to relatively unimportant 
phenomena. The computed values are subject to an error 
of between five and ten per cent. Aside from this error 
there is that due to the difficulty of measuring high densities 
with accuracy, so that the observed densities for long times of 
development are less reliable. The lower densities cannot be 
used because of the fog error. 

In the succeeding chapters the equation D = 
D oo (1 — ^ ~^ iog///o) ^iii be applied in determining develop- 
ment characteristics, and it is considered that in addition to 

* All developers M/20, with 50 grams of sulphite and 50 grams carbonate per liter. 

91 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

the above, the data given there support this equation. This 
seems to be the simplest equation which can describe the 
development process with any degree of accuracy. No doubt 
it will be possible to find a more accurate expression, but this 
will involve the use of correction factors or constants unknown 
at the present time, as in Sheppard's equation (equation 20, 
page 79). The use of one more constant than contained in 
our equation above necessitates separate experimental work 
for the determination of the new constant or one of the others. 

The following form has been suggested : 

D = Doo {1 " e -K(t-to)by (39) 

For X-ray exposures and in certain other cases this was found 
of somewhat wider application than the form we have used. 
But it contains an additional constant ft, which requires that 
one of the constants be determined by experiment, t^ will 
be most convenient, since it represents the abscissae of the 
intersection of the D-t curve with the time axis. Equation 
30 becomes, in the log form 

logK +b log (t - Q = log log j)^Zj) ^ (^1) 
from which is obtained 

dD 



dt 



= Kbt^^ (Da>-D). (32) 



By use of equation 31 the constants may be evaluated. 

Log log -=r — °° is plotted against log t for a straight line in a 

manner analogous to that already used. The slope of this 
straight line is 6, and the ordinate at log / = will be log K; 
Iq is obtained as indicated above. The entire process is some- 
what more lengthy than desirable. 

Twenty or more cases of widely different character were 
computed by both equation 28 (Nietz) and equation 30 
(Wilsey). The following table gives the results of the compar- 
ison, the experiments with bromide added to the developer 
being withheld for the time being. 

In Experiments 132 and 145, 50 gm. of sulphite per liter 
were used, as before, but no sodium carbonate. The concen- 
tration of the developing agent was M/20. The emulsion 
used was Seed 30. All the computations are for the standard 
exposure. 

92 



THE THEORY OF DEVELOPMENT 



TABLE 16 



Experiment 
Number 



129 
130 

132 

135 

137 

145 

133 
136 
144 
140 



Developer 



Dichlorhydroquinone 

Paramethylamino orthocresol 

sulphate 

Paraphenylene diamine hy 

drochloride (no alkali) .... 
Monomethylparaminophenol 

sulphate 

Paramino methylcresol hydro 

chloride 

Diaminophenol hydrochloride 

(no alkali) 

Dibromhydroquinone 

Toluhydroquinone 

Bromhydroquinone 

Paraminophenol hydrochloride 



(Wilsey) 



3.60 

4.00 

1.60 

3.60 

4.00 

3.60 
3.80 
4.00 
3.40 
4.20 



K 



.50 

.65 

.08 

.49 

.28 

.36 
.39 
.28 
.35 
.23 



.42 

.32 

.78 

.47 

.62 

.52 
.46 
.74 
.72 
.50 



(Nietz) 



D 



CO 



3.60 

4.00 

1.78 

3.60 

4.00 

3.60 
3.80 
4.40 
3.80 
4.20 



K 



.53 

.60 

.34 

.58 

.72 

.55 
.68 
.63 
.66 
.30 



These results show that the two equations yield practically 
the same value for the equilibrium constant Z> oo • As would be 
expected, K varies widely in some cases, Wilsey*s constant b 
influencing the variation, t^ is not recorded as it is deter- 
mined experimentally in Wilsey's method and in the other is 
an empirical constant larger than the observed t^. Wilsey's 
equation has the advantage that, although more complex and 
therefore more cumbersome, it more nearly describes the 
development process from beginning to end. It generally 
gives nearly the same values for Z) oo as the form D =^ Dm 
(1 - e "^ ^°8 </<^,) and in addition fits the beginning of the 
reaction somewhat better (beyond a small initial period of 
acceleration). In the experiments detailed in Table 16, 
equation 30 fitted the data from two or three minutes on, as a 
rule. It is somewhat difficult to attach much physical 
significance to the constants of this equation. 

CONCLUSIONS 

In Table 17 the various velocity equations under discussion 
are summarized. In brief, the findings for each case are: 

I. The simple form describes the early stages of the reaction, 
and these only under limited conditions. It is necessary that 
the time of appearance be very short and that the reaction 
be one which does not damp itself quickly — i. e., does not 
proceed rapidly to nearly its maximum. A density-time 
curve of nearly hyperbolic form (such as often given by 
monomethylparaminophenol sulphate and paraminophenol 
hydrochloride) cannot be fitted except for a very short range 
of time. 

93 





2 




1 




■S'3 






ft 


"2 


z 


5 


irt 


1 




1 


Q 




Q 








S 


Q 






S" 


Q 




1 


1 




Q 










Q 










Q 


J^ 


-a 


X 


t<T- 


!< 


1< 


i^ 


9N 


i\^ 








Z 


T 





THE THEORY OF DEVELOPMENT 

II. Much more satisfactory than I, but not generally appli- 
cable, it nearly always fails to fit the data in the later stages. 
This indicates that photographic development shows, after a 
time at least, departures from the first order reaction law. 

Equation II is useful especially in the determination of /q, 
which, computed by this equation, is practically the time of 
appearance and gives more reliable results than could be 
obtained by the visual method. 

III. This equation is of general application. It fits practi- 
cally all cases beyond the initial stage and is easily applied 
to the data, t^ is an empirical constant. In some experi- 
ments equation III yields values o( Dao which are quite high 
compared with those observed on long development, but it is 
quite possible that development continues for hours. Experi- 
mental verification of the value of the maximum density 
was obtained in nearly all cases. In some doubtful experi- 
ments development probably was not long enough and the 
densities obtained were too high to permit of accurate 
measurement. 

The fact that equation III indicates that the velocity is 
inversely proportional to the time is not satisfactorily ex- 
plained. The writer assumes that various complex phenomena 
affect the result in such a way that \/t in the velocity equation 
represents a close approximation to the real function. Further 
study would be required to determine the true relation. 

For general comparisons equation III is believed to be quite 
the most satisfactory form from the standpoint both of 
convenience and of accuracy. 

IV. Equation IV sometimes holds over a wider range than 
equation III and is generally equally satisfactory, though it is 
not so easily applied. One of the constants must be deter- 
mined experimentally, and doing this for t^ simplifies the meth- 
od. As an empirical expression this form most accurately 
describes the relation between time of development and 
density developed. 

V. Equation V cannot be applied because of the large 
number of unknown factors involved. 

Glancing down the column marked ''First Derivative,*' in 
Table 17, it is seen that the velocity function has been made 
more and more complex. More correction factors have been 
applied to account for the phenomena occurring. No doubt 
we should find if we could apply equation V that it would fit 
the data more perfectly than the preceding forms, as the 
corrections are larger in number. Equation V was deduced 

95 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

for development with ferrous oxalate by the use of certain 
simplifying assumptions. 

For alkaline development, which is so much more complex, 
any number of other involved equations might be set up, none 
of which would be more than a purely empirical expression. 
Since either equation III or equation IV supplies the need, 
and apparently gives a reliable indication of the end-point 
of the reaction, it seems justifiable to apply them to the data 
obtained. 1 

> Since this was first written, an equation based on the inclusion of terms for a paralysing 
action of reaction products has been developed by Sheppard (Phot. J., 59: 135. 1919) 
and is now being fovestigated. 



96 



CHAPTER VI 
Velocity of Development (Continued) 

Maximum Density and Maximum Contrast and 

their Relation to Reduction Potential and 

other Properties of a Developer 

CHARACTERISTICS OF THE VELOCITY EQUATION 

The character of the velocity equation 
D = Doo (1 - e -Kiogt/to) 

is more or less evident from inspection of the exponential and 
logarithmic forms and of the derivative, but the interpretation 
of these into photographic results is not so. clear. For this 
reason a brief analysis is made. If / ^ t^, D = 0. When 

/ = 00, Z) = Doo. The factor (1 - g-^iog///o) = ^ 



D 



and 



00 



therefore expresses the fraction developed at the time t. 

The effect of changing each of the three variables, K, t^ and 
D 00 , one at a time, is as follows : 

The higher the value of K^ the greater the density in the 
time /, and the greater the fraction developed. 

For variable t^, the fraction developed at a given time be- 
comes less with increasing t^. The entire curve {D — t) is 
shifted, each density being displaced horizontally by the 
increase in t^. Hence the density produced in a given time is 
decreased if t^ is increased. 

Increasing Doo produces greater density in a given time of 
development. The fraction developed is always the same for 
equal times. 





D-t curves K=3.10 (bottom), 
.30, .50, .80 

Fig. 33 



97 



D-t curves for to== .1, .5, 1.0, 
2.0, 3.0 and 4.0 (bottom) 

Fig. 34 



MONOGKAFHS ON THE THEORY OF PHOTOGRAPHY 

These relations are shown respectively by Figs. 33, 34, and 
35. 

The logarithmic form K (log i - logO ' — " 
obvious relations already described. 



The derivative is 
dl 



'■ (Da> 



-D). 



For the curve in Fig. 34, where (^ = 1 -0, S: = 0.3 and fl a> - 3.0, 
the velocity varies with time as shown by the continuous 

line in Fig. 36, in which the ordinate is -j- or the velocity. 

at 
These values represent a typical case. In practice there is the 
period of induction, shown by the dotted line. 









I 








] 


■=r 


























^. 


L 





fotD(D=l,* 

Fig. 35 



One of the chief characteristics of this equation is the length 
of time required to reach nearly complete development. For 
example, in Fig. 35 the fractions developed are as follows: 

t (1 -e-KiM'/'o) -fraction 

developed 

2 min. .43 

4 min. .57 

.63 

.67 



6 min 
8 min 
10 min 
15 min 



.70 
.74 



The time required for a definite fraction to be developed may 
be found by equating (1 - e — ^ io«'/'o) to the desired 
fraction, inserting the values of K and (^ and solving for t. For 

any fraction a the time t = t^e k "^ P^. For the theoretical 
curve in Fig 34 ((^ = 10, K = 0.3, and Da, - 3.0), for 



THE THEORY OF DEVELOPMENT 

which the velocity curve is shown in Fig. 36, the time for 

11 . ,.1 2.30 .^ ^. 2.30 

ninety per cent development is accordingly i^e "kT "(l-O) ^~T 

= 2,140 minutes. The higher the value of K and the 
lower the value of Z^, the shorter the time required. In most 
cases the time for ninety per cent development varies from 
thirty minutes to two or three hours. 



DETAILS OF THE EXPERIMENTS 

The procedure has already been outlined. The density- 
time curves secured for a standard value of the exposure 
(standard log E) were such that in all cases the densities lay 
well up on the plate curve. Other results showed that under 
these conditions the fog error is eliminated. In general, the 
density-time curve for these conditions gives the most reliable 
photographic data which can be secured. It is, of course, 
affected by any erratic behavior of the developer, but usually 
less so than other data for the same emulsion and developer. 

In all cases the times of development ranged from that 
necessary to produce the first visible density to at least IS 
minutes and, in the majority of cases, 25 to 30 minutes or 
more. As a rule the values of the constants Z> <» , -^, and i^ 
were found for the particular equation which fitted the data 
over the maximum range from the longest observed time back 
toward the beginning. In most cases there was little doubt as 
to these values. The average error in drawing a new curve 
and recomputing Z? oo , or in a repetition of the experiment with 
an ordinary developer and emulsion, is between five and ten 
per cent. In some cases the developer or the emulsion or both 
reacted in unusual ways, and the results were of little value. 
We believe the results given below to be as accurate as any 
it is possible to secure under like conditions. 

VARIATION OF MAXIMUM DENSITY WITH EXPOSURE 

If the density- time curves are drawn for different values 
of log E for a given developer and emulsion and the maximum 
density computed for each, different values of Doo result 
which, plotted against the logarithms of the corresponding 
exposures, give a new plate curve for the equilibrium condition. 
This is illustrated in Fig. 37. Each point represents a com- 
putation oi Dm from a density- time curve at the indicated 
log E value. The point M can be determined separately by 
methods already explained, it representing the common inter- 

99 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 












u 






/" 


» 






c 


?o 






/ 


^ 






• • MM ■ " 



Fig. 37 



Fig. 38 



section point of the H. and D. curves for the given conditions. 
In Fig. 37 the curves intersect on the log E axis as usual, and 
the value of a (the log E coordinate of the point of intersection) 
is 0.12. Consequently a straight line or plate curve may be 
drawn from M through the series of maximum densities, as 
shown. Increasing fog error prevents the locating of more 
points for the lower log E values. From other information 
and a consideration of the plate curves it does not seem logical 
to take a value of log E much lower than 1.4. 

The curve shown is for M/20 paraminophenol hydrochloride 
on a Seed 30 emulsion, a was determined from a number of 
experiments, using various concentrations of bromide. 

Fig. 38 represents a similar result from M/20 dibromhydro- 
quinone on a fast emulsion. Here a is obtained from but one 
determination with no bromide, and, therefore, is not so 
accurate as the preceding value. 

Such experiments show that within reasonable limits, the 
plate curve for infinite development may be drawn. Also, this 
method increases the accuracy of the determination of Z) <» at 
any particular value of log E. 

MAXIMUM CONTRAST ( Y oo ) AND A NEW METHOD FOR ITS 

DETERMINATION 

It is impossible to treat separately and in a definite order all 
phases of the present problem. For convenience in presenting 
the data, the maximum contrast, y » , will be discussed here. 



100 



THE THEORY OF DEVELOPMENT 

This term (yoo) requires careful interpretation. Too is 
the theoretical contrast reached on infinite development, or 
the slope of the plate curve when development has reached 
equilibrium. In practice this is never attained, since all 
developers and emulsions give appreciable fog on prolonged 
development, and the fog is greater the lower the density of 
the image. Hence the lower portion of the straight line of the 
plate curve in Fig. 38 will be raised by fog, the contrast thus 
being lowered. But the image tends to give the contrast 
indicated by the lines in Figs. 37 and 38 and this value is the 
characteristic constant for the given condition. The highest 
contrast which can be obtained practically will be reached at 
some intermediate time and will then decrease, the maximum 
being always lower than y cx> as defined. Fig. 39 shows these 

relations for a developer giving 
bad fog on prolonged develop- 
ment. Ya is the contrast ob- 
tained. At about eight and 
one-half minutes' development 
Ya is nearly equal to Yoo, 
which was found by the method 
described below. The devel- 
oper used was M/20 hydro- 
quinonewithoutbromide. With 
certain developers, and always 
when bromide is used, the 
maximum value of Ya niay continue for a long time, the 
period of decrease being delayed. Thus over an observed 
range of ten to fifteen minutes the y — t curve may be an 
exponential of the same type as the D — t curve. 

Where it is possible to draw the curve for the plate at 
maximum development, as in Figs. 37 and 38, Yoo can be 
determined from the slope of the straight line. If this can 
not be done, it may be computed as follows: The relation 
between density and gamma was expressed as 

Z> = Y (log E - a) + ft. 

From data on the D — y relation, especially with bromide, 
where upon prolonged development y <» is closely approached, 
there is every reason to believe that this relation holds at the 
limit; — that is. 

Do, - Yoo (log£ -a) +b; (33) 

from which 

101 




Fig. 39 




MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Consequently, 7oo may be calculateSd if I>a> is known (from 
a velocity curve at some particular value of log E) and the 
values of a and b are also known. In the complete study of an 
ordinary developer all these can be determined with a fair 
degree of accuracy. 

In Fig. 38, for example, the value of Dm at log E = 2.4 is 

4 20 
4.20, i> = 0, and a = -0.60. Therefore, r ex, ^t^ttt^^^W^ = 1.40, 

2.40 H- 0.60 

which the figure also shows. 

In Fig. 37, log E =1.8 (on the straight line portion). Dm =3.20, 

S 20 
b =0 and a = 0.12. Therefore, y « = , o^ nio = ^-^2. 

As previously stated. Dm is usually determined more ac- 
curately than a. Hence the accuracy of Yoo is governed 
largely by the accuracy of a. In Fig. 37, a is well determined. 
In Fig. 38 it is the result of but one set of observations. 

Some advantages of the above method, as well as its further 
applications, are discussed in a later chapter. (See Chapter 
X.) 



VARIATION OF Z) 00 AND Y cx> WITH THE DEVELOPER 

From the chemical standpoint Z> oo is more important than 
Y 00 , as a constant, the latter being merely a consequence of 
the former and of the relative location of the intersection point 
of the plate curves. From the photographic standpoint Yoo 
and the maximum value of Ya are of greater importance, as 
they are more obvious indicators of the character of the 
emulsion and of the developer. In the present instance we are 
interested mainly in the relations for the density at equilibrium, 
though results for the contrast are included. 

As a result of the experimental work, the view that the 
inertia point, the value oi Dm for fixed exposure, and y m are 
fundamental constants of an emulsion must be abandoned. It 
has been shown that the inertia may change with the developer. 
Sheppard and Mees also found this, but did not find the 
variation great, few developers being used. Aside from the 
work of Sheppard and Mees, very little has been done on the 
relations of Dm and Too as here considered. There is no 
doubt that some developers can reduce more silver for the 
same exposure, and to greater or less degrees of contrast, than 
others. Consequently, Dm and Yoo are not fixed constants 

102 



THE THEORY OF DEVELOPMENT 

for an emulsion. They may be used as such only when a 
certain developer is used, the variations then being assumed 
as due to the emulsion. 

The available evidence on these equations is given below. 
It is quite conclusive in many respects, and the continual 
recurrence of certain relations throughout the work strengthens 
the hypotheses. 

In the following results D cx> and K were found by means of 
the equation D= Doo (1 -g— ^^°«'/S applied to the 
D — t curve for a fixed exposure, a and h were found from 
Z> — Y curves for the sanje exposure, and y cx> was then 
computed from equation 34. 

Experimental conditions were constant for each set. 

Table 18 gives the results of experiments on an ordinary 
emulsion of medium speed. Values of the reduction potentials 
(TTgr) of the developers as previously found, are included for 
convenience. 

TABLE 18 

DEVELOPER TTb, I> oo Too 

M/25 Bromhydroquinone 21 3.7 2 .29 

M/20 Monomethylparaminophenol sulphate ... 20 3.9 2.33 

M/20 Chlorhydroquinone 7 2.7 1 .62 

M/20 Paraminophenol hydrochloride 6 3.2 1 .99 

M/20 Toluhydroquinone 2.2 3.3 1.75 

M/20 Paraphenylglycine 1.6 2.8 1.55 

It is evident here that the maximum density Z>oo and the 
maximum contrast y oo show a marked tendency to increase 
with increasing reduction potential. It was concluded from 
these data that the relation would hold, but further work 
showed exceptions to the rule. Hydroquinone, for example, 
though a developer of high bromide sensitiveness, (i. e., low 
reduction potential), can produce high maximum density and 
contrast. Consequently, as before when an attempt was made 
to give a classification on the basis of reduction potential, these 
exceptions show that the reduction potential is not always the 
chief governing characteristic. But we believe that the 
reduction potential often conditions the result, and that the 
general trend is in the direction of the results shown in Table 
18. 

Table 19 gives the results of four developers of Special 
Emulsion IX, a fast ordinary emulsion on patent plate glass. 



103 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

TABLE 19 

DEVELOPER ^Br D oo 7<» 

M/20 Pyrogallol 16 3.90 1.71 

M/20 Dimethyl paraminophenol sulphate 10 2.80 1.47 

M/20 Paraminophenol hydrochloride 6 3 .00 1 .40 

M/20 Paraphenylglycine 1.6 3.40 1.32 

Table 20 gives the data from twenty experiments on emul- 
sions for some of which the speed data are given in Table 10, 
Chapter IV. The results from three developers in Table 19 
are included. 

TABLE 20 

Variation of D » , 7 « and K with emulsion and developer 
I M/20 Pyrogallol 
* II M/20 Dimethylparaminophenol sulphate 
III M/20 Paraminophenol hydrochloride 



EMULSION 



Special Emulsion IX 

Special Emulsion VIII 

Special Emulsion XII 

Special XIII.., 

Emulsion 3533 

Special Bromide XIV 

Film Special Emulsion XV. 



TT 



Br. 



I 


II 


III 


Doo 


700 


K 
.53 


I>oo 


7oo 


K 


Z?« 


7oo 


3.90 


1.71 


2.80 


1.47 


.64 


3.00 


1.40 


3.50 


3.58 


.31 


2.50 


3.30 


.36 


2.10 


1.98 


3.60 


1.90 


.65 


2.80 


1.76 


.45 


3.15 


1.85 


4.00 


5.7 


.31 


4.00 


5.9 


.34 


3.50 


5.6 


4.00 


1.22 


.57 


3.20 


1.18 


.61 


4.20 


1.84 


5.00 


5.9 


.38 


3.60 


^ ^ 


.3( 


3.70 


3.40 


• • • • 


■ • * ■ 


• ■ • 


2.80 


1.84 


.27 


2.60 


2.00 


16 


10 


6 



K 



.58 
.33 
.50 
.21 
.40 
.26 
.56 



In analyzing the table and comparing the results it is seen 
that of the three developers at the same concentration, pyro- 
gallol can reduce the most silver for the same exposure. This 
IS an indication that on the average it probably develops 
greater theoretical contrast. M/20 paraminophenol hydro- 
chloride on Emulsion 3533 seems to be an exception to both 
rules. The relation between paraminophenol and dimethyl- 
paraminophenol is somewhat indefinite. These developers are 
nearer each other in reduction potential than is the higher to 
pyrogallol, and they resemble each other in chemical proper- 
ties to a much greater extent than either resembles pyrogallol. 
Consequently the above results are not surprising. Other 
results to be given below show that developers differing widely 
in their chemical nature generally develop to different degrees, 
but that compounds which react similarly do not differ much 
in this respect. 

To test this hypothesis further equivalent concentrations of 
a number of reducing agents were used on the same emulsion. 
In Table 21, these are arranged in order of /><», beginning 
with the highest. If two developers give the same Dm , the 



104 



THE THEORY OF DEVELOPMENT 

one with the higher K and lower t^ is placed first, it being 
assumed that in general the faster is the more powerful. 
Values of Z)oo , T oo , K, and t^ are included. 

TABLE 21 

Different developers on the same emulsion,^ arranged according to values 

of Doo 



DEVELOPER Z? oo ^Br 7 oo K t^ 

M/20 Toluhydroquinone 4.40 2.2 1.67 .63 1.35 

Diaminophenol plus alkali* .... 4.2 40 . 1 . 40 .60 0.6 
Paraminophenol* 4.2 6. 1.84 .44 1.0 

Paramino-metacresol 4.0 9 . 1 . 33 .72 1 . 24 

Methylparamino-orthocresol ... 4.0 23 . 1.26 .60 .Z^ 

Pyrogallol* 4.0 16. 1.22 .57 0.78 

Chlorhydroquinone* 4.0 7. 1.82 .52 1.3 

Hydroquinone* 3.8 1. 1.26 .95 1.80 

Dibromhydroquinone 3.8 8 . 1.27 .80 . 80 

Paramino-orthocresol 3.8 7. 1.27 .70 0.87 

Bromhydroquinone 3.8 21 . 1 . 73 .66 1.27 

Eikonogen 3.8 .... 1.43 .47 1.7 

Monomethylparaminophenol* . . 3.6 20 . 1 . 50 .58 .70 

Diaminophenol, no alkali 3.6 .... 1 . 63 .55 .36 

Pyrocatechin 3.6 .... 1 . 68 .52 .60 

Dichlorhydroquinone 3.6 11. 1 . 29 .53 .80 

Edinol 3.6 .... 1.22 .46 1.9 

Phenylhydrazine, no alkali 3.5 1.0 . . .• . .03 8.5 

Dimethylparaminophenol 3.2 10.0 1.18 .61 0.75 

Ferrous oxalate* 3.1 0.3 1.29 .55 0.97 

Benzyl paraminophenol less than 

(Duratol) 2.4 5 0.98 .34 2.27 

Paraphenylene diamine 1.7 0.4 0.58 .34 2.10 

Of the developing agents in Table 2 1 , those marked with an 
asterisk were of high purity, the others, excepting Edinol, 
Duratol, and Eikonogen, which were the commercial product, 
were somewhat better than commercial purity. 

This table does not by any means show that Z>oo always 
varies with the reduction potential, if the latter as previously 
measured is considered. But by this method, developers may 
be compared on a basis which is more or less independent of the 
observer, the degree of development, and numbers of special 
factors, and it is quite certain that several definite tendencies 
are indicated. These may be summarized as follows: 

^ Seed 30 Emulsion 3533 

105 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

D 00 and y oo for a single emulsion may vary greatly with 
different reducing agents. 

The value of the equilibrium density, D « , tends to be 
greater the higher the reduction potential of the developer. 
Exceptions to this rule may be accounted for in a number of 
ways, on none of which there is definite information. (See 
effect of sulphite on the maximum density obtained with 
hydroquinone. Chapter IX.) 

Y 00 shows an unordered variation with any of the proper- 
ties of the reducing agents. The lowest values are obtained 
for developers of the lowest reduction potential, but this re- 
lation does not hold with higher values. The intersection 
points of the H. and D. curves show similar unsystematic 
shifting. Because the speed of the plate is a function of some 
other property than the reduction potential of the reducing 
agent, y <» is also. For developers giving about the same 
plate speed, y <» tends to be higher with increasing potential. 

The unsubstituted aminophenols stand at the head of the 
list in Table 21, next the hydroxybenzenes and their halogen 
substitution products, and the amines are at the bottom. 

Hydroquinone and its mono- and dichlor- and brom- 
substitutions seem to be nearly identical in this classification, 
though their reduction potentials vary greatly. This may be 
because the mechanism of their oxidation is the same, and 
that other conditions also are similar, these masking any 
effect of reduction potential. 

Most cases which show a systematic variation of Z> oo with 
reduction potential also show systematic variation in what is 
erroneously termed the ''rapidity*' — that is, the time required 
to develop a definte intermediate density. If, for example, 
we note the densities developed in, say,- two minutes for each 
case, these will tend to be in the same order as the values of 
D cx> . This is evident from the character of the equation 

Z> = Doo (1 - e-^^o«'/S, (see also Fig. 35), since if 

K and t^ are nearly constant the density for a fixed time will 
vary with D oo • From the data given it will be seen that the 
variation in K is not great and that for many compounds t^ 
also does not vary widely. Some of these facts will be clearer 
from the following discussion. 

The analogy of the relations to Ohm's law may be roughly 
illustrated by the experiments detailed in Table 21. Of 
course we should not expect this relation to hold with any 
accuracy since velocity is not usually a reliable measure of 

106 



1 THE THEORY OF DEVELOPMENT 



potential, but the fact that it gives even approximately the 
right order for the developers below, as we know them, is inter- 
esting indirect evidence. By analogy 

,, , . Potential 

Velocity = 



Resistance 

or 

Potential = Velocity x Resistance. 

According to Nernst and others the principal factors of the 
resistance here are the diffusion phenomena. For two develop- 
ers used on the same emulsion, where the period of retardation, 
shown by /o» 3,nd the velocity constant K are each the same for 
both cases, the diffusion effects and minor factors of the 
resistance may quite reasonably be assumed to be equal. 
Hence the potentials will be directly proportional to the 
velocities for these conditions, or 



Potential Velocity 



'i f«>.-) 



X 



Potential Velocity dD K 

dt Std. / §td. 

Taking the velocities at the time / in both cases gives us for 

K{Da. -D) 
the above-r^TTj t^- If Kx=^ K std. the equation would 

be further simplified, but we have no instances in which this 
relation is more than approximately true. Consequently in 
the table below the developers are grouped according to equal 
retardation times and are intercompared by the ratios of the 
velocities. No more data were available for this comparison, 
as it is necessary to have both to and K the same for the 
different developers. The values given are for the developers 
and the emulsions referred to in Table 21. All velocities 
are computed for two minutes from the derivative of 
D=Dcx> (1 - e -^ ^°8 '/'o) , - i. e., dD/dt = (K/2), (Deo - D). 



107 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



TABLE 22 

Relative Reduction Potentials, Computed by Comparison of Velocities 

for Equal Resistances 



Potential, 



dD/Dt^^, , 



Potentialstd. ^^I^hox Std. 

All developers M/20 except ferrous oxalate, which is M/10. 



DEVELOPER 


/o 


K 


Doo 


After 
2 minutes 


Velocity at 
2 minutes 


Relative 
Potential 


PvrotEallol 


.78 
.75 
.80 


.57 
.61 
.53 


4.00 
3.20 
3.60 


1.27 
1.48 
1.38 


.67 
.52 
.59 


13 


Dimethylparaminophenol 

DichlorhvdroQuinone 


Std. - 10 
11 






Ferrous oxalate 


.97 
1.00 


.55 
.44 


3.10 
4.20 


0.70 
1.04 


.66 
.70 


5.7 


ParaminoDhenol 


Std. « 6 






Dibromhvdroauinone 


.80 
.87 


.80 
.70 


3.80 
3.80 


1.38 
1.40 


.97 
.84 


8 


Paramino-orthocresol 


Std. =» 7 






Paramino-metacresol 


1.24 
1.30 
1.30 
1.27 


.72 
.52 
.63 
.66 


4.00 
4.00 
4.40 
3.80 


1.30 
1.24 
1.42 
1.36 


.97 
.72 
.94 
.81 


9.5 


Chlorhvdroauinone 


Std. » 7 


Toluhydroauinone 


7 


Bromhydroquinone 


8.4 



The comparison is by groups, in each of which the condi- 
tions are approximately fulfilled. 

Arranging these values in order and comparing them with 
those previously found by the depression method gives the 
results in Table 23. 



TABLE 23 

Relative Reduction Potentials 

From velocity 
ratios 



Pyrogallol 

Dichlorhydroquinone 

Dimethylparaminophenol , 

Paramino-metacresol 

Bromhydroquinone 

Dibromhydroquinone . . . 
Paramino-orthocresol . . . , 

Chlorhydroquinone 

Toluhydroquinone 

Paraminophenol 

Ferrous oxalate 



13 
11 
10 

9.5 

8.4 

8 

7 

7 

7 

6 

5.7 



From previous 
data 

16 

* 

10 

__* 

21 

♦ 

7 

7 

2.2 

6 

0.3 



Although the above values are not entirely consistent, there 
is reasonable evidence that the assumptions of equal resistance 
are approximately correct, and that for such cases the veloci- 
ties calculated from the velocity function are a measure of 
the potentials. There is further evidence that a developer of 



* Not determined 



108 



THE THEORY OF DEVELOPMENT 

lower reduction potential reduces less silver. If bromide is 
added to a developer, its reduction potential is lower than if 
no bromide were present; and as its potential is lowered (more 
bromide is added) the maximum amount of work it can do, 
measured by the equilibrium density, Z>oo, decreases. The 
systematic variation oi Deo with the reduction potential under 
these conditions is easily understood, as no doubt the com- 
plicating factors which vary from one developer to another are 
constant here. Resistance factors due to addition of bromide 
are evident only in a change in t^j not in Ky as will be shown 
later. 

It seems quite probable that in many cases, comparing the 
velocities gives a rough measure of the reduction potential, and 
that the classification according to the values of the equilibrium 
point alone furnishes information in this direction. We should 
expect the more powerful developer to drive the reaction 
farther in the presence of its oxidation product. If, however, 
the oxidation products are removed by side reactions, or if 
other physical or chemical factors exert control over the de- 
velopment process, the end point and the velocity become a 
false measure of the energy. This is probably what occurs 
with hydroquinone and some of its substitution products, 
causing them to develop as much density finally as monome- 
thylparaminophenol, for example. 

THE LATENT IMAGE CURVE 

If different amounts of silver can be reduced by different 
developing solutions, what determines the limit to which the 
process can go? Can the latent image be fully developed? 
To these questions a definite answer can not yet be given. It 
is not possible at present to determine the quantity of latent 
image present in an emulsion which has been affected by a 
definite quantity of energy. However, a few generalizations 
concerning the relations between the developer and the 
quantity of latent image developed may be given. 

The grain is considered the unit of the latent image. If a 
single nucleus exists in the grain, the latter is developable. 
That is, it requires photochemical change of but one molecule 
to render the entire mass of the grain capable of reduction. 
The grain may contain any number of nuclei. Consequently 
different emulsions, even of the same speed, may possess 
entirely different numbers of developable grains (per unit 
area) for the same exposure, and the relation between the 
number of developable grains and the exposure may vary with 

109 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

the latter. Therefore, the only logical measure of the latent 
image is the number of nuclei formed per unit area; but the 
measure of the effective latent image, or of the reducible 
halide as understood here must be the number of developable 
grains. The only way the latent image manifests itself is 
by reduction to metallic silver. The result of this process 
may be studied in its relation to the energy received by the 
emulsion, and this relation Hurter and Driffield deduced and 
expressed in the form mentioned earlier in this monograph. 
But this throws no light on the questions under consideration. 
It is conceivable that grains containing more nuclei are more 
susceptible to development, though this point is open to dis- 
pute. However, if this were true, it would afford an easy 
explanation of the fact that more energetic developers reduce 
more silver. Some of the grains, being of different suscepti- 
bility, or of different oxidation potentials, would be reduced 
by a developer of one reduction potential, while for other 
grains the potential required would be higher. Accordingly 
with different developers there would be a kind of sorting 
process, each developer reducing what it could, the one of high- 
est reduction potential finally reducing the largest number 
of grains. 

Under these conditions the latent image would be con- 
sidered as never fully developed. That is, referring to Fig. 40, 
for log Ei, developer I produces Da>i, developer II, of higher 
reduction potential, reduces Dcon, and developer III de- 
velops to the density Dcom- 
But III does not necessarily 
develop all the grains; so it 
would be assumed that the 
limit of developability should 
be represented by Dl , and the 
latent image curve would lie 
above any actually obtained. 
Its straight line portion is in- 
""' Fin 4a dicated in the figure as the 

^ dotted line Li. 

In the discussion of equation 20 in Chapter V, it was stated 
that p^, the equilibrium value of the density. Dm, tends to 
approach the limit represented by the density of the latent 
image fully developed, depending on conditions. The latter, 
mentioned elsewhere, include all the complex phenomena of 
development. But nothing has been said as to the direction 
from which p f (Deo) approaches D^. It is possible that, as 
the complicating factors are eliminated from the development 

110 



THE THEORY OF DEVELOPMENT 

process, the limit Z)l niay be approached from either direction . 
Or it may be said that some developers (perhaps most), de- 
velop more density than that corresponding to the latent 
image, and others less. Perhaps it will be possible to find an 
''ideal'* developer which will reduce, grain for grain, all of 
the latent image. This hypothesis of course rests upon the 
assumption that there is considerable reduction due to con- 
tamination and autocatalysis, and to physical development. 
Apparently there is no definite proof that development by 
contamination — i. e., reduction of a grain adjacent to one 
rather fully exposed and undergoing development — takes 
placed However, this might be possible, provided the 
grains are sufficiently close together, if it is assumed that a 
single nucleus makes a grain developable. That some false 
nuclei (nuclei not formed by light) are present and promote 
growth of the silver deposit is more than likely, and that 
physical development takes place to some extent can not be 
doubted. It may therefore be supposed that the process of 
photographic development consists in building on to a skeletal 
framework of latent image nuclei, rather than in building up 
to the complete structure. This conception would account 
for the fact that so little energy in exposure is required to give 
visible density on development, the very small quantity of 
latent image being sufficient to initiate development, which 
spreads as it gathers velocity. 

According to this assumption the latent image curve might 
lie, say, at Za, or still lower, and under most curves obtained. 
There would seem to be considerable indirect evidence in favor 
of this view. 

* This question is under investigation in the Laboratory. — Ed. 



Ill 



CHAPTER VII 

Velocity of Development (Continued) 

The Effect of Soluble Bromides on Velocity 

Curves and a Third Method of Estimating 

the Relative Reduction Potential 



THE GENERAL EFFECT OF BROMIDES ON THE VELOCITY AND 

ON THE VELOCITY CURVES 



If the concentration of potassium bromide in a given de- 
veloper is varied and density-time curves (velocity curves) 
are plotted at a fixed exposure for each concentration, the 
effect of the bromide after a sufficient concentration is reached 
consists in a depression of the density developed in a fixed 
time, and in a marked increase in the period of retardation at 
the beginning. Only typical cases may be cited. Fig. 41 
gives the velocity curves for M/20 paraminophenol on Emul- 
sion 3533, with three concentrations of bromide. The ob- 
served densities are not given, the curves being those put 

through the observed points 
and the agreement being suffi- 
ciently good. Sixteen concen- 
trations of bromide were used, 
with the results given in Table 
31 (see page 87). Many simi- 
lar experiments were carried 
out. The curves are for fifteen 
minutes' development only, 
whereas development was con- 
tinued for thirty minutes. 

The result shown in Fig. 41 is often masked if a developer 
which shows greater retardation with bromide is used (as for 
example, hydroquinone) or if development is stopped too soon. 
Consequently published results on the effects of bromide on the 
velocity are somewhat at variance with each other and with 
those recorded here. The present experimental work indi- 
cates definitely certain results which accord throughout with 
the illustrations given, these being among the best and clearest 
examples obtainable. 

112 



« 









tn 










^ 




C«^LJBS* 




l^ 










T 





Fig. 41 



THE THEORY OF DEVELOPMENT 

Tlie curves show a marked parallelism for longer times. 
This suggests a depression of the curve, as for the plate 
curve, a subject to be treated later in this chapter. The 
values of Z>oo which are found from the equation 
Z)=Pqo (i_e~^^^* '/'«) decrease with increasing bromide con- 
centration, and the period of delay before development begins 
increases. The latter values, as indicated by the points on 
the time axis, were found by a special method briefly described 
on page 87. [Use of D = Z>oo (1 - .« - ^ ^'"'^OJ 

As is to be expected, if the velocity is plotted against the 
time it is found that well beyond the period of retardation the 

velocity has not changed. Con- 
sequently, the effect of bro- 
mide on the velocity consists 
entirely of a change of velocity 
at the beginning (an increase 
in the retardation). This is 
shown in the four curves in 
Fig. 42, where the slope of the 
D-t curves is taken as the ve- 
locity and plotted against the 
corresponding times. The in- 
itial period is roughly indicated. 




^^ 




r 



Fig. 42 



VARIATION OF Doo WITH BROMIDE CONCENTRATION. 
A THIRD METHOD OF ESTIMATING THE RELATIVE 



REDUCTION POTENTIAL 

The nature of the variation of 
the maximum or equilibrium den- 
sity, D 00 , with the bromide con- 
centration has been noted. When 
Z) 00 as determined for each con- 
centration is plotted against the 
logarithm of the corresponding 
bromide concentration a straight 
line for a considerable range re- 
sults. Typical cases for different 
emulsions and developers areillus- 
strated. Some of these are from 
the data for the determination of 
the density depression, d, used in 
Chapter II, but not all of that 
material could be used here, as the 
density-time curves were not al- 
ways obtained for a sufficiently 
wide range. Fig. 43 gives results, 

113 



LOCJao 




Fig. 43 




MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

for the four developers indicated, on Seed 23 emulsion of 
May, 1917, and Fig. 44 gives one curve for each, on different 
emulsions, as follows: 



^4- 




__ 




_ 




— 




^^ 




E 












Ill 













Fig. 44-A 


Fig. 44-B-C 


Fig. 44A 
Fig. 44B 
Fig. 44C 


M/2S Bromhydroquir 
M/20 Hydroquinone 
M/20 Dimethylparan 


one on Pure Bromide II: 
on SpecUl Emulsion Vlll; 



Fig. 45 shows the most com- 
plete curve obtained, the data 
being for M/20paraminophenol 
hydrochloride on Emulsion 
3533, an ordinary fast emulsion. 
Some of the curves shown 
are better than the average. 
Many of the less consistent 
F'e- 45 cases may be explained by the 

fact that it was not possible to secure a sufficient number of 
observations. All the data were treated as in the depression 
study, the observations being least-squared for slope and in- 
tercept after it was evident that a straight line function was 
under consideration. 

Table 24 is an analysis of the results for the slope. It was 
found that the slope resembles that for the depression curves 
and the values of m, the slope of the d-\og C curves as given 
in Chapter III, Table 4, which are reoeated here for compari- 
son. The slopes of the Z)(D-log C curves are negative, a 
fact which may be ignored for the moment, the numerical 
values being of chief interest. 



THE THEORY OF DEVELOl^MENT 

TABLE 24 

Comparison of Slopes of D oo-log C and d-\og C Curves 

Numerical Values of m 

SEED 23 EMULSION OF MAT, 1917 

i^ 00- log C d-\o% C 

Bromhydroquinone m = . 34 w =« . 20 

Monomethylparaminophenol .41 .28 

Toluhydroquinone .56 .52 

Paraminophenol .54 .36 

Chlorhydroquinone .40 .50 

Hydroquinone .82 .80 

Average .51 .44 

PURE BROMIDE EMULSIOK, II 

Bromhydroquinone .48 .28 

Chlorhydroquinone .38 .38 

Paraphenylglycine .66 .70 

Average .51 .45 

SEED 23 EMULSION OF JUNE, 1919 

Ferrous oxalate .35 .54 

Hydroquinone .44 .98 

Paraphenylglycine '. .36 .87 

Average .38 .80 

Seed 30 emulsion of July, 1919 

Paraphenylglycine .50 .54 

Pyrogallol 54 .42 

Dimethylparaminophenol .40 .46 

Average .48 .47 

Average for four emulsions .47 .54 

Mean of thirty cases m = . 50 

The data summarized in the table make it appear probable 
that the slope of the Z) oo-log C curve is always the same 
and equal to the slope of the depression curve. Wide varia- 
tions occur in relatively few cases; of thirty determinations, 
fifteen lie within twenty per cent of the mean and six more 
within thirty per cent. (It is difficult to attain greater accuracy 
under the conditions.) m is therefore accepted as the funda- 
mental constant expressing the rate of change of the equi- 
librium point with the logarithm of the bromide concentra- 
tion, and, at the same time, the rate of lowering of the inter- 
section point of the plate curves. The further bearing of 
these facts and other evidence from the table will be discussed 
in a following section. 

115 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



A new relationship for the maximum density, analogous to 
that for the density depression, may now be formulated. 
In Fig. 46 I and II are the Z><x> - log C curves for the develop- 
ers I and II used on the same emulsion. The slope of each = 
tan <f> = -m {m being considered positive) = - 0.50 (as 
found above). In general 



Z>oo = -f»(logC - logC'o), 



(35) 




UKcC 



Fig. 46 



where log C'o is the intercept on 
the log C axis. If the Z>oo- 
log C curve is a straight line, 
as shown, C© represents the 
concentration of bromide which 
is required to restrain develop- 
ment completely. That is, if 
the concentration of bromide 
present is C'©, this is just suf- 
ficient to prevent development 
at the given exposure. The lower region of the curve is, however, 
much in doubt, as at very high concentration of bromide new 
reactions are indicated. Also, the photometric constant 
changes (the silver becomes very finely divided and of a brown 
or red color by transmitted light) because of the state of divi- 
sion and perhaps also the change of distribution of the silver 
particles. So far as observed, therefore, the curve appears 
to dip down, as shown by the dotted lines. Hence we are 
unable to determine, without many observations of this 
region, the value of the concentration of bromide which will 
prevent development. It is very probable that for different 
developers the values of C'^ will stand in the same order and at 
about the same relative values as the concentrations required 
to stop development. 

Whether or not this is true, it is possible to compare develop- 
ers for the relative concentrations of bromide at which the 
same maximum density is produced. These will be in the 
same ratio as the anti-logs of the intercepts and probably in 
the same ratio as the concentrations required for complete 
restraint. The order of developers classified in this way for 
relative energy should be correct for compounds which do not 
shift the entire curve from its true position. According to 
relations pointed out in Chapter VI, some developers are able 
to reduce more silver than others of the same reduction po- 
tential because of physical or chemical factors other than their 
relative potentials. Possibly certain of these factors tend to 
decrease the amount of silver reduced. Consequently it is to 

116 



THE THEORY OF DEVELOPMENT 

he expected that some developing agents will not be in their 
true positions in a classification made in this way, as is prob- 
ably the case in the classification made by the previous method. 
However, the maximum densities are somewhat more accu- 
rately determined here, since several concentrations of bro- 
mide are used and therefore an average curve can be obtained, 
and some of the errors present in the second method are 
eliminated. 

The method of comparison used is as follows: The average 
value of w found is 0.50 (Table 25). A straight line of slope 
— m (see equation 35) was therefore put through the observed 
points in all cases, as in the usual treatment of such data. 
Thus a series of parallel Z> « — log C curves for a number of 
developers on each plate is obtained, as typified by curves I 
and II in Fig. 46. For each emulsion a convenient standard 
value of. Dm is taken (Z>oo std. in the figure), log Ci and log 
Ci are obtained, and from these, Ci and Cs, the concentrations 
of bromide required to bring the developers to the same 
equilibrium density. These are in the same ratio as (C'o)i 
and (C'o)2. Ci and d are the relative resistances required to 
produce the same value for the total amount of work done 
(in reduction). Again, in analogy to mechanical measure- 
ments, the amount of work done is proportional to the force 
at work only if all other conditions are constant. This is not 
always true in photographic development, so that this method 
of classification is less reliable than that previously described. 

Having obtained the values of the bromide concentrations 
which correspond to the standard maximum density, the 
developer for which the most consistent data were obtained 
was chosen as the standard for each emulsion. Assuming as 
before that the ratio of the resistances (bromide concentra- 
tions) measures the relative reduction potentials, values of 
the latter for comparison with previous results can be obtained 

C . C 

by multiplying the ratio -pr^ , that is, -p^ , by the value of 

Cstd. Ci 

TT Br found for the standard developer by the first method. 
Or, the relative reduction potential may be numerically ex- 

Cx 

pressed as equal to -pr-^ {'"' Br) std. 

Cstd. 

Table 25 gives the results obtained in this way. C is the 

concentration of bromide corresponding to the maximum 

density stated. The developers used as standards on each 

emulsion are indicated, with the values of ir Br as given in 

Chapter III. 

117 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



TABLE 25 

Concentrations of Bromide Required to give the Same D n for Different 

Developers on the Same Emulsion 

All values for m =0 . SO 

For D c» Relative Wfir as 

= 3.0 Reduction found 

Potential previously 

Ct 

Seed 23 Emulsion of May, 1917 ^ C^. ('^Br)std. 

M/25 Bromhydroquinone 25 83 21 

M/20 Monomethylparaminophenol .18 60 20 

M/20 Toluhydroquinone 035 12* 2.2 

M/20 Paraminophenol 018 (Std. and -6) 6 6 

M/20 Hydroquinone 002 1.7 1 

M/20 Chlorhydroquinone 003 1* 7 

M/20 Paraphenylglycine 0016 0.5 1.6 

For Doo 
Pure Bromide Emulsion, II =2.4 

C 

M/25 Bromhydroquinone 08 (Std. and =21) 21 21 

M/20 Chlorhydroquinone 013 3.4* 7 

M/20 Paraphenylglycine 028 5.9 1.6 

Seed 23 Emulsion of June, 1919 For D oo 

= 3.4 

M/20 Paraphenylglycine 06 3.7 1.6 

M/20 Hydroquinone 016 1.0 1.0 

M/10 Ferrous Oxalate 0014 .09 0.3 

Seed 30 Emulsion of July, 1919 For D » 

= 3.2 

M/20 Pyrogallol li (Std.-16) 16 16 

M/20 Paraphenylglycine 002 0.9 1.6 

M/20 Dimethylparaminophenol. . . .25 70* 10 

An asterisk is used to designate those results which are 
inconsistent with the determinations by the first method. 
The numerical values throughout are of greater range, but 
most of the developers are placed in the same order as before. 
After obtaining these results it was felt that the method is of 
some value, yielding additional information on the develop- 
ment process. 

The three methods used for estimating the reduction poten- 
tial are then: 

1. Measuring the density depression or lowering of the 
intersection point; 

2. Classifying according to the equilibrium point; and 
velocity; 

118 



THE THEORY OF DEVELOPMENT 

3. Comparing the concentrations of bromide at which the 
same amount of reduction is accomplished, or the concentra- 
tions required to restrain development completely. 

Of these the first is most free from error. The phenomena 
described above, throw more light on the density-depression 
method, and are accordingly of more importance in that con- 
nection than in giving determinations of the reduction 
potential. 

EFECT OF BROMIDE ON Y oo 

The effect of bromide on the contrast has received consider- 
able attention from time to time, but many of the published 
results and conclusions are erroneous. Some practical aspects 
of the subject are made clearer in the discussion of fog (Chapter 
VIII). Bromide in any normal developer may, as shown, 
cause a depression of density and cut down fog. Relations 
already indicated obtain, with the following practical result. 
The contrast obtainable in a given time may be lowered if 
sufficient bromide is present, but upon continued development 
the same contrast will be reached. The gamma for a fixed 
time of development is never increased by bromide except in 
so far as the increased contrast is due to the absence of fog. 
Practically, the printing contrast, Ya of the negative may be 
higher than when no bromide is used, because of the absence 
of fog. Gamma and the effective contrast should not be 
confused. 

Yoo is not affected by bromide except in excessively high 
concentrations. That is, on ultimate development the theo- 
retical contrast is independent of the bromide concentration. 
In practice the maximum effective contrast is usually (because 
of prevention of fog) increased by bromide to a certain extent. 
The relations for Too as defined are more important theo- 
retically, and for a given developer they aid in describing the 
character of an emulsion. 

The method for the determination of y oo has been given in 
Chapter VI. Knowing the values of a, 5, Z) oo , and log £, t oa 
is obtained from the equation 

^* " log£-a ~ k 

The effect for bromide on the separate factors is known, a is 
not changed by bromide. Hence the value log E — a is 
constant. Dm decreases as a straight line function of the 
logarithm of the bromide concentration, b increases negatively 
in the same manner and at the same rate. Hence there should 
be no effect on y oo . 

119 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Making no assumptions for the time being, we may consider 
the data obtained for y » . 

The following tables show for the highest bromide concen- 
trations, a slight lowering of r <» which is probably not real. 
At these high concentrations the photometric constant changes 
in that the density observed is too low in its indication of the 
mass of silver. Hence Dm is also too low, and y <» accord- 
ingly falls off as the concentration increases. But it is doubt- 
ful that the actual mass of silver decreases faster than the 
normal rate even for as high bromide concentrations as those 
used here. A study of the photometric constant would be 
of value in this connection. 





TABLE 26 










Doa- 


-h 


^a and h observed 




7 


» - log £- 


-A ' 


D 00 computed from 
observed D — T curve 


C (mols per liter of 
potassium bromide) 


M/20 dimethyli>ara- 

minophenoi on 
Special Emulsion IX 


M/20 paraminophenol 
on Emulsion 3533 







Too 

1.48 




7oo 

1.84 


.0025 








1.75 


.00354 




9 




1.80 


.005 








1.75 


.0078 








1.68 


.01 




1.45 




1.65 


.014 








1.71 


.02 




1.45 




1.71 


.0283 








1.70 


.04 




1.43 




1.65 


.057 








1.53 


.08 




1.47 




1.53 


.114 








1.59 


.16 
.32 




1.38 
1.31 


(1.37) 
Relation fails in this region 



I 



Mean 1.43 1.68 

This slight downward trend may be due entirely to a change 
of grain size affecting the density readings at the higher con- 
centrations, as noted above. In such a case all other measure- 
ments as recorded previously would be affected similarly, of 
course, but this does not change the relations. Within the 
limit of error (ten per cent) the value of 7oo is constant. 

120 



THE THEORY OF DEVELOPMENT 



Table 27 gives data for Seed 23 Emulsion of May, 1917, 
from material referred to in the foregoing. 



I 

8 



I 

O 



II 

8 
J- 



(0 

> 






o\ 

O 

G 
O 

B 






vo 



00 

o 



o 



s 



o 



o 
o 



U 

G 
O 

(d 
Ui 

c 
u 

^T 

O CO 

II >S. 
U 



fO o\ »o 
r*5 c^ *>• 



0\ CSI lO »o 

0\ >0 to IT) 



CSI CSI 1-H 




CM CM 



ra 



CM cq ^^ 



CM 



CM i-H 



CM 
lO 



c>a 00 0\t^ "^ 

• • _! 

CM '-I ^,-1 '-I 



00 






2:;S^ 



eo 



00 C^ On 00 ^ ^ cm 
tJ< 00 vo 0\ "^ *0 t^ 



CS| 



CM CM* 



CO O^ CM lO 

^ rj< vO VO 



r^ 



O 
»o 



vpT*<rJ<Tt<f*0000ro 



rq CM 



O 

C 
0) 

ji 

a 

o 

G 

S S <u 

RJ O C 

J3 C O 

a, 3 •- 
^ o o^ 

>^^ 



o 

c 

0) 

a 
o 

c 



i^g- -s 



C S 3 

S PQ H 



(4 

u 
pLi 



C 

o 

c: 

3 

?• 

u 

t-i 
IS 

u 



c 
o ^ 

2 o. 



121 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

In the experiments represented in Tables 26 and 27 fog is 
negligible where concentrations of bromide are above .005 to 
.01 M. The time required for a definite intermediate contrast 
increases rapidly as the higher concentrations are reached. 

PROOF THAT THE DENSITY DEPRESSION MEASURES THE SHIFT OF 
THE EQUILIBRIUM, i, 6,, d = (Dco)o " (^ m) x 

As more data were secured and subjected to more careful 
analysis, the evidence became stronger that the lowering of the 
maximum density for a given concentration of bromide is the 
same as that of the density depression. This corresponds to 
the expression 

d = {Dco)o - (^00 )x, 

where d is the density depression ( = — 6) and (Doo)o and 
(D 00 )x are the maximum densities for the concentrations (of 
bromide) and x respectively. Direct experimental verifica- 
tion of this relation is not possible because of the errors in- 
volved, as may be seen from an example, d for the concentra- 
tion X was found to be 0.40 + .05; (Doo)o was 4.2 + .4, and 
(Z)oo)x, 3.9 + .2. The error in the latter case is less, as the 
value is taken from a curve through several observations, 
while the former, (Z)oo)o» is a single determination. The 
value of {Doo)o — (^oo)x is therefore indeterminate and 
between the limits 0.9 and - 0.3, which renders the proof that 
d = (Z> 00 )o - (^ 00 )x impossible by this means. But other 
evidence is available. 

In discussing the equation 7oo = » °° j^ it has been 

shown that 7oo and a are constants independent of the bro- 
mide concentration, and that Dcx> and b vary at the same rate 
with bromide concentration, since —b=d and 

d =fw(logC -log Co), or 6 = -w(logC -logCo) 

Also, Doo = - m (log C - log C'^). 

That is, the rate of change of both b and Z>oo with log C is 
— m, (Both diminish as C increases, b becoming larger 
negatively.) Consequently, as the bromide concentration is 
increased a definite amount, the change in b is the same as that 
in Z> 00 . From the equation 

Doo-fe Day-b 



00 = constant = 



log E—a cons tan t 



it is evident that (Z>oo - 6) is a constant. Since both vary, 
the change in - b is always equal to the diminution in D 



CO • 

122 



THE THEORY OF DEVELOPMENT 

The change of b from C = to C = X is the density depression 
and it is therefore equal to the shift of the density equilibrium 
point, or (D 00)0 - (Z> 00 )x . 

Table 24, giving slopes for both d - log C and Doo - log C 
curves, furnishes indirect evidence in this same direction. 
This evidence lies in the fact that both sets of data are derived 
from the same sources, and that while there are accidental 
errors in some of the individual determinations arising from 
plate curves out of place, there is quite marked parallelism 
between the values in the two columns. A variation in the 
rate of density depression is accompanied by a similar change 
in the maximum density curve. This is due to a real relation 
between the two, as there is no factor common to the two 
methods of computation. 

As pointed out, there is no direct experimental verification 
of the fact that d = (-D00 )© — (^00 )x . Other cases examined 
showed more concordant results than expected. From the 
nature of the errors, the agreement is considered partly 
accidental. 

TABLE 28 

Comparison of Density Depression and Lowering of Equilibrium Density 

Seed 23 Emulsion of May, 1917 

C* d (Da,)o-(Dco)x 

M/20 Paraminophenol 01 .20 .22 

.02 .12 .08 

.04 .26 .35 

.07 .38 .45 

.10 .57 .63 

M/20 Chlorhydroquinone 01 .05 

.02 .22 .17 

.04 .32 .32 

.08 .55 .36 

.16 .67 .60 

.32 .80 .52 

M/20 Paraphenylglycine 01 .65 .16 

.02 .70 .35 

.04 .92 .92 

M/20 Hydroquinone 005 . 10 .02 

.01 .36 .04 

.02 .50 .33 

.04 !72 .55 

.08 1.12 .92 

M/20 Monomethyl paraminophenol 01 .14 .50 

. \j£ ... ... 

.04 .00 .60 

.08 .32 .90 

.16 .38 1.10 

.32 .50 .70 

.64 .48 1.00 

* Mols of potassium bromide per liter. (much too high) 

123 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



However, the change of Z>cx> with bromide, the constancy 
of Y 00 and of a, and the relations for b are so well established 
that no more direct proof is needed. The equation : 

d = (Z>oo)o - (I>oo)x 

is valuable as a step in the theory of the bromide depression 
method, since it shows that when the lowering of the 
intersection point of the H. and D. curves is measured as 
described in the first three chapters, in reality the change in 
the equilibrium is being measured; and this means that the 
method is capable of a satisfactory chemical interpretation. 
Further, the expression is useful in working out the more com- 
plete relations for the effect of bromide on the velocity curves, 
as is done below. 

EFFECT OF BROMIDE ON K 

The constant K in the velocity equation 

D ^ Deo (1 -e-^iog</<o) 

includes, (as it does in another form developed by Sheppard 
and Mees), the factors diffusivity, diffusion path surface of 
developable halide, and perhaps other unknown quantities. 
But K does not include the same set of factors here as it 
does in the other velocity equations, though the general 
nature of these quantities is as indicated. We should not 
expect a variation of bromide concentration to have any 
effect on K^ since the individual components are not supposed 
to change. That K in the velocity equation used is practically 
constant was proved by considerable data. Two complete 
cases are given in Table 29. 

TABLE 29 



Constancy of K with Variable Bromide Concentration 




Mols of 

potassium 

bromide 

per liter 


M/20 parami- 

nophenol 
hydrochloride 

on 
Emulsion 3533 


M/20 

dimethylpa- 

raminophenol 

on Special Mols of 
Emulsion IX. potassium 
^cperiment bromide 
106 per liter 


M/20 
dimethylpa- 
M/20parami- raminophenol 

nophenol on Special 
hydrochloride Emulsion IX, 
on Experiment 
Emulsion 3533 106 


C 


K 


K 


C 


K 


K 


.0 


.30 


.53 


.0283 


.48 


• • • • 


.0025 


.42 


• 


» • • 


.04 


.51 




63 


.00354 
.005 


.45 
.44 


• 
• 


■ ■ • 
> • • 


.057 
.08 


.44 
.51 




56 


.0078 
.01 


.51 
.37 


• 


1 • • 

44 


.114 
.16 


.44 
.47 




42 










.228 


.45 




1 • • 


.014 


.47 


• 1 


• • 


.32 


.45 




.37 


.02 


.43 




42 


.45 


.44 




1 • • 










Mean 


.44 




48 



124 



THE THEORY OF DEVELOPMENT 

In Wilsey^s equation, D = D^ (1 - e -^(^-'<») * ), K 
decreases and h increases with bromide concentration, as 
shown by computations from the paraminophenol data used 
in Table 30. As stated elsewhere, the maximum density 
calculated by this equation is often identical with that obtained 

from the form Z) = Doo (1 — ^ ""^ '°« '/'«>) . Differences may 

occur for other types of curves, but none was found in the 
cases computed here. (For methods see Chapter V.) Table 
30 gives the values of Z> oo and K obtained by the two equations 
and of h in Wilsey's equation. 

TABLE 30 
Effect of Bromide on K 



D = Doo 


(1-e- 


-K log ///o) 


D = Deo 


(1 


— e- 


-K{t- 


-Q *) 


C 


£)oo 


K 


Doa 




K 




b 





4.20 


.30 


4.20 




.23 




.50 


.0025 


4.00 


.42 


4.00 




.19 




.59 


.005 


3.90 


.44 


3.90 




.15 




.60 


.01 


3.50 


.37 


3.50 




.27 




.50 


.04 


3.30 


.51 


3.20 




.11 




.81 


.08 


3.00 


.51 


3.00 




.05 




1.11 


.32 


2.20 


.45 


2.20 




.03 




1.03 



VARIATION or Iq and /a WITH BROMIDE CONCENTRATION 

/q in the velocity equation Z> = Z>oo (1 - g— xiog<//o) is 
an empirical constant. When the D - t curve is well fitted by 
the equation, t^ indicates the length of the period of retarda- 
tion. Its relation to the bromide concentration is taken up 
here principally because it is necessary as a constant in an 
equation to be used later. 

^o is a straight-line function of the bromide concentration 
and the relation is 

(/o)x = ^ C + (Oo» 

where (/o)x is t^ for the concentration x, C is the concentra- 
tion X, and (^o)o is t^ for zero concentration of bromide. The 
straight-line relation is used for greater accuracy in the de- 
termination of (IqJq below. 

ttt , the time of appearance for a fixed exposure, has usually 
been measured visually, but this procedure involves too many 
indefinite factors. A better method is to read off from the 
D - t curves the time of development required for a definite 
low density. A density of 0.2 used in this way yields more 
reliable information than visual measurements. The time of 

125 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

development required to give a density of 0.2 at the standard 
exposure is a straight line function of C (the potassium bro- 
mide concentration) just as t^ is. Sheppard found ^a visual 
to be proportional to log C. As a matter of fact, this is an 
approximation over a range up to .05 normal, but the complete 
relations for t^ and ^ have been investigated and the expression 
found to be of the form stated above : 

If the intercepts on the time axis are well determined for 
the D - t curves, these values will be very close approximations 
to the true times of appearance. The values of these intercepts 
(/q and ^ ) can be found by fitting the equation 

to the first part of the curve only and thus evaluating t^. 
When this was done t^ was proportional to C and not to log C 
as before. 

EFFECTS OF SOLUBLE BROMIDES ON VELOCITY CURVES AS 
SEEN FROM MORE PRECISE DATA 

Having investigated the general effects of bromide on the 
velocity curves and on the various factors appearing in the 
velocity equation, it is possible to examine more closely the 
effect on the curves themselves, and especially on other 
relations between the equilibrium values obtained with differ- 
ent concentrations of bromide. The possibility that the 
velocity curves might be considered as shifted downward, or 
depressed, by the action of bromide in the same way that the 
plate curve is, was suggested to the writer. It was thought 
that if a suitable mathematical analysis of the data was made, 
additional information would be secured concerning the 
chemical phenomena involved. Experimental proof of various 
hypotheses was necessary, however, and it was found that for 
this purpose complete data as well as great accuracy were 
necessary. It was extremely difficult to meet these require- 
ments with some of the developers used, and consequently the 
experimental data were more limited than is to be desired. 
Again, however, there is abundant indirect proof of the assump- 
tions made. 

To increase the accuracy represented by the data, more 
plates were used for each bromide concentration, and develop- 
ment was carried out for longer times (up to thirty minutes) . 

All the quantities which are functions of the bromide con- 
centration (Dooy Iq, by etc.,) were determined from smoothed 

126 



n 



THE THEORY OF DEVELOPMENT 

curves through the various observations. A relatively large 
number of concentrations was used. Quantities constant and 
independent of bromide concentration {K and a) were averaged 
from all the observations. In this way a table of values was 
secured which contains the least error for the conditions. 

Table 31 contains .complete data for M/20 paraminophenol. 
The observed values and those obtained from smoothed curves 
through the observations are placed side by side. The nature 
of the agreement is thus shown in detail. 



TABLE 31 
Average Data for Paraminophenol ^ 



c 


I>co 


Doo 


d 


d 


K 


Too 


To) 


to 


to 


u 








V 










C9 


.C 












t 












^ 








«*-.s 




:i 










T 


V 








o2 




u 
























1 








L 


i 




Xi 


JC3 




Mols per li 
potassium bi 


o 




•a 

JQ 

O 




1 


11 

II 

uo 


«M OB 

a- 

ii 


u-oS 


1 

fa3 


8 


o 

1 


.0000 


4.20 
4.00 


4.00 
3.94 






.30 
.42 


1.84 
1.75 


1.80 
1.73 


(1.0) 
1.8 


1.9 
1.95 


.15 
.15 


.64 


.0025 


.0 


.0 


.67 


.00354 


4.00 


3.86 


.10 





.45 


1.80 


1.69 


2.0 


2.0 




.69 


.005 


3.90 


3.79 


.09 


.04 


.44 


1.75 


1.68 


1.85 


2.05 


.15 


.73 


.0078 


3.60 


3.71 


.22 


.12 


.51 


1.68 


1.68 


2.6 


2.1 


. . . 


.74 


.01 


3.50 


3.63 


.27 


.19 


.37 


1.65 


1.68 


.88 


2.1 


.15 


.74 


.014 


3.60 


3.56 


.30 


.27 


.47 


1.71 


1.68 


2.0 


2.2 




.79 


.02 


3.40 


3.48 


.32 


.34 


.43 


1.71 


1.67 


1.85 


2.2 


.20 


.79 


.0283 


3.40 


3.41 


.48 


.41 


.48 


1.70 


1.68 


2.5 


2.3 




.83 


.04 


3.30 


3.33 


.47 


.49 


.51 


1.65 


1.67 


2.65 


2.4 


.25 


.86 


.057 


3.20 


3.26 


(.30) 


.57 


.44 


1.53 


1.68 


2.3 


2.6 


.50 


.96 


.08 


3.00 


3.19 


.50 


.64 


.51 


1.53 


1.68 


4.0 


2.8 


.85 


1.03 


.114 


3.00 


3.10 


.62 


.71 


.44 


1.59 


1.67 


3.6 


3.2 


1.4 


1.16 


.16 


2.80« 


3.02* 


(.34) » 


.79 


.47 


1.37 


1 .67 


4.0 


3.7 


2.1 


1.31 


.228 


2.50 


.... 




.... 


.45 


.... 


.... 


4.5 


• • • • 


3.1 


• • • • 


.32 


2.20 


.... 


.... 


.... 


.45 


.... 


.... 


5.5 


a • • • 


4.5 


• • • • 


.45 


2.00 


.... 


.... 


.... 


.44 


.... 


.... 


6.5 


.... 


• • ■ • 


.... 



Average Average Average 
- .44 =1 .68 =1 .69 

^ Maximum fog at C =0, and after 30 minutes' development, was 0.60. 

* Do) falls off (error in photometric constant, etc). 

* Straight-line relation fails at about C > 0.16. 

A number of relations which have been pointed out are 
illustrated in this table. That Z>oo decreases with log C at the 
rate — w is shown by the agreement between the second and 
third columns. The constancy of K and of y <» are shown. 
We believe the results of the entire experiment, in which five 
hundred plates were used, to be as consistent and accurate 
as it is possible to secure under like conditions. The greatest 

127 




Fig. 47 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

error lies in the determination of the constants and variables 
for C =0 (no bromide), but this has been minimized by using 
the mean curves and extrapolating to zero. 

The averaged data thus ob- 
tained are more accurate for any 
concentration of bromide than 
the observations at that con- 
centration. By using these re- 
sults the densities for the D — t 
curves may be calculated, and 
these, with the exception of the 
initial period, where the velocity 
equation does not apply, give 
the result of observations on 
the velocity curves. Fig. 47 
gives the D - t curves for developement up to fifteen minutes 
with several concentrations of bromide. These were computed 
from the equation Z> = D <» (1 - e —^ ^<>« '/'<>) by using the 
averaged data from Table 31. These curves should not be 
considered merely computations, for teyond the initial period 
they represent the average results based on all the observa- 
tions. Many observations were made for the range up to 30 
minutes' development, and in nearly all cases the observations 
agree with the curves beyond the initial stage. The extent 
of the discrepancy between observations and computed curves 
at the beginning is indicated for the concentrations 0.0 and 
0.16 M bromide. The exact nature of the agreement between 
the observations and the computed curves may be seen by 
comparing the values of Deo, K, and t^ as observed and as 
obtained from smoothed curves. These may therefore be 
considered as experimental observations of greater precision. 

On examining the nature of these curves it is seen that they 
are parallel beyond the induction period. Hence, as previously 
indicated, the velocity is unchanged by bromide. Moreover 
it appears that the curves have been moved downward. That 
the lowering of the density at any time / (ignoring the begin- 
ning) is the same as the lowering of the maximum density, is 
demonstrated experimentally. That is, for D^ and Z>x (densi- 
ties for concentrations and x) at time /, 



Do -Dx = Deo -D 



00 x< 



Additional data similar to those in Table 31 are given in Table 
32 for M/20 dimethylparaminophenol on Special Emulsion IX. 



128 



THE THEORY OF DEVELOPKENT 

TABLE 32- 





Da. 


D„ 


d 


• 


d 




K 


T = 


r<n 


t. 


'o 








11 




T 

1 






h 


If 


1 

S 


1 






1 


ll 


1 


1 




1 


|| 


1 


3 


1 






; 


1 


1 




1 


II 


r 


l! 


1 




c 






















■<«. 'o 





3,90 


3.90 








,53 


1,48 


1.43 


,55 


.48 


-.73 


.01 


3.80 


3,86 


+ 


14 


■^os 




,44 


1 45 


1,45 


,41 


.49 


-71 


.02 


3.70 


3,70 


+ 


24 


,23 




,42 


1,45 


1,45 


,53 


,51 


-,67 


.04 


3.60 


3,56 


+ 


31 


.38 




.63 


1,43 


1,45 


,70 




-,58 


.08 


3,40 


3.41 


+ 


54 


.54 




,56 


1.47 


1.45 


.72 




-,45 


.16 


3.40 


3,26 


+ 


41 


.68 




,42 


1,38 


1,45 


.90 




-,22 


.32 


3.30 


3,10 


+ 


33 


,83 


(Extrapo- 


,37 


1,31 


1,44 


1,10 


i'.ll 


+ .11 












lated) 














.64 


3.10 


2,98 


+ 35 






.28 


1.28 




1,55 


1,72 


+ .54 



■ Maximum foi at C - 0. after [w«iiyiniauKed»dopiiieiit. -0,82, 
' d is low at high concentrations of bromide, due to secondary reaction. 

The relations for the depression of the curves are well shown. 
The assumptions made, all of which are founded on the results 
of the experiments, and all of which have been discussed, are 
summarized below: — 

With variable bromide concentration the following relations 
Jiold over a wide range : 

1. a is constant and independent of bromide concentration; 

2. b increases negatively with increase of bromide according 
to the equation. 

b = -m(iogC -logCJ; 

3. d, the density depression, ^ — b, and therefore 

d = m (logC - logC,); 

4. The course of the reaction with time of development is 
represented by the equation 

D = Da> (I - £-«:'<'«'■"•) 
for all concentrations of bromide; 

5. When the equation above is properly used, Doo represents 
the equilibrium value for the density; 

129 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

6. Dm varies with bromide exactly as b does. Hence 

d=Dcoo~^oox\ 

7. K is constant and independent of the concentration of 
bromide ; 

8. /q is a linear function of the concentration of bromide; 

9. Dq — Dx = Dooq — Doo X beyond the initial period. 



THE DEPRESSION OF THE VELOCITY CURVES 

The velocity equations for a given developer with concentra- 
tions of bromide .0 and x (C = and C = x ) for a common time 
of development, /, are : 

forC = iDo = ^ooo (1 - e-^»°«'/S) (unbromided) (36) 
Dx = Z>oo X (1 - e-^»o8'/^) ( bromided ) (37) 
and the depression is the difference between the two at the time 
/. Such a value of t must be chosen that only the region where 
the velocity is not affected by bromide (i. e., beyond the 
period of induction), is considered. It is convenient to express 
equation 37 somewhat differently. The general form of the 
velocity equation is 

D ^ Doo (1 - e-^io«*/S, (38) 

which may be written 

K (log t - log tj = log 

Doo 



D 



C30 



Do.-D' 



(39) 



Log 



Do. - D 




Fig. 48 



plotted against log / is a straight-line of slope K 



and intercept log t^ on the log t 
axis. It has been shown that K 
is constant for variable bromide 
concentration. Hence, two ve- 
locity curves of the same form as 
(39) forC = OandC = x have the 
same slope Kj and may be drawn 
as parallel straight lines. Refer- 
ring to Fig. 48, then, K is the same 
for both cases — that is, a^, = a x- 
In the triangle ABC, AC is the 
difference between the inter- 
cepts. Calling AC, Xr and AB, 

Yr, 



/, 



Xr = log /o - log ^o = log 



130 



o 



THE THEORY OF DEVELOPMENT 



o 

X 



and Yr = KXr = Klog-T' - (40) 

o 

o 

The equation for the bromided curve (C = x) is 

Poo 

log-R V = Klogt -- K log t, , (41) 



Z X 



But from the equation 40 

K log <o, = Y, + is: log /oo • (42) 

Making this substitution in (41) and converting to the ex- 
ponential, we may write the equation for the curve C = x in 
the form 

D^ =Da>^ (1 -e-^io«'/<o+Yr). (bromided) (43) 
on now subtracting (43) from (36) we get the depression 

Z>^ - Z>^ = J9oo o (1 - e-^^^^'^K) - Z>c»,(l - e-^»o8'/^+Y,) 

(44) 

which by algebraic treatment and use of the assumption, based 
on experimental evidence, that D^— Dx = Day^ — Z^oox 
reduces to the expression 

Z)o -^x - Doo^ (eY- - 1). (45) 

Also, Z>a>o - -^003, = Doo^ {cYr - 1) 

from which D^^ e^' =-Dooo- (^^) 

Substituting the value of Yr gives for the depression, from 
equation 45: 

d =Z>coo- Do.. =^o -Dx =^oox (^""^^^IT -^) ("^^^ 
and the relation 



% 



^^x^^'^^'V = ^ 



00 o' 



First let us test equations 47 and 48 by using them on the 
results given in Tables 31 and 32. Table 33 gives the results 
for paraminophenol (See Table 31). All logarithms are to 
the base e. 



131 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

TABLE 33 

Depression of Velocity Curves by Bromide. M/20 paraminophenol on 
Emulsion 3533 

Tabic from 
31 Fig. 47 



.0025 


.67 


3.94 


1.01 


3.98 


.04 





• • • 


.06 


.00354 


.69 


3.86 


1.022 


3.94 


.08 





• • • 


.14 


.005 


.73 


3.79 


1.041 


3.95 


.16 


04 


• • • 


.21 


.0078 


.74 


3.71 


1.045 


3.88 


.17 


.12 


■ • • 


.29 


.01 


.75 


3.63 


1.046 


3.80 


.18 


.19 


.24 


.37 


.02 


.79 


3.48 


1.068 


3.72 


.24 


.34 


.36 


.52 


.04 


.86 


3.33 


1.102 


3.67 


.33 


.49 


.50 


.67 


.057 


.96 


3.26 




3.75 


.49 


.57 


• • • 


.74 


.08 


1.03 


3.19 


1.188 


3.79 


.60 


.64 


.67 


.81 


.114 


1.16 


3.10 


« • • • • 


3.90 


.79 


.71 


• • • 


.90 


.16 


1.31 


3.02 


1.342 


4.05 


1.03 


.79 


.96 


1.02 



Column No. 

1 2J 3J 4 5 6« 7J 8 9 

D900 " 4 .00 

Log to « .64 

K « .44 

1 These values are taken from Table 31. 

* Computed depression. 

* Depression from mean curve through observations. 

If equations 47 and 48 hold when applied to the data, the 
values in column 5 will always equal 4.00 (see equation 48) 
and the values in columns 6, 7, 8, and 9 will be in agreement 
(equation 47). The relations derived are very closely ap- 
proximated. In column 5 there is a slight drop in the values 
for the intermediate concentrations, (Poo © "" -^oo x) in 
column 9 is a little high, apparently because Z>cd © ^s too high 
(i. e., the value 4.00 as determined from the average of the 
observations at other concentrations should be about 3.90). 
Column 5 also indicates that D o© © is somewhat high. But the 
agreement is fairly satisfactory considering the nature of 
photographic data of this kind. 

Table 34 gives similar computations for M/20 dimethylpara- 
minophenol based on data given in Table 32. 

TABLE 34 

Depression of Velocity Curves by Bromide. M/20 dimethylparamino- 

phenol on Special Emulsion IX 
log <o « - .73 
K'^o* 0.46 



_ _ d 

D _ DfXio—DtKix j= from ob- 



curve 



.01 


-.71 


1.009 


3.86 


3.90 


.04 


.04 


.08 


.02 


-.67 


1.028 


3.70 


3.80 


.10 


.13 


.23 


.04 


-.58 


1.071 


3.56 


3.82 


.34 


.25 


.38 


.08 


-.45 


1.138 


3.41 


3.88 


.49 


.47 


.54 


.16 


-.22 


1.264 


3.26 


4.13 


.64 


.86 


.68 


.32 


+ .11 


1.471 


3.10 


4.55 


Does not hold, to 


for these cases 


.64 


+ .54 


1.794 


2.98 


5.33 


is too high 


■ 










Dooe 


= 3.90 









132 



THE THEORY OF DEVELOPMENT 

The agreement is satisfactory, but it is seen that in both 
cases the relations fail at concentrations of bromide greater 
than 0.16 M. Indeed, as indicated elsewhere, the fact that 
the various 'Maws'' seem to break down in this region may be 
because of our inability to determine the mass of silver by the 
measurement of density, as at about C = 0.16 M. in both 
cases the deposits begin to appear brownish by transmitted 
light. However, from other data it is suspected that a reaction 
occurs between the bromide and the silver halide at very high 
concentrations, or that the bromide exerts some physical 
influence. 

By combining certain of the equations derived here with 
others previously established new relations may be shown, 
most of which, however, have little practical application. 

The general conclusions relative to this subject may be 
summarized as follows: 

A comparison of the bromide concentrations at which two 
developers can produce the same maximum density gives a 
comparison of the concentrations theoretically required to 
prevent development at the given exposure. In general this 
gives a measure of the relative reduction potentials of the two 
developers, but it will not serve for those cases in which factors 
other than the reduction potential control the character of 
development. 

The maximum contrast, y <» » is unchanged by bromide. 

The depression of density, or lowering of the intersection 
point, d, has been shown to be equal to the shift of the equili- 
brium, or 

The velocity constant K is not affected by bromide. 

/q and /a » the retardation time and time of appearance re- 
spectively, are linear functions of the bromide concentration. 

The only effect of bromide on the velocity of development is 
a change during the period of induction. After this stage the 
velocity is independent of the bromide concentration. 

The effect of bromide on the velocity curves consists in a 
downward displacement beyond the initial period. This dis- 
placement is equal to the normal density depression rf, as 
indicated by equation 47 above. 



133 



CHAPTER VIII 

The Fogging Power of Developers and the 
Distribution of Fog over the Image 

THE NATURE OF FOG 

Though important from theoretical and practical stand- 
points, the subject of so-called chemical fog has received 
relatively little attention from photographic investigators. 
Some more or less incomplete microscopic studies have been 
published, but they are not of importance in the present 
discussion. Theoretically it should be possible to secure from 
the study of fog much information on the mechanism of the 
selective reduction of the latent image, the fact on which the 
entire practical application of photography rests. Present 
knowledge of the properties of developing agents does not 
offer any conclusive evidence as to which of these properties 
is the factor controlling this selective action. 

No attempt has been made in the present instance to investi- 
gate the subject generally, but material gathered in connection 
with work already described furnishes much information on 
fog, and additional experiments have been carried out where 
necessary. Several series of experiments performed with 
different developers on the same emulsion gave data on the 
relative fogging powers of developers, and miscellaneous 
results throw light on several much-discussed questions. 

The term fog as used here refers to the deposit resulting from 
the development of "unexposed" silver halide. Inasmuch 
as it is impossible to prepare emulsions which do not contain 
some grains affected by light, however small the proportion 
of such grains may be, some of them may be finally reduced, 
thus contributing to the result known as chemical fog. Fur- 
thermore, it has been shown that certain compounds have the 
power of rendering silver bromide developable, turpentine 
being a notable example. Without considering the nature 
of this action, we shall refer to substances of this kind as having 
the power of nucleation — that is, of forming nuclei in the 
presence of which reduction and deposition of silver may 
ensue. Aside from such phenomena, radio-active substances 
are present everywhere to some extent, and they no doubt 
contribute developable grains to the aggregate. Hence an 
emulsion always contains reducible nuclei. The deposit 

134 



THE THEORY OF DEVELOPMENT 

resulting from the developable grains in an "unexposed'' 
emulsion (due to light, radio-activity, and chemical nucleation) 
is termed emulsion fog. 

It is not known how large a proportion of the total reduction 
of presumably unexposed silver bromide is due to emulsion 
fog. Though this percentage is probably relatively small, there 
is at present no verification of this. Although nucleation may 
be effected in different ways, the resultant grains probably 
do not differ. From what has been said it is evident that the 
nature of the developer has a considerable effect on the degree 
to which the development of these unexposed grains takes 
place, and its influence on this may differ from its effect on the 
development of the image because of the greater dispersity 
and different arrangement of the fog grains. Considering 
this, it is not necessary to account for all of the fog by assuming 
that new grains are rendered developable, since it is possible 
that most of the grains forming the fog image possess nuclei 
and are developable before the developer is applied, the differ- 
ence in the developing properties of different reducers account- 
ing for the variation in the fog density obtained. However, 
if this were true, and no other grains were developed, we should 
probably find the fogging power of developers standing in the 
same order as certain of their chemical characteristics, 
especially their reduction potentials. This has not been 
found to be the case. Therefore the conclusion is that in 
addition to grains rendered developable by the action of light 
on the emulsion and those in the emulsion which are develop- 
able from whatever cause, there is development of new grains 
which are not capable of reduction except by some specific 
action of the reducing solution. This is termed chemical 
fog, and is believed to predominate. 

Chemical fog may be produced in several ways and may 
vary in physical and chemical structure. Like the image, 
it may result from either chemical or physical development. 
If from chemical, the reducing agent or its salts are supposed 
to have the power of nucleation, in which case the grain is 
developed in situ. The fog may differ from the image grain 
in rate of development, in internal structure, and in arrange- 
ment. Oxidation products of the developer may form a 
complex with the spongy silver in either case, whether develop- 
ment is chemical or physical. Fog developed physically 
results from solution of the silver bromide reduction, and 
deposition from the solution on nuclei in the emulsion. In 
this case the structure of the fog image is usually decidedly 
different from that of the developed image, and the fog lies 

135 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

partly on the surface of the latter. It is often so fine-grained 
that it has selective scattering power for light, in which case 
it is differently colored in reflected and in transmitted light. 
The terms pleochroic and dichroic are applied to this kind of 
fog. Dichroic fog is common and often troublesome. 

We cannot distinguish, except in a very general and quali- 
tative way, between fog due to these various chemical causes, 
nor between chemical fog and emulsion fog, for that matter. 
Consequently we must deal with the entire resultant effect. 
It would not be surprising to find (as was found) that the 
relations for fog are somewhat different from those for the 
image. 

Mees and Piper believed fog to be chiefly a matter of 
reduction potential. The latent image being at a higher 
oxidation potential than unexposed silver bromide, the 
selective reduction of the latter results from proper adjustment 
of the reduction potential of the developer. A developer of 
too high potential reduces the unexposed silver bromide. 
Also, the reduction potential necessary for development of 
either exposed or unexposed halide is lowered by increased 
solubility of the silver salt in the developer. Accordingly, 
solvents of silver bromide are powerful fogging agents. This 
is illustrated by thiocarbamide which, Mees and Piper state, 
so increases the solubility of the silver bromide that a developer 
to which it is added reduces the whole of the silver halide. 
Time is required, however, for the thiocarbamide to lower the 
resistance sufficiently, so that normal development begins 
first. The bromide in the gelatine emulsion then raises the 
resistance (locally) and prevents the action of the thiocarba- 
mide. The extent to which the fog is prevented is propor- 
tional to the amount of bromide locally liberated. 

Now, although the action of thiocarbamide is accurately 
described by Mees and Piper, there is one fact which is not 
explained by the assumptions made. It appears that the 
developer can reduce no more silver with the thiocarbamide 
than without it. The action of each substance seems to pro- 
ceed independently, except that, as stated, the by-product 
of one interferes more and more with the other. But the 
thiocarbamide does not make it possible for the developer to 
reduce any more or different grains than it could alone. This 
experiments recently carried out tend to show. 

Consequently the explanation previously given must be 
modified by assuming the thiocarbamide capable of nucleation, 
rather than able, because of higher reduction potential, to 
reduce silver grains which the developer can not. Further- 

136 



THE THEORY OP DEVELOPMENT 

more no connection can be shown between fogging power and 
reduction potential, it being a notable fact that many 
developers (in the purest possible state) of remarkably low 
reduction potential can produce excessive fog in the absence 
of alkali. It therefore seems more logical not to begin with 
the assumption that fogging propensity is governed by reduc- 
tion potential. 

There is little doubt, however, that increased solubility of 
silver bromide is associated with greater fog density. The 
production of nuclei, or the chemical action resulting in this, 
is doubtless increased by higher solubility — i. e., greater 
concentration — in the same manner that other chemical 
reactions are. 

FOGGING POWER 

The term fogging power has been used rather freely thus far, 
though no precise definition of it has been given. Mees and 
Piper defined it as 

^ K ' 

where F is the "rate at which the developer reduces unexposed 
silver bromide, and K is the rate at which the image is 
reduced." F is not actually the fogging rate, but these 
investigators found that fog plotted against time of develop- 
ment gave a straight line through the same origin for different 
cases, from which they concluded the fogging rate to be 
proportional to the density at any time. Accordingly they 
used observed densities (for fog) at ten minutes* development. 
In certain cases this did not prove satisfactory. 

i^ is the constant used in the equation D = Z>oo (1- e ""^0- 

The writer finds from extensive experiments that the above 
relation for F is inaccurate. As shown below, the fog-time 
curve is not a straight line, and for different developers 
the origin may vary greatly. Also, the velocity equation 
D =Z)oo(l — e ""^0 is not sufficiently well followed by the 
development of the image. (See Chapter V.) The definition 
of fogging power should therefore be revised. 

It has been shown that the normal development process 
(for the image) is described fairly accurately by the equation 

Z> = Z>eo(l - e-^»°8'/S. (28) 

Experimental data show that the fog-time function is also an 
exponential. Accordingly it was attempted to fit the expres- 
sion above to the fog curve, but without success. However, 

137 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



it was found that the fogging action could be expressed by the 
first-order reaction law with a correction for the period of 
delay. This equation, discussed in Chapter V, has the form 

J9 = Z>oo(l - e-^<^^o)). (26) 

The fogging velocity is therefore given by 

dD 



dt 



= K{Do. - D). 



Equation (26) was applied to many experiments and found 
to fit the data closely. Observations of fog were made on all 
plates developed for the previous work, the readings for the 
fog density being made on the half of the plate which had not 
been exposed. 

Fig. 49 illustrates the kind of data secured. The upper 
curve is for the image. The computed points (black dots) 
were obtained from the equation 

The lower curve is for the fog. The computed points (black 
dots) were derived from 

D = Doo(l - e-^^'-'o)). 

The developer was M/20 hydroquinone (with 50 grams 
sodium sulphite and 50 grams sodium carbonate per liter) 
used on Seed 30 emulsion with no bromide. Many developers 
used in the same way indicated the same general result so far 

as velocity equations are con- 
cerned. 

Thus there is evidence that 
development of the image and 
of fog do not follow the same 
law, and that the velocity 
functions are different. 




IW.E. 



Fig. 49 

Velocity of development 
Fogging velocity 



dP 

dt 



K_ 

t 



{Dm — D) Image 



dP 
dt 



^ K{Po^- D)Fog. 



This is to be explained by the theories outlined above. 
If chemical fog predominates, as is supposed, and especially 
if this results largely from physical development (as is also 
likely), the development of fog grains is probably less restricted 
than development of the image, where the grains are fixed in 
place and have a definite distribution. In other words, the 

138 



THE THEORY OF DEVELOPMENT 

production of fog would be more likely to follow the ordinary- 
laws for a chemical reaction not subject to interference, 
namely, the first-order reaction law. The development of 
fog is then freed from one of the most complicating factors, 
the presence of gelatine. 

It is now obvious that fogging proceeds to a definite limit, 
or equilibrium value, just as the image does; but some of the 
relations for equilibrium values previously applied do not 
hold for fog. 

Table 35 gives data on the development of fog and of the 
image for numerous reducing agents on Seed 30 emulsion. 
The reducers in the first section of the table are arranged 
in order of reduction potential (see column 10). Values in 
the second section are reasonable determinations from velocity 
and other data. Columns 2, 3, and 4 give values of Doo, 
Ky and t^ for the fog, computed from equation 26 above. 
Column 5 shows the fog observed after 10 minutes* develop- 
ment, column 6 after 20 minutes'. Columns 7, 8, and 9 are 
the image characteristics computed from equation 28 for 
comparison. Column 11 shows the amount of fog remaining 
to be developed after 10 minutes and column 12 the fogging 
velocity after 10 minutes* development. It is evident that 
none of the characteristics of fog vary with the reduction 
potential of the developer. 

It is inconsistent to seek a definition of fogging power 
analogous to that of Mees and Piper. K for the image 
(applying the new velocity equation) is not the rate of develop- 
ment except for a particular set of conditions which are 
practically unattainable. The velocity of development for 
the image is 

Hence K is the velocity only when ^ = 1 and at the same time 
Doo — D = \. And it is now seen that F, the fog at time 
t, is not simply proportional to the fogging rate. 

Developers were then classified according to values of Z>oo 
for the fog image, or the maximum or equilibrium value for 
the fog, as given in Table 36. Here the values of F2o'and the 
fogging velocity are roughly in the same order. (The order 
is correct for developers of equal i^Pog values and constant 
Iq,) Accordingly it may be said that the fogging powers of 
two developers are to each other as the values of the maximum 
fog. This, though only an approximation, is a practical 

139 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 



iili i sisisii s^sis ; 









.SKS S SKSSSS^ sssss sss 



sss a ssKssss ess^s sss ■; 



SSSS 8 SS8SSSS SSSSS S3S j 



S SS3 R KSSgSSS 



* ^§£3 5 SSSKSSS nSoS 



2|22q :£ gSS=S2S SSSS= . 



SSSS3SS£SS5S3°S : 



ih 



THE THEORY OF DEVELOPMENT 

classification as it indicates roughly the relative amounts of 
fog produced at a given time. But a fogging agent with higher 
K or greater t^ will be out of place on this scale. 

In Table 37 the developers are arranged in order of fogging 
velocity after 10 minutes. This seems on the whole the best 
classification, as the fog for a definite time is given in approxi- 
mately the right order and other properties are in a more 
consistent order, though no definite rules may be established. 

The three experiments marked with an asterisk are obviously 
out of order. In the case of paraminophenol and phenyl- 
hydrazine this is due to the high value of /q, the time at which 
fogging begins. 

Thus it is obviously impossible to attach much significance 
to reduction potential so far as fogging tendencies are con- 
cerned. Two other possibilities present themselves. Either 
the fog is due to substances other than the developer, or the 
developers must be assumed to have the power of nucleation 
or the ability in some way to develop the unexposed grains, 
and in a manner not related to the reduction potential, but 
depending rather on other chemical properties. The first of 
these assumptions is untenable unless the second is true. 
It can be shown that small quantities of foreign substances 
produce great changes in the fogging power. But the effect 
,of bromide on fog is such as to make it quite certain that these 
foreign substances are of low reduction potential. This may 
be due to their low concentration, but the maximum fog 
values should be influenced in the same way. And we are 
again confronted by the evidence that fog cannot be accounted 
for by reduction potential. A number of the developing 
agents in the above list were very pure, so that any foreign 
substances present must have been in exceedingly low 
concentration. 

If we accept the explanation that the developers have other 
(and comparatively unknown) specific properties which con- 
trol their solvent action on silver bromide and their power to 
reduce silver from it without the aid of large numbers of 
nuclei affected by light, the results may later be shown to be 
in accord. This opens up new questions which cannot be 
answered from present information. 

THE DISTRIBUTION OF FOG OVER THE IMAGE 

From the time of Hurter and Driffield's first investigations 
numerous workers have assumed that fog is evenly distributed 
over the image, and have accordingly subtracted the fog 
readings from density values for sensitometric strips. More 

141 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

TABLE 36 
Classification of Developers According to Maximum Fog 

Fogging 
Velocity 
after 10 
minutes 



Paramino-metacresol 

Toluhydroquinone 

HydroQuinone 

Diaminophenol -f- alkali 

Monomethylparaminophenol . 

Pyrogallol 

Methyl paramino-orthocresol 

Dibromhydroquinone 

Dimethylparaminophenol. . . . 

Dichlorhydroquinone 

Diaminophenol, no alkali. . . . 

Paraminophenol 

Paramino-orthocresol 

Phenylhydrazine, no alkali . . . 

Chlorhydroquinone 

Bromhydroquinone 

Ferrous oxalate 

Pyrocatechin 

Edinol 

Duratol 



Paraphenylene diamine.no alkali 













F after 


(.Doo) 


(Ooo) 


''^Br 


(K) 


{K) 


20 


Fog 


Image 


Fog 


Image 


minutes 


2.60 


4.00 


(9.5) 


.16 


.72 


2.51 


♦2.45 


4.40 


2.2 


.19 


.63 


2.34 


1.50 


3.80 


1.0 


.12 


.95 


1.32 


1.30 


4.2 


(404-) 


.11 


.60 


1.20 


1.30 


3.60 


20 


.11 


.58 


.90 


1.30 


4.00 


16 


.05 


.57 


.88 


1.20 


4.00 


23 


.10 


.60 


1.03 


1.00 


3.80 


(8) 


.07 


.80 


.76 


.99 


3.20 


10 


.08 


.61 


.70 


.75 


3.60 


(11) 


.06 


.53 


.49 


.70 


3.60 


(30) 


.14 


.55 


.62 


.70 


4.20 


6 


.11 


.44 


.44 


.65 


3.80 


7 


.09 


.70 


.57 


.65 


3.50 


1.0 


.05 


.03 


.18 


.60 


4.00 


7 


.16 


.52 


.55 


.60 


3.80 


21 


.07 


.66 


.55 


.43 


3.10 


0.3 


.10 


.55 


.38 


.40 


3.60 




.15 


.52 


.38 


.30 
fog 
negligible 


3.60 




.11 


.46 


.27 


2.40 




• • • 


.34 


.05 


fog 












negligible 


1.70 


0.4 


• • • 


.34 


.05 



.083 
.066 
.053 
.041 
.088 
.035 
.044 
.032 
.041 
.025 
.034 
( .053) 
.022 
.031 
.024 
.021 
.015 
.018 
.011 



♦See note on p. 140 



TABLE 37 
Classification of Developers According to Fogging Velocity 



Fogging 
velocity 
after 10 
minutes 

Monomethylparaminophenol 088 

Paramino-metacresol 083 

Toluhydroquinone 066 

Hydroquinone 053 

Paraminophenol 053 

Methylparamino-orthocresol 044 

Diaminophenol 041 

Dimethylparaminophenol 041 

Pyrogallol 035 

Diaminophenol, no alkali 034 

Dibromhydroquinone 032 

Phenylhydrazine, no alkali 031 

Dichlorhydroquinone 025 

Chlorhydroquinone 024 

Paramino-orthocresol 022 

Bromhydroquinone 02 1 

Pyrocatechin 018 

Ferrous oxalate 015 

Edinol Oil 



Fogging 




velocity 




after 2 


TT 


minutes 


Br 


.90* 


20 


2.51 


(9.5) 


2.34 


2.2 


1.32 


1 


.44* 


6 


1.03 


23 


1.20 


(40) 


.70 


10 


.88 


16 


.62 


(30) 


.76 


(8) 


.18* 


less than 1 


.49 


(11) 


.55 


7 


.57 


7 


.55 


21 


.38 


« • • • 


.38 


0.3 


.27 


• • • • 



142 



THE THEORY OF DEVELOPMENT 



recently several investigators have questioned this procedure, 
and one or two have suggested what may now be proved, 
that fog (over the image) decreases as the image density 
increases. From the beginning of the present investigation 
the total density was read, and the fog determined separately. 
The total densities only were used in studying the results, 
and it was assumed that the higher densities were free from 
fog. In certain cases this led to results somewhat different 
from those obtained by other workers, but the former are so 
much more consistent throughout that they are considered 
excellent indirect evidence on the question of fog distribution. 

Some features of this indirect proof are given below. The 
results always indicate that there is much less fog over the 
high densities than over the low densities. 

Fig. 39 is an exaggerated example of how the contrast, 
T, decreases with time beyond a maximum, a fact which 
can be explained reasonably only by the growth of more fog 
over the low densities. 



Fig. 51 



Fig. SO gives other evidence that the high densities are 
relatively free from fog. The curve is density plotted against 
time, both for the image and for the fog. The developer was 
M/20 monomethylparaminophenol. Plates were developed 
for ten and fourteen minutes in the presence of impurities 
causing excessive fog. The great increase in chemical fog 
may be seen from the fog curve at the times mentioned. At 
the same time the image densities at log E - 2.4 for the same 

143 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

plate He on the normal density- time curve for the image. 
These are unaffected by the fog. 

Fig. 51 represents development of a Seed 23 emulsion with 
M/20 hydroquinone at bromide concentrations 0, .001, .004, 
and .016 M. The plates are developed to equal gammas. 
The fog for the upper curve is 0.48 and for the lower 0.02. 
Examination of the curves shows that the bromide cuts down 
the fog to a greater extent than it does the image, though 
this could be shown much better by plates more badly fogged. 
The lowering of the curves is due to the normal depression by 
bromide, previously described. 

. The procedure of subtracting the fog from all densities can 
be shown to be erroneous. If the fog is subtracted from the 
upper curve and the curve for C = .016 M., the resultant curve 
for no bromide will lie below that for C = 0.016 M. — ^a result 
which would indicate that the developer produces greater 
image density with bromide than without it. In this particu- 
lar instance it is probable that there is practically no fog over 
the image in the region of correct exposure (the straight line 
region). Such cases occur frequently. 

The relation of fog density to bromide concentration has 
not been thoroughly investigated owing to the low fog densi- 
ties when any appreciable concentration of bromide is used. 
In general, it is found that the addition of a very small amount 
of bromide greatly reduces the fog — that is, the absolute 
depression of fog is greater than that of the image. Experi- 
ments of a preliminary nature and indirect evidence indicate 
that fog density may be a function of bromide concentration 
somewhat different from image density. Whether or not this 
is true we are not prepared to state. 

With reasonable evidence that high densities are free from 
fog, and the well founded assumption that the laws for the 
growth of the image, as previously described, are at least 
nearly correct, more definite ideas of the distribution of fog 
over the image may be expressed. Experimental data for a 
developer giving very bad fog (impure monomethylpara- 
minophenol) are given in Fig. 52. The observed points are 
for five and ten minutes* development. From complete data 
for the developer the intersection of the H. and D. straight 
lines was found to be at log E = .32 and on the log E axis. 

The straight lines for the image were drawn from the 
density-time curve for log E = 1.8. Having subtracted the 
fog from the total density for the lowest exposure (log £ = 0), 
and having made observations with enough bromide to elim- 
inate most of the fog, it is possible to draw fairly correctly 

144 



■: THEORY OF DEVELOPMENT 



the toe of the curve for the image. Although this is not 
absolutely correct, the relations are probably very closely 
approximated. Other evidence strengthens this belief. 



^ 


i 

/ 



\ ■ 










.._ 


\ 


\ 


\ 










\ 


^ 


\ 


x_ 









Aft 


rlOm 


nutes 










hogE ' 
Total D 
Image 
Fog 



2,45 
,20 
2.25 


.3 
2,30 

-38 
1.92 


,6 
2,30 

,68 
1.62 


.9 
2.34 
1 14 
1.20 


1..2 
2.40 
1.60 
.80 


1.5 

2.52 
2,27 
,25 


1.8 2.1 

2.82 3.10 

2,82 3-10 




2.4 

3.36 

3.36 




After 5 minutes 


Total D 

Image 

Fog 


1.38 
,16 
1.22 


1.28 
,32 
,96 


1.26 
.61 
,65 


1.42 
1.04 
-38 


1.72 
1.55 
,17 


2.16 
2.07 
,09 


2.60 
2.59 
,01 





On subtracting the image density as read off from the image 
curve which is free from fog, the value of the fog may be 
obtained for a given image density. (See Table 38) . 
Plotting the value of fog thus obtained against the image 
density for both five and ten minutes' development gives the 
two curves of Fig. 53, which are approximately straight lines 
over a range of image densities. These curves indicate that 
the fog varies with the image density as follows : 
F = k (Di - DO. 
145 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Here k is the slope of the straight line and is negative. 
F is the fog for the image density Di, and Di^ is the intercept 
on the horizontal axis, or the density over which there is no 
fog. As seen from the figures, the statement that Di^ is the 
minimum density over which there is no fog is not exact 
because of departure from the straight-line relation at higher 
densities. 

Assuming for the time being that these conclusions are 
correct, a relation between fog and bromide concentration 
may be formulated. Each image density represents the 
formation of a certain amount of soluble bromide in the emul- 
sion, and the concentration of the bromide may be roughly 
estimated as follows: No matter what the exact chemical 
mechanism of development may be, one ion of bromine is 
formed for each ion of silver reduced, and the bromine will be 
present combined with sodium (if the alkali is sodium 
carbonate). One gram atom of silver (108 gms.) therefore 
corresponds to one gram molecule (103 gms.) of sodium 
bromide, and the two are produced in equal amounts. Density 
is proportional to silver by the photometric constant, P. 

firm . Acf 

P is defined as 77777 when D = 1.00. P has been found 

100 cm.* 

to be 0.0103.1 For a density of 1.00 therefore about 0.01 
gm. of sodium bromide is produced in an area of 100 sq. cm. 
of the emulsion. The emulsion when swollen has a thickness 
of about 0.2 mm. (0. 02 cm.). The volume of 100 sq. cm. is 
therefore 2 cc, and the maximum concentration of sodium 

bromide would be — -^z — = .005 gm. per cc, or 5 gm. per ^ 

liter. This is roughly 0.05 M., which represents the concen- 
tration if no diffusion takes place. Of course the concentration 
is lowered by diffusion. But the concentrations present 
may be estimated as : 

For D = 0.5, C = .025 M. or less; 
1.0, .05 M. or less; 

1.5, .075 M. or less; 

2.0, . 10 M. or less; 

From Table 38 and the above it is evident that for ten 
minutes' development (Fig. 52) the concentration of bromide 
required to prevent fog is less than 0.14 M., and for five 
minutes* development less than 0.10 M. This corresponds 
to greater depression for the fog than for the image and is 
quite in accord with other experimental results. 

^ Sheppard, S. E., and Mees, C. E. K., Investigations, 1. c, p. 41. 

146 



THE THEORY OF DEVELOPMENT 



If the same laws held for the depression of fog as for the 
depression of the image, fog would be (in Fig. 53) a straight 
line function of log D rather than of D. It may be that 
diffusion effects account for the difference, as the bromide 
produced in the emulsion diffuses out and the concentration 
changes. 

It being impossible to separate chemical fog and image 
density by chemical means, no direct proof of the above is 
obtainable. However, strong evidence in this direction is 
afforded by a study of the fog caused by thiocarb amide. 

THE FOGGING ACTION OF THIOCARSAUIDE 

The practical applications of the action of thiocarbamide 
have been investigated by Waterhouse and more recently by 
Perley, Frary, Frary and Mitchell, and others. It was found 
in general that a hydroquinone developer containing sodium 
carbonate gives the clearest reversal with thiocarbamide when 
a careful adjustment of the ingredients of the developer is 
made. As partial reversal was sufficient for the present pur- 
pose, time was not taken to obtain the maximum effect. The 
developer used was: 

Hydroquinone M/20 . , 5.5 gms. ; 

Sodium Sulphite 50 gma,; 

Sodium Carbonate. ... 15 gms.; 

Waterto 1000 cc8. 

The concentration of thiocarbamide was 0.003 M. As it 
was very difficult to secure consistent results for each determin- 
ation, eight to sixteen plates were developed under similar 
conditions and their densities averaged. Even so there are 
obvious errors. The times of development were such as to 
p:ive always the same contrast. The curve for hydroquinone 
m the absence of thiocarbamide was first determined (lowest 
curve, I., Fig. 54). Curves for the densities due to the 



=^ 










^ 


:x 


# 




^ 






/- 







MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

developer with thiocarbamide were then obtained, using 
different concentrations of bromide. These (Fig. 54) show 
the reversal effect, which decreases as more bromide is added. 

These data indicate, first, that there is a general deposition 
of fog over the plate (the plate curve is raised), which is due 
probably to increased solubility of the silver halide, and 
general reduction by physical development. It is evident that 
the fog of the reversed image (as, for example, the density at 
log E = 0.8) is depressed more by bromide than a density 
lying higher on the normal image side of the curve. If it is 
assumed that the hydroquinone develops the same density in 
all cases, a fact which separate experiments indicate, the 
difference between any given curve and the curve for the 
developer alone may be taken as the fog value. When these 
fog values are plotted against the corresponding image densi- 
ties — i. e., the densities for the developer alone — the series of 
curves in Fig. 55, which bear a marked resemblance to those 
of Fig. 53 (obtained by a different method) results. The 
only difference between the two sets of curves is that in Fig. 
55 the physically developed fog is in constant amount over 
the plate, as indicated by the horizontal lines. These curves 
require the assumption that the fog is of two kinds, as already 
indicated — the fog resulting from physical development, and 
that causing the reversal effect. The latter is due no doubt 
to grains in the emulsion which are rendered developable — 
that is, the thiocarbamide, like some other compounds con- 
taining sulphur, has the power of nucleation as previously 
interpreted. The fog produced in this way appears to be 
exactly like that formed in the experiment with monomethyl- 
paraminophenol discussed above, and, similarly, becomes less 
as the image density decreases. The parallelism is carried 
still further if the values of the intercepts on the horizontal 
axis are treated as in the former experiment. These represent 
the image densities (bromide concentration in the emulsion) 
required to prevent the fog. But here bromide is in the 
developer also, so that, as the bromide in the developer is 
increased, less is required in the emulsion. Consequently 
the concentrations in the emulsion and in the developer should 
be added. The concentrations present in the emulsion (see 
page 146) are found as follows: For the upper curve 
(C = 0.001, Fig. 54), the intercept gives about 1.2 in density, 
which, as found above, corresponds to a bromide concentration 
somewhat less than 0.06 M. Listing all these intercept values 
with corresponding concentrations of bromide we have : 



148 



THE THEORY OF DEVELOPMENT 

Concentration of 
Concentration of Di^ (Intercept) bromide in emulsion 
bromide in developer from Fig. 55 corresponding to Di^ C -\- C^ 



001 M. 


1.2 


.06 M. 


.06 M. 


0035 M. 


1.0 


.05 M. 


.05 M. 


01 M. 


.8 


.04 M. 


.05 M. 


015 M. 


.7 


.035 M. 


.05 M. 


02 M. 


.6 


.03 M. 


.05 M. 



These values of C (the concentration of bromide in the 
emulsion) represent the maximum, as diffusion lowers the 
concentration to a certain extent. 

C + C is approximately constant and indicates that for 
the conditions a bromide concentration slightly under 0.05 M. 
is required to eliminate fog. Experimentally it was found 
necessary to use 0.03 M. in the developer, which would indicate 
that 0.01 to 0.02 M. is present in the emulsion. 

The consistency of all the. data obtained on fog, and espec- 
ially of the results of particular experiments like the above, 
lead to the conclusion that fog is distributed over the image 
in the manner indicated in Figs. 53 and 55. In certain cases 
general deposition may occur, as with thiocarbamide, sodium 
sulphite at fogging concentrations, etc., but this may be 
separated from the general result by the methods shown. 
Further, it is believed that fogging agents are alike in their 
action, and that their fogging tendencies are due to their power 
of nucleation rather than to their reduction potentials, prop- 
erties which appear to bear no relation to one another. 

Various practical considerations, which, however, may not 
be discussed here, are evident from the above. Since fog may 
be greatly restrained by the use of bromide, it appears 
advisable to use high reduction potential developers with 
sufficient bromide to eliminate fog completely. Fig. 51 shows 
how the contrast in the lower region of the plate curve (the toe) 
may be increased if fog is normally present. Except in so far 
as fog elimination is concerned it is not possible to increase 
the contrast appreciably by the use of soluble bromides under 
any normal conditions. 



149 



CHAPTER IX 

Data Bearing on Chemical and Physical 
Phenomena Occurring in Development 

Note — No attempt will be made here to deal with 
theories of the mechanism of development, nor even 
to connect fully the data with such theories. Far too 
little experimental data is available on the questions 
involved. Such data as have been accumulated 
are published for the purpose of adding to the 
information concerning the phenomena and of 
illustrating the use of the methods herein described. 

THE EFFECT OF NEUTRAL SALTS 

1. Potassium Bromide. 

Liippo-Cramer attempted to explain the restraining action 
of bromide as a colloid-chemical phenomenon. This view 
was controverted by Sheppard on the basis of experimental 
results similar to those recorded in preceding pages. The 
normal effect of bromide as described is much more logically 
explained chemically, as has been done by Sheppard, and in 
this monograph. The laws governing the normal action of 
soluble bromides have already been stated. However, at 
high concentrations of bromide new phenomena, which may 
be analyzed by similar methods, appear. 

It has been found that the laws formulated for bromide 
action cease to hold at concentrations of 0.16 M. or there- 
abouts. The point at which this departure occurs seems to 
vary with the developer, and appears more marked the 
higher the reduction potential of the developer. The latter 
may be an accidental relation, as monomethylparaminophenol 
(of high reduction potential) does not show the effect at con- 
centrations as high as 0.64 M. Pyrogallol exhibits it to a 
very marked degree, and the following results, for some of 
which curves are shown, illustrate what happens when this 
developer is used with 1.28 M. bromide (152 gms. per liter). 
It is remarkable that in this case the developing agent contin- 
ues to act in the presence of nearly twenty-five times its own 
weight of bromide. 

150 



THE THEORY OF DEVELOPMENT 

Fig. 56 gives the plate curves obtained. The times of 
development, the values of y, and the fog (F) are given on 
each curve. Other relations, derived from the above plate 
curves and other data, will be discussed. Fig. 57 represents 
the density-gamma curve at log E « 3.0, and Fig. 58, the 
D -/dev. curve for the same exposure. Other data obtained 
follow : 









mt^ 


\^ 






^<f 


^ 




^ 




^ 

y 


10> 






1 — ' 


10^ 



LMI •%» 



D 



Fig. 56 



<L— — — — *^~ '* 

H ■ ■ I 



m 




• a 






o\ 


\ 














1 

• 


c 




C 
















< 


/ 






X 




y 


/" 


/ 


•^ 








« 








• 


■ 


r- 






T^^ 



V 

I 



IMI'M 



Fig. 58 



Fig. 57 



1. Inter section of Plate Curves, There is no common point 
of intersection of the H. and D. curves at concentrations 
greater than 0.08 M. — that is, the range of gammas over which 
this relation holds becomes smaller as the concentration 
increases. 

2. Density-depression. As seen from the above, the depres- 
sion cannot be found by the usual method. This may be 
determined for an intermediate value of y, however; and 
it is found to decrease at concentrations greater than 0.08 M. 
From the data it is seen that the effect is due to the shift of 
log i, the inertia constantly decreasing as more bromide is 
added. 

3. Maximum Contrast. It is evident that the maximum 
attainable contrast decreases rapidly as the bromide concen- 
tration increases. 

4. Maximum Density. The maximum densities for the 
higher exposures (log E =3.0, etc., see Fig. 56) show normal 

151 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

relations except that at C = 1.28 the value is slightly low. 
At the low exposures (log E =2.0) the maximum densities 
reach a minimum (plotted against the concentration) and 
then increase with the concentration. The density- time 
curves for the high exposure (log E =3.0) are of normal 
shape, and are fitted by the usual velocity equation. For 
the low exposure (log £ = 2.0 and under) the shape of the 
D—t curve is changed and after fifteen minutes the density 
increases more rapidly than for log £ = 3.0 for the same time 
of development. 

5. Fog, The fog on the unexposed portion of the plate 
shows normal relations until a concentration of 0.08 M. is 
reached, after which it increases somewhat. 

A careful analysis of these results shows that the new effect 
of the bromide is evident principally in the low densities, and 
that it consists in two separate phenomena. First, with 
pyrogallol the bromide has the same effect as a fogging agent 
— i. e., it renders a certain amount of silver bromide develop- 
able. It is difficult to account for this fact, as it has been 
observed for no other developer. There is no doubt as to the 
effect, however, as it was reproducible and consistent. As 
with normal fog, the high densities (as seen from the normal 
character of the D-t curve) seem unaffected. Whether or 
not this is true, the growth of fog does not account entirely 
for the nature of the plate curves shown. The latter rather 
strikingly resemble the type of curve obtained for the develop- 
ment of certain papers. It seems probable, therefore, that 
the potassium bromide reacts on the silver bromide to form 
a complex, thereby producing in effect a different emulsion. 
Complex ions result from the dissociation of the new salt, and 
all the relations are changed as this is formed in larger amounts. 

Experiments with other developers lead to similar conclu- 
sions, though with them the results are slightly different, 
especially regarding fog, as noted above. With monomethyl- 
paraminophenol no unusual effects were noted even with a 
bromide concentration of 0.64 M. With bromhydroquinone, 
paraminophenol, and dimethylparaminophenol, the normal 
relations fail at about C = 0.16 M., and the deposit becomes 
more and more colored with increasing bromide concentration. 
With the exception of fog, the effects in general are similar to 
those for pyrogallol. It is therefore believed that potassium 
bromide at high concentrations reacts with the silver halide 
to form a complex of indefinite composition, depending on the 
concentration. Aside from this there may be absorption 

152 



THE THEORY OF DEVELOPMENT 



and an effect on the gelatine, but it does not appear that 
either accounts for the result. 

2. Potassium Iodide. 

The so-called accelerating effect of potassium iodide and 
potassium ferrocyanide when added to certain developers is 
fairly well known. Luppo-Cramer has described similar 
results with other neutral salts. To some of these the methods 
described above have been applied, though this was done more 
for the purpose of determining the range over which the 
laws hold than with any intent of investigating the action of 
neutral salts. 

Sheppard and Meyer have also investigated the effect of 
potassium iodide. Results recorded here may be interpreted 
in accordance with their conclusions. 

It has been found that potassium iodide shows most marked 
effects with hydroquinone and those developers for which the 
period of retardation is long. With monomethylparamin- 
ophenol and other "fast" developers the accelerating effect, 
if present, is masked. M/20 dimethylparaminophenol, a 
developer for which the bromide effect has been especially 
well established and which appears to be a normal developer, 
was used in the experiment described. However, this devel- 
oper shows a short period of induction, so that the experiment 
does not show the acceleration referred to above. Experi- 
ments with other neutral salts illustrate this acceleration, 
and data for this developer furnish information on less obvious 
phenomena. 

There was little difficulty in applying the methods. A 
well defined intersection point, which always lay on the log E 
axis, was obtained. The D -t curves were of normal shape 
and the constants Z>oo, X", and /q were computed. In the 
following table the data are summarized. 

TABLE 39 
Effect of Potassium Iodide on M/20 Dimethylparaminophenol 



^KI 


a 


b 


D after 
2 minutes 


Poo 


K 


to 


Too = 

D^—b 

los E— a 





.50 





1.52 


2.80 


.64 


.59 


1.47 


.005 


.82 





.84 


2.60 


.27 


.46 


1.64 


.0075 


-.40 





.96 


2.60 


.33 


.48 


1.44 


.01 


.20 





.70 


2.50 


.44 


.88 


1.56 


.02 


.44 





.58 


2.00 


.34 


.80 


.70 


.028 


.70 





.45 


.90 


.53 


.50 


.28 


.04 


1.00 





.16 


0.30 


.93 


.88 


.09 



153 



UONOGKAPHS ON THE THEORY OF PHOTOGRAPHY 



Some of these results are plotted against the iodide concen- 
trations or the logarithms of the concentrations for the sake of 
emphasis. Fig. 59Ashows how different is the relation between 
Poo and I<^ C for iodide from that for bromide. (In the latter 



caseDm — log C is a straight line of slope 0.5 



'<f log.oC 






Fig. 59A-B 



Fig. 60 



Fig. 59B shows a still more striking variation from bromide t 
where y to is constant and independent of the bromide concen- 
tration. In Fig. 60, K and a are plotted against the concen- 
tration. Both are constant with bromide. Here both are 
variable. 

3. Other Neutral Salts. 

The character of the action of potassium ferrocyanide, 
potassium oxalate, potassium citrate, potassium sulphate and 
potassium nitrate was partially investigated. For this pur-. 
pose a hydroquinone developer was used, the basic formula 
being: 

Hydroquinone M/40. ., , 2.75 gms.; 

Sodium Sulphite 3.75 gms.; 

Sodium Carbonate 12.5 gms.; 

Water to 1000 cc. 



The constants for the developer alone were determined 
first, and the neutral salts were then used in the concentrations 
given below. Table 40 gives the data for the density after six 
minutes' development (D6'), Da>, K, t^ (the time required for 
a density of 0.2 [ Id = 0.2 ], proportional to the time of 
appearance), and the fog for six and twelve minutes. 

154 



THE THEORY OF DEVELOPMENT 

TABLE 40 
Hydroquinone with additions of neutral salts 

Emulsion 3533 



Experi- 








NoBro 


mide 


Used 








ment 


Neutral salt used 


Concen- 
















No. 




tration 


Dt' 


^00 


K 


to 


'D = 0.2 


F.' 


Fit' 


197 


None 


• • ■ • • 


.83 


3.60 


.86 


4.5 


4.3 


.38 


1.16 


196 


K4 Fe (CN)6 


.01 M. 


1.17 


3.80 


.77 


3.6 


3.5 


.71 


1.60 


198 


K4 Fe (CN)« 


.05 M. 


.91 


3.60 


.61 


3.6 


3.7 


.40 


.95 


200 


K4 Fe (CN)6 


.25 M. 


1.32 


3.40 


.48 


2.2 


2.4 


.52 


.92 


199 


Kj Ci O4.H, 


.25 M. 


1.25 


3.60 


.60 


2.8, 


2.75 


.50 


.98 


201 


K. C6 Hs O7. Hs 


.25 M. 


.80 


3.40 


.55 


3.7 


3.7 


.23 


.56 


202 


K1SO4 


.25 M. 


1.36 


3.60 


.73 


3.00 


2.7 


.56 


1.04 


203 


KNOi 


.25 M. 


1.13 


3.60 


.55 


3.00 


2.5 


.49 


1.08 



It is seen that the period of retardation for the developer 
alone is very great, (t^ = 4.5 minutes, and the time of appear- 
ance is about 4.3 minutes.) Each of the salts used decreases 
the period of induction, potassium ferrocyanide having the 
greatest effect, potassium citrate the least. The accelerating 
effect may also be seen from a comparison of the densities 
produced in six minutes. Other relations are obvious frofti 
the table. It is notable that while t^ has been changed, the 
variation of K is less, and Z^oo is practically unchanged. In 
accordance with the discussion of the effect of bromide on 
velocity curves (Chapter VII) this means that the neutral 
salts change the relations for the initial period only. That 
is, the velocity is practically unaffected in the later stages of 
the reaction, though the velocity change at the beginning is 
quite marked. 

Therefore we are inclined to attribute the effect of such 
salts, in distinction from halide salts, principally to physical 
effects on the gelatine and possibly to adsorption. 



THE EFFECT OF CHANGES IN THE CONSTITUTION OF 

THE DEVELOPER 

The developing solution used was hydroquinone with (1) 
variable alkali concentration; (2) variable sulphite concen- 
tration; (3) variable hydroquinone concentration. 

The standard formula for hydroquinone used was 

Hydroquinone M/20 ... 5.5 gms. ; 

Sodium carbonate 50 gms. ; 

Sodium sulphite 75 gms. ; 

Water to 1000 cc. 

All the data were obtained in the usual manner. The results 
are shown in Tables 41, 42 and 43, and the data for K and Z>oo 
plotted (for convenience) against the logarithm of the variable 
concentration are given in Figs. 61, 62, and 63. In each case 

155 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

the concentrations of two of the constituents of the developer 
are constant, the other being varied as indicated. 

TABLE 41 

Hydroquinone Developer with Variation of Sulphite Concentration* 
Emulsion 3533. No bromide. Log E = 2.4 



Experiment 


^NasSOi 






D after 








F after 






No. 


a 


b 



2min. 


D^ 


K 


io 


10 min. 


'd-.« 


Too 


155 


6.25 


-.40 


.95 


3.80 


.54 


1.25 


.75 


1.0 


1.35 


149 


12.5 


•-.40 





1.22 


3.60 


.86 


1.6 


1.12 


.80 


1.28 


148 


25 


-.34 





.80 


3.20 


1.04 


2.20 


.76 


1.0 


1.17 


126 


50 


-.66 





1.12 


3.80 


.95 


1.80 


.99 


1.0 


1.24 


ISO 


75 


-.30 





.83 


3.80 


.41 


1.35 


.70 


.75 


1.41 


151 


100 


-.24 





.74 


4.50 


.38 


1.65 


.67 


.75 


1.70 


156 


150 


-.40 





.84 


4.00 


.52 


1.50 


.81 


.75 


1.43 



1 Hydroquinone M/20 (5.5 gm. per liter); 

Sodium carbonate 50 gm. per liter; 

Sodium sulphite variable. 
' Concentration of Nai SOi in grams per liter. 

TABLE 42 

Hydroquinone Developer with Variation of Carbonate Concentration ^ 

Emulsion 3533. No bromide. Log E = 2.4 



Experi- 






















ment 


^aaCo's 






Z) after 








F after 


'd«.« 




No. 


a 


b 


2 min. 


DoQ 


K 


to 


lOmin. 


Yoo 


191 


4.45 


-.20 








4.00 


.70 


4.0 


• ■ * 


3.3 


1.54 


157 


3.13 


+ .04 








2.80 


.83 


5.3 


.26 


3.7 


1.19 


158 


6.25 


-.08 








4.20 


.63 


4.2 


.58 


2.75 


1.76 


159 


12.5 


-.48 





.22 


3.80 


.73 


4.0 


.64 


1.90 


1.32 


160 


25 


( - .06) 





.42 


4.40 


.72 


3.5 


.65 


1.60 


1.79 


150 


50 


-.30 





.83 


3.80 


.41 


1.35 


.70 


.90 


1.41 


161 


100 


+ .04 





.76 


3.60 


.75 


3.0 


.47 


.90 


1.52 


162 


200 


+ .17 





.21 


3.20 


.50 


5.3 


.21 


2.00 


1.43 



^ Hydroquinone M/20 (5.5 gms. per liter). 

Sodium sulphite (75 gms. per liter). 

Sodium carbonate variable. 
* Concentration of Nas COi in grams per liter. 

TABLE 43 

Hydroquinone Developer with Variation of Hydroquinone Concentration* 

Emulsion 3533. No bromide. Log E = 2.4 



Experi- 


C 


















ment 


Hydro- 






D after 








F after 


t 


No. 


quinone' 


a 


b 


2 min. 


Dao 


K 


to 


10 min. 


D-.» 


163 


2.75 


-.74 





.26 


4.50 


.81 


4.0 


i.iot 


1.90 


150 


5.5 


-.30 





.83 


3.80 


.41 


1.35 


.70t 


.25 


164 


11.0 


W.15 





.94 


3.80 


.57 


1.69 


.42 


.65 


169 


22.0 


-.94 





0.00 


4.40 


.50 


3.3 


.90 


3.15 



1.45 
1.41 
1.68 
1.31 



t Very marked increase in fog. 
1 Hydroquinone variable. 

Sodium sulphite 75 gms. per liter. 

Sodium carbonate 50 gms. per liter. 
' Concentration of hydroquinone in gms. per liter. 



156 



ffi^' 


TT- 










U-t^. 


nrasi 



THE THEOBY OF DEVELOPMEKT 

l&E_a a. 





















^ 






















\ 


/ 


N 












































i 








li 








N 




















N 




■4- 














rac 



5; 



Variable Hydroquinone 

Fig. 63 

The results may be sum- 
marized as follows: 

1. With variable sulphite: 

a is approximately constant; 

jvith increasing con- 

K rises to a maximum and then 



All the other properties — fog, time of appearance, etc. — 
exhibit unordered variation, showing that they are the result 
of complex chemical interadjustments. 

itration of carbonate is increased: 



Ti and then increases, indicating somewhat 
of a change in speed, though there is irregularity; 

The density developed in two minutes increases rapidly at first 
and then diminishes; 

D CO rises to a maximum and falls off; 

K appears to decrease gradually (see curve, Fig. 62); 

■f " shows unordered variation; 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

The time of appearance drops to a minimum, after which it 
increases. This applies to k also. 

3. The experiments with hydroquinone are hardly of suffi- 
cient range for conclusive evidence. However, it appears 
that, as the concentration increases: 

a increases rapidly (the speed of the plate decreases) and then 
falls off; 

The density developed in two minutes parallels a; 

D 00 drops to a minimum and then increases; 

K decreases; 

Y cx) rises to a maximum, then decreases. 

The time of appearance and t^ show the same variation as a. 
We shall not attempt to explain these effects at this time. It 
is expected that, later, electrochemical data will be available 
which will throw light on the chemical reactions involved, 
which are not clear at present. Even so, a few general 
conclusions may be presented: 

1. There is a variation of plate speed with changing alkali 
or hydroquinone concentration but not with sulphite; 

2. The increase of maximum density with increase of sul- 
phite is probably due partly to the formation of sulphite fog 
and partly to the fact that the sulphite reacts with the oxida- 
tion products with possible regeneration of the developing 
agent; 

3. The effect of alkali apparently consists (aside from 
chemical considerations) partly in a physical change of the 
gelatine. The results may be accounted for by a hardening of 
the gelatine at high concentrations of alkali, which is in accord 
with work on gelatine. 

THE EFFECT OF VARYING THE SULPHITE CONCENTRATION 
WITH MONOMETHYLPARAMINOPHENOL 

When it was found that the maximum density increased 
with sulphite concentration in the. case of hydroquinone, the 
same experiment was tried with monomethylparaminophenol 
to determine whether the relations for the relative reduction 
potentials of the two developers as previously found by the 
maximum density relations were to be explained on this basis. 
Three different sulphite concentrations were used. The 
constants are given in Table 44. 



158 



THE THEORY OF DEVELOPMENT 

TABLE 44 
Variation of Sulphite Concentration with Monomethylparaminophenol* 

Emulsion 3533. No bromide, log E = 2.4 



Experi- 
ment 
No. 


^Na,SO, 
(gms./l.) 


a 


h 


D after 
2 minutes 


Poo 


K 


to 


153 
135 
152 


20 

50 

100 


+ .60 


+ .24 







1.60 
1.66 
1.44 


3.10 
3.60 
3.50 


.43 
.58 
.47 


.37 

.70 

67 



The effect is very slight compared with that for 
hydroquinone for the same concentration range. It therefore 
appears likely that certain developers like hydroquinone 
give higher densities than those corresponding to their reduc- 
tion potentials because of side reactions between the sulphite 
and the oxidation products. 

The above experiments illustrate only partially the range of 
application of the methods which have been described. Not 
every phase of this work is new, but considerably more exten- 
sive use has been made of those features which appear to be 
most useful in the study of chemical reactions pertaining to the 
development process. 



* Monomethylparaminophenol M/20 (9 gms. per liter): 
per liter. 



Sodium carbonate 50 gms. 



159 



CHAPTER X 

General Summary of the Investigation, with 

Some Notes on Reduction Potential in its 

Relation to Structure, Etc. 

REDUCTION POTENTIAL AND THE EFFECT OF BROMIDE ON 
DEVELOPMENT (aSIDE FROM THE EFFECT ON VELOCITY) 

Soluble bromides in a developer offer resistance to its 
action in any or all of the following ways : 

1. As products of a reversible reaction; 

2. By lowering the concentration of silver ions available for 
reduction ; 

3. By reaction with the silver halide to form complex ions 
from which the silver is reduced with greater difficulty. 

No one of these alone accounts for the magnitude of the 
observed phenomena, so that probably all are involved. The 
second is no doubt of most importance at normal concentra- 
tions. The third appears to be a decided possibility at higher 
concentrations of bromide, though no direct data are available.^ 

In the absence of the last reaction (No. 3 above), the rela- 
tions for the measurement of the potential by means of the 
bromide effect may be formulated from theoretical considera- 
tions, the reduction potential being some function of log [Br] 

r +1 
corresponding to the equilibrium value of -iA?iL To obtain this 

L met. J 

it would be necessary to determine the amount of bromide 
against which a reducing agent can just develop. But this is 
not possible, as the oxidation products are unstable and the 
measure of the energy thus derived depends on time. 

The amounts of bromide theoretically required to restrain 
development completely (i. e., the concentrations against 
which the developer can just act) may, however, be determined 
by assuming that the relations which obtain for lower con- 
centrations of bromide hold to the limit. The values so 
obtained give reasonable results. (See chapter VII.) 

1 With pyro alone a reverse action appeared, i. e., bromide rendered silver bromide more 
susceptible to reduction. 

160 



THE THEORY OF DEVELOPMENT 

Otherwise, the actual connection between the chemical 
theory and the first photographic method used for determining 
the reduction potential must be sought in general laws and in 
analogy. It is assumed that: 

1. Bromide increases the reaction resistance; 

2. The more powerful the developer the greater the con- 
centration of bromide required to produce a given change in 
the amount of work done; 

3. The change in the total amount of work done is measured 
by the shift of the equilibrium, — i. e., by lowering of the 
maximum or equilibrium value of the density for a fixed 
exposure ; 

4. The reduction potentials of two developers are therefore 
related to each other in the same way as the concentrations 
of bromide required to produce the same change in the total 
amount of work done. 

No assumption is made as to the form of the function relat- 
ing reduction potential and bromide concentration. An 
arbitrary scale is used, which can be converted when suitable 
data are available. 

Owing to the difficulty of presenting the various related 
phases of the subject, the proof that the first method (the 
density depression method as originally suggested by 
Sheppard) measures the shift of the equilibrium was deferred 
until Chapter VII. Assuming for the time being that the 
connection could be established, the action of bromide on the 
plate curves and all associated effects were investigated. 

For theoretical purposes only the straight line portions of 
the plate curves were considered. For each curve 

D = Y(logE -\ogi) (1) 

where y is the slope of the straight line ( = tan a = -r-j =r), 

and log i is the intercept on the log E axis. Log E has a 
fixed value throughout. 

For a family of such curves (i. e., for plates developed for 
difi"erent times) the following results were obtained ; 

1. When no bromide is present, and development is not 
interfered with by a solvent of silver halide, the curves inter- 
sect in a point on the log E axis,that is, log i is constant. 
Deviations from this rule are due to errors or to conditions 
already explained ; 

2. When sufficient bromide is present the curves intersect 
in a point below the log E axis. 

161 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Both these rules were first stated by Hurter and Driffield. 
The new phases of the present investigation, which affords 
additional proof of these laws, consist largely of a different 
method of interpretation and a much wider application of the 
results. 

In deducing the various relations, development for different 
times under fixed conditions was considered as yielding a 
family of straight lines meeting in a point, the coordinates of 
which are: 

a. abscissae, log E units; 

b. ordinates, density units. 

The equation for any curve expressed in terms of the coordi- 
nates of the point of intersection is 

D ^ -r (log E - a) +b, (2) 

It is easily proved that so long as the straight lines meet in a 
point the relation between density and gamma is expressed 
by the equation of a straight line. If the curves do not meet 
in a point the D — y function is not a straight line. 

The D — y curve is therefore the criterion used for a study 
of effects on the intersection point. The equation for this 
curve may be written 

Z> = 6 (t -^) (3) 

or Z) = 6 r - 0^, (4) 

and by comparing (2) and (4) it is seen that 

= log £ -A (5) 

and & = - ^ 0. (6) 

From (5) a = log E - 0. (7) 

In equation 3, is the slope and A the intercept on the y 
axis. Equations 6 and 7 show how the coordinates of the 
point of intersection may be found. 

The effects of bromide on a, 6 and were determined, and 
it was found that : 

a is independent of C (the bromide concentration) ; 

b increases negatively as C increases. 
Hence the effect of bromide is to lower the intersection point. 
Accordingly the depression of density may be interpreted as the 
lowering of this intersection point, and it is obvious that the 
depression will be independent of y if a is constant. This 
may be seen from the expression for the depression — 

d ft + ^'o + (^ - O r, (8) 

162 



THE THEORY OF DEVELOPMENT 

in which d = depression, and b and b^ are the ordinates, a and 
Cq the abscissae of the point of intersection for bromide and 
for no bromide, respectively. This equation is developed 
with no assumption as to the constancy of a, but experimental 
data have shown that a is constant. Hence a = a^ and 
a — a© = 0. Also, b^ for normal development = 0. Therefore, 

d b (9) 

and the depression is measured by the normal downward 
displacement of the point of intersection. 

From equation 7, 6 = log E - a. Both log E and a are 
constant. Hence is constant. Therefore for any given 
developer, over a considerable range of bromide concentra- 
tions, the D — y curve is a straight line of slope which is 
constant for different bromide concentrations. The D — f 
curves for different concentrations of bromide are therefore 
parallel. 

The relation between the depression of density (or lowering 
of the intersection point) and the logarithm of the bromide 
concentration was found to be represented by a straight line 
for a considerable range. The equation is 

d =m(logC -log Co), (10) 

where m is the slope. Log C©, the intercept on the log C axis, 
gives the concentration of bromide which is just sufficient to 
cause a depression. 

A number of experiments with different developers and 
several emulsions demonstrated that *w, the slope, is approxi- 
mately constant. 

dd ^ - 

d logio C 

This indicates that the rate of change of depression with log C 
is constant and independent of developer, emulsion and 
bromide concentration. 

Therefore different developers give density depression curves 
of the same slope (lines parallel to each other), but different 
values of the intercept, log Cq. A comparison of the intercepts 
is thus the same as that for the logarithms of the concentra- 
tions of bromide required to give the same depression, or the 
same change in the amount of work done. 

If "^Br = reduction potential (using Br to indicate de- 
termination by the photographic bromide method) 

^Br - kC, (11) 

163 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

by arbitrary definition, as the form of the function is not 
known. Possibly it may be '"'bt. = k log Cq, or some other 
more involved form, k is intermediate, as the absolute 
energy can not be measured by present methods. But by 
referring to a definite standard developer, relative values may 
be assiged to ir^r. From the above : 

( Br)x (Co) x_. 



(^Br ) Std. (^o) Std. 

As has been stated, this method measures the shift of the 
equilibrium, or the change in the amount of work done; and 
from other considerations it is shown that this method is least 
subject to error. Consequently the values given are the most 
reliable data we have on the relative potentials. 

THE SPEED OF EMULSIONS 

If H is the speed, and E the exposure corresponding to a 
definite density in the region of correct exposure 

^ccl or ^= ^- (13) 

No uniformity exists as to the units in which to express E and 
as to the value of ^. In practice k has been assigned the 
value 34 and E is expressed in visual c. m. s. (of some definite 
source). A photographic light unit is needed, and k should be 
expressed in powers of IQ for greater convenience. Here, k = 
100 and E is expressed in candle-meter-seconds of acetylene 
screened to daylight quality. 

In accordance with the conceptions relating to the common 
intersection point, relations for the speed of a plate are worked 
out in terms of the coordinates of the point. For the general 
case 

log U = Log ^ - a + y (14) 

From this it is evident that if b has an appreciable value 
(i. e., if the inertia changes with y ), the speed depends on the 
contrast. If ^ = 100 and y =1.0, equation 14 becomes 

log H = 2 -- a + b, (15) 

The use of a and b as fundamental constants is advocated. 
It is shown that the inertia point is not a fixed characteristic 
of an emulsion. 

164 



I 
I 



THE THEORY OF DEVELOPMENT 

A few slow emulsions contain bromide, probably absorbed, 
and give a real value for h. With such emulsions the speed 
increases with time of development or with 7, as shown by 
equation 14. 

If the developer contains sufficient bromide the effect is the 
same as if the bromide were in the emulsion. 

Experiments show that the speed of a given emulsion may 
vary widely with the reducing agent used, especially when the 
latter is of the concentration used in this investigation. The 
variations of speed observed can not be accounted for by any 
of the better-known chemical properties of the reducing agent, 
reduction potential included. 

The speed may also be changed by adjustment of the con- 
centrations of the ingredients of the developer. 

Most of the phenomena observed are not of practical import- 
ance, though further study may reveal methods of advantage. 

The practical application of speed determination by the use 
of the D — y curve is indicated. By this means a and b can 
be found, and equation 14 or 15 is then used. 

THE VELOCITY EQUATION, MAXIMUM DENSITY, ETC. 

Five forms of the velocity equation have been considered, 
and, on applying these to experimental data determined for a 
wider range of time than usually employed, the following was 
found to describe most accurately the development process: 

D ^ Doo {I - e^io8'/'o.) (16) 

In the logarithmic form this is 

K (log t - log O = log j)^Zd • (^ ^^ 

The constants /q, K, and Z>oo are evaluated by plotting log 
against log /, such a value of Doo being chosen as 



Doo 



will give a straight line when observed values of density are 
inserted and plotted against the corresponding values of log t, 
K is then the slope and log t^ the intercept on the log / axis. 

This equation is selected as giving the most accurate values 
of Z> 00 , the equation fitting the density-time curve (observed) 
accurately beyond the initial stage. Other equations fitted 
the beginning but showed departures after a time. The 
equation used by Hurter and Driffield and by Sheppard and 
Mees, D =Z>oo (1 — e ""^0» gives values of Z>oo too low 

16S 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

for almost all developers having an appreciable period of 
retardation. It fits the data fairly well for a few developers 
of the ''rapid" type — i. e., those with which the time of 
appearance is extremely short. 

The derivative of equation 17 gives an expression for the 
velocity — 

f = f (Z?„ - D). (18) 

This opens up new questions as to effects giving rise to such 
a form, but these can not be answered at present. From 
other considerations, and from comparison with a more com- 
plete equation derived theoretically by Sheppard, it is believed 
that the velocity is not strictly an inverse function of the time, 
but that this relation represents an approximation to various 
correction factors of which we have no definite knowledge. 
See Sheppard*s equation. Chapter V. 

It is evident that development can not be described by the 
simple first order velocity equation except in a very few spec- 
ial cases. Equation 16 includes these cases and is of much 
more general application. 

The method of determining the maximum density curve 
for a given emulsion and developer is also described. Z>oo is 
computed for different values of log E in the region free from 
fog (the higher exposures) and plotted against the corres- 
ponding values of log E, If the point of intersection is known 
the straight line and upper portion of the curve may be drawn. 

Equation 2 above may be assumed to hold to limiting values 
of D and y. Hence, 

Doo = r 00 (log E - a) + b 

This gives a new method for the computation of the limit of 
contrast to which a plate can be developed. It is shown that 
this limit can not be reached practically because of fog. 

The method of computing y oo given (equation 19) yields 
much more consistent and accurate values than is possible by 
the method of Sheppard and Mees,^ and it imposes no re- 
strictions on the times of development nor on the values of y 
necessary for the plates used. Several weaknesses of 
the older method also become apparent. The equation 
Z> =Z) 00 (1 — e — ^0 was used, y was substituted for D on the 

1 Sheppard, S. E. and Mees, C. E. K., Investigations, 1. c. pp. 65 and 293. 

166 



THE THEORY OF DEVELOPMENT 



assumption that y is proportional to D (i. e., the H. and D. 
straight lines meet in a point on the log E axis). From two 
equations for h and /2 where ti = 2ti, the result was 



Too = 



Ti T2 



1 ^e -^'i 1 -e -^'2 ' 
from which 

K ^-^ log ^' 



t T2- Ti 

Others have attempted to apply this to all cases, and the 
reasons for its failure are now quite clear. If bromide is 
present in emulsion or developer, D may not be replaced by y 
as was done, for from equation 3Z) = 0(y— ^) for such a case. 
Also, the equation Z) =i)oo (1 — e "~^0 holds only approximately 
for a very limited class of developers when used without 
bromide. Consequently the equation fails to give consistent 
results when there is the slightest departure from the restric- 
tions placed upon it. 

There is definite experimental evidence that Z)oo varies 
with the developer. (See Chapter VI, Tables 18, 19, 20 and 
21.) It is believed that in the absence of side reactions which 
complicate the result, the maximum density D » tends to be 
greater the higher the reduction potential of the developer. 
The most marked exceptions are hydroquinone and its halogen 
substitution products. It is known that in the case of hydro- 
quinone sodium sulphite and sodium carbonate react with 
the oxidation products, resulting in a regeneration of the 
reducing agent, possibly according to this scheme: — 

I. Hydroquinone ^ ^ J Hydroquinonate; 

Naa SO, 
Na2 CO, 

II. Hydroquinonate > Quinonate; 

Ag Br 
Naa SO3 
Na2 CO, 

III. Quinonate > Hydroquinonate +Oxyquinonate; 

Na2 SO, 

IV. Oxyquinonate > Quinonate + Dioxyquinonate, 

Na2 CO, 

as found by Luther and Leubner. Therefore the hydro- 
quinone compounds are capable of yielding a higher value for 
the equilibrium point than is normally the case. 

167 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Further, increase of sulphite in the hydroquinone developer 
increases the maximum density (see Chapter IX), which is 
not the case with monomethylparaminophenol. 

If the hydroquinones are excluded, other developers, 
classified according to their equilibriunk densities, stand 
approximately in the order of their reduction potentials. 

Too depends not only on Doo (equation 19), but also on a. 
The latter is the principal factor in plate speed which shows 
no regular variation with the developer. Hence, in general, 
Yoo does not vary with the reduction potential of the de- 
veloper, though it may do so in a certain class of compounds 
which are relatively free from the type of complicating reac- 
tions already mentioned. 

Certain groups of developers show approximately the same 
retardation time and the same value of K, Within such a 
group the resistance factor of the Ohm's law analogy may be 
considered as constant. Hence the relative velocities are 
measures of the relative reduction potentials, or at least 
approximate them. 

Potential 

Velocity - ; . (20) 

Resistance 
and if Ri = Rt 

Potentiali = Velocityi 

(21) 

Potentialj Velocityj 

The various terms of the resistance (see Chapter I, p. 22) 
are included in the reaction resistance as indicated by t^ and 
K, and for the same emulsion other possible terms of the 
numerator in equation 20 are the same. The resultant com- 
parison by equation 21 may not give a true numerical result 
for the relative potential, but it will be of the right order. 

An additional classification of certain compounds was made 
by this method, this placing them in approximately the same 
order as that obtained by preceding data. 

It is indicated that the curve corresponding to the latent 
image fully developed, with no reduction of unaffected grains, 
may lie below such maximum density curves as may be 
obtained from preceding methods. It is possible also that in 
some cases the latent image is not fully developed, but it is 
believed that in general the number of grains affected by light, 
and considered as units of the latent image, may be less than 
the number actually developed. This accounts partially for 

168 



THE THEORY OF DEVELOPMENT 

the small amount of energy required to produce a developable 
image. However, no experimental proof of this hypothesis 
is available. 

Considerable data were secured on the effect of soluble bro- 
mide on the velocity curves and on the maximum density. 
If the bromide concentration is increased with a certain 
developer, and if Z>oo as determined for each concentration 
is plotted against the logarithm of the corresponding con- 
centration (log C), a straight line is obtained, as for the 
density depression. The equation for this curve is 

Do, ^ -m (log C - log C'o), (22) 

where — w is the slope, log C'o is the intercept on the log C 
axis, and C'^ represents the concentration of potassium bro- 
mide theoretically required to prevent development, or the 
concentration against which the developer can just act. 

It is shown (Chapter VII) that the slope of theDoo -log C 
curves is very nearly the same as that for the d —log C curves, 
except that the former is negative. 

The mean of thirty determinations gave 0.50 as the value of 

dd dD oo 

= m . 



d logio C d logio C 

Consequently, different developers yield Doo — log C curves 
which are parallel, as for the depression curves. A compari- 
son of the intercepts is therefore a measure of the reduction 
potential, assuming that the latter varies with the concentra- 
tion of bromide against which the developer can just function. 
(See Chapter I.) As it is neither necessary nor convenient to 
compare the intercepts, the concentrations of bromide at 
which the same Dm was produced were compared. (This is 
the same as comparing the intercepts.) This classification of 
developers gives results which on the whole are comparable 
(as to order) to those of the depression method. 

It is shown that this method is affected by the possibility 
that a developer may give maximum densities higher than 
those corresponding to its reduction potential, as in the case 
of the method of equilibrium values and the velocity 
comparison. 

While Doo varies with the bromide concentration. Too is 
constant and independent of C. (See Chapter VII, Tables 
26 and 27.) 

169 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

It IS proved (Chapter VII, p. 127), that the density de- 
pression measures the shift of the equilibrium, or that the 
lowering of the maximum density is the same as the depression 
of the intersection point. From equation 19 

Too = 



log £ — a 



Yoo, log £, and a are constants, and Z>oo and h vary at the 
same rate with log C Hence Z> » — ^ = T a> (log E — a) ^ 
constant and the change m — h equals the change m Day for a 
definite increment in log C. The change of — 6 from C = to 
C = X is (/ (tf = -ft) and is equal to the shift of the density 
equilibrium point or (Z>oo)o ~ (^oo)x. This may be written 

-ft =^ = (Z?co)o - (^co)x (23) 

which means that the law of density depression applies also 
to the limiting value of the density. This relation confirmed 
by experiment, places the first (density depression) method for 
determining the reduction potentials on a much firmer basis. 

Bromide has no effect on K, the velocity constant (Chapter 
VII, Table 30). 

Iq of the velocity equation and fe the time of appearance, 
are found to be straight-line functions of the concentration 
of bromide, C. The relations are 

(/o)x = ^C + (Oo, (24) 

where (/o)x is the value at the concentration x, and (/o)o that 
for C = 0. For the time of appearance 

(O^ = k'C + (/a)o. (25) 

From complete data for two developers used with many 
different concentrations of bromide, and averaged data from 
smoothed curves for all the functions as now determined, it 
may be shown that the only effect of bromide on the velocity 
is a change during the period of induction — i. e., at the be- 
ginning. After a time the velocity becomes independent of 
the bromide concentration (See Chapter VII, Figs. 42 and 47.) 

The effect of bromide on the curves (a downward normal 
displacement of the curve beyond the initial period), which is 
equal to the depression, d, may be expressed mathematically as 

d =Z?coo -^cox ^D^ - D^ = Z^cox (e^»o«Voo-l). (26) 

This signifies that the density depression d is normally not 
only independent of y, but beyond the initial stage is inde- 

170 



THE THEORY OF DEVELOPMENT 

pendent of the time of development also. Practically this 
statement requires careful analysis, because while the depres- 
sion is in a sense independent of y and of t even at the begin- 
ning, the value of D^ — Dx (the actual difference between the 
densities obtained for C =0 and C = X at a definite time 
during the early stage) is not independent of the time of 
development. The discrepancy is due entirely to the period 
of induction, but it should be remembered that the ordinary 
useful values of y niay be obtained entirely within this 
period. It is emphasized again that equation 26 applies only 
to the range of unchanged velocity. 

The relation between the maximum densities corresponding 
to C = and to C =X was found to be 

Z>coe^^°«'ox/'oo=Z)ooo. (27) 

The combination of equations 26 and 27 with others preceding 
gives rise to new and complex relations which have not been 
thoroughly analyzed . 



THE FOGGING POWER OF DEVELOPERS AND THE DISTRIBUTION 

OF FOG OVER THE IMAGE 

The term '* emulsion fog'* is used for the deposit resulting 
from the development of grains which contain nuclei and are 
consequently capable of reduction before the developer is 
applied. These nuclei may result from the action, during 
or after the making of the emulsion, of light, of chemical sub- 
stances possessing the power of rendering the grains develop- 
able, or from radio-activity. 

It is supposed that emulsion fog forms a relatively small 
proportion of the total deposit usually referred to as chemical 
fog, but this is not known. The two can not be separated. It 
is evident that the developer may play a large part in determin- 
ing to what extent development of emulsion fog takes place. 
It is possible, however, that in addition to the reduction of 
these previously nucleated grains, new grains in the emulsion 
are rendered developable by some specific action of the reduc- 
ing solution. The term chemical fog is applied more strictly 
to the deposit resulting from the latter cause. 

Chemical fog may be produced by physical or chemical 
development, and may show differences from the image in 
structure and in grain distribution. 

For the present, studies of fog must be confined to the total 
effect, from whatever cause. It is pointed out, however, that 

171 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

the complex nature of the fog production probably accounts 
for the fact that the relations for fog are diflFerent from those 
for the image. 

Fog tends to a definite limit or equilibrium density. The 
growth of fog with time was found to be described quite 
accurately by the equation 

D = Doo (I -e-^('-0), (28) 

where Z>oo is the ultimate or equilibrium density and to the 
time at which fogging begins. The fogging velocity is 

^ ^ K{Da> -Z>). (29) 

Accordingly, the growth of the image and that of the fog 
do not appear to follow the same law. (Compare equation 
16 and 18 with 28 and 29.) Equation 28 is the first order 
reaction law corrected for a period of delay. It is probable 
that most of the fog results from physical development and 
that the process is therefore freed from some of the restric- 
tions imposed on the development of the image, where the 
grains are fixed in place and have a definite distribution, and 
the gelatine plays a part. Fog does not vary with reduction 
potential nor with other common properties of a developer. 
(See Chapter VIII, Table 36.) 

It is difficult to find a quantitative expression for fogging 
power. The best, and one which indicates fairly well the 
relative amounts of fog obtained in a definite time, is obtained 
by using the fogging velocity at an intermediate time, such 
as ten minutes. (See Chapter VIII, Tables 35, 36, 37). 

The character of the possible action of fogging agents is 
indicated by the fact that with thiocarbamide the developer 
reduces, in the presence of the fogging agent, no more grains 
than it does alone. Other indirect evidence indicates that 
fogging agents have the power of nucleation, and that this 
action is increased by increased solubility of the silver halide. 
The fogging agent may therefore be considered as rendering 
developable and reducing grains which the developing agent 
can not effect. That this is not a matter of reduction poten- 
tial is quite certain. The developing agent may have the 
same power of nucleation, which means that very pure reduc- 
ing agents of low reduction potential may produce much fog. 

The distribution of fog over the image was studied from 
the standpoint of preceding work, and it was found that fog 
is practically absent from the high densities, but increases as 

172 



THE THEORY OF DEVELOPMENT 

the image densities decrease. Experimental data interpreted 
in the light of the general laws for the growth of the image and 
the effect of bromide led to the equation 

F ^k{Di - Di) (30) 

for the fog. Di is the density of the image corresponding to 
the fog F, and Z>j is the density required practically to prevent 

fog (i. e., the growth of this density is rapid enough so that the 
free bromide formed prevents fog). Equation 30 is a straight 
line of slope k, and k is apparently equal to unity. 

The fogging action of thiocarbamide was studied and found 
to be apparently the same as that of ordinary fogging agents or 
developers giving fog. Results obtained here, as well as the 
work on the concentration of bromide present after develop- 
ment, confirmed equation 30. 

Direct and indirect evidence indicates that fog is more 
restrained by bromide than is the image. This indicates also 
that most fogging agents are of relatively low reduction 
potential. 

Further investigation by similar methods should yield 
valuable results on phenomena of fundamental importance. 

DATA BEARING ON CHEMICAL AND PHYSICAL PHENOMENA 

OCCURRING IN DEVELOPMENT 

The effect of neutral salts, potassium bromide, 
iodide, ferrocyanide, etc. 

From experiments with pyrogallol and other developers at 
very high concentrations of bromide it was concluded that at 
such concentrations bromide has a dual effect: — 

1. It appears to act like a fogging agent in that new grains 
are rendered developable; 

2. It probably forms complexes with the silver bromide, 
giving new characteristics to the emulsion. 

The two effects are no doubt related. That the result is 
not due primarily to action on the gelatine is indicated by 
the fact that for the higher densities the velocity curve is of 
the normal shape and the velocity is not greatly changed. 

The so-called *' acceleration" of development produced by 
certain neutral salts, such as potassium iodide, was investi- 
gated by the usual methods. Potassium iodide was especially 
studied, and its effects were found to be quite different from 
those of bromide or of the other neutral salts used. (See 
Chapter IX, Figs 59 and 60.) This is undoubtedly due to a 
reaction with the silver halide. 

173 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Acceleration by other neutral salts may be attributed to 
effects on diffusion and to adsorption of the developer. 

The period of induction is shortened by these salts, but the 
velocity beyond this period is not greatly changed and the 
maximum density is not affected. 

All the results described depend upon the character of the 
emulsion used. 

The effects of changes in the constitution of the developing 
solution are detailed for hydroquinone, and less extensively 
described for monomethylparaminophenol. The bearing of 
these results is indicated. 

RELATIONS BETWEEN REDUCTION POTENTIAL AND 
PHOTOGRAPHIC PROPERTIES 

Although the present investigation offers more quantitative 
data on both the reduction potentials and the photographic 
properties of developers than have hitherto been available, 
it is still insufficient to permit the formulation of general rules. 
With the methods well in hand, it should be possible to obtain 
the information necessary. At present a few relations which 
appear well founded may be emphasized : 

The degree to which a developer is affected by bromide 
depends on its reduction potential. If a developer is of low 
potential, a given amount of bromide will have a greater 
effect in lowering the density than if the developer has a high 
potential. This is exclusive of the effect of bromide on the fog 
(if the latter is appreciable), which may be an important 
practical consideration. 

The speed of an emulsion varies with the reducer, but this 
is apparently no function of the reduction potential. A care- 
ful study of the data shows that even if reducers of low fogging 
power only are considered, (so that the fog error is minimized), 
the speed does not vary with the reduction potential. 

If high contrast is desired and prolonged development is 
necessary to secure it, it is desirable to use bromide to prevent 
fog. Under these conditions, a higher effective plate speed can 
be secured from a high reduction potential developer with as 
much bromide as may be necessary to eliminate fog. 

The maximum density tends to increase with increasing 
reduction potential. 

Because of the interrelation of speed and maximum density i 
the maximum contrast shows no regular variation with 
reduction potential. 

174 



THE THEORY OF DEVELOPMENT 



Table 45 



of ■•duottaa Vetcatlftl falu** 




OH 
■•A. rot. 1.0 







7 (?) 



0" 

IHfKl 

0.4 



IttolMr 

■ttlvlattra 







CM. 



Oil 



a. 2 



Sld«-cii«tii 
■•thylkUon 





O.CH. 



».• 



0" 

RR.CIIt 
X(CX,). 



94 VMctlv* 
group 




OH 



^-^ 



OH 
irootor than 1 





81 



81(7) 







nia.iici 

6.0 




f-^ CH.r^ 



CNi 



CH(CI,)« 



MH.. H«SQ. raa.HCL IHa.Kl 

a 

7 94- lewor than' p-t-p 



ON 




mi.cR,.Hafo. nfTc. 



lomr tbaa 



«6«» 



10 




«(CM,).. 



JSojfiA 




nia.BCl 



SO to 40 



RHa.IiCl 



CI 




6 (t) 




.HCl 



CB. 



28 



ini.CH,.Bal2« 



Bjift. 




1.0 



la.CNaOMH 








OlaOl 



looo 



175 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Apparently no relation exists between the time of appear- 
ance of the image and the reduction potential. <a is an indica- 
tor of the diffusion rate and the reaction resistance, neither 
one of which is necessarily influenced by the potential. 

No constant relation exists between K, the velocity constant, 
and the potential. For developers of practically the same 
resistance factors, the velocity varies approximately as the 
potential — i. e., it increases with increasing '"'sr. 

The fogging power of developers is not a function of the 
reduction potential. 

Other relations which form the basis for the measurement of 
reduction potential are not included here, as they have been 
discussed. 

It is evident that factors other than the potential control 
the developing properties of organic reducers. Hence the 
ordinary practical working properties of a developer are 
neither safe nor generally useful criteria of its relative energy . 

REDUCTION POTENTIAL AND CHEMICAL STRUCTURE 

Table 45 gives the only quantitative measurements obtained 
on the relation between structure and reduction potential. 
It will be remembered that the values given are based on a 
comparison of the developers at the concentration M/20, 
with the same concentrations of sulphite and carbonate 
throughout. 

A survey of the table indicates that the effect on the 
energy produced by the various substitutions, (mentioned in 
Chapter I., in connection with the rules of Lumi6re and of 
Andresen), is not as readily predicted as these rules would 
indicate. Although it will be necessary to measure many 
more compounds before generalizations can be made, certain 
tendencies are clear. 

It is evident that the aminophenols are most energetic, the 
hydroxyphenols next, and the amines the least, the amount of 
reactive energy depending on the number and position of the 
active groups. It is consistently the case where only two 
active groups are concerned, and if three groups are concerned 
the measurements and experiments with other compounds 
show that a mixture of hydroxyl and amino groups imparts 
greater energy to the substance. 

The introduction of a single methyl group in the nucleus or 
in an amino-group increases the energy. 

Substitution of two methyl groups for the hydrogen of an 
amino-group appears to be of doubtful advantage over the 

176 



THE THEORY OF DEVELOPMENT 

preceding. Contrary to Lumi^re, we find dimethylparamino- 
phenol to be a developer, and oif greater energy than para- 
minophenol, though lower than the monomethyl substitution 
compound. 

Nuclear substitution of a halogen in the hydroxy-phenols 
raises the energy. 

The series of substituted paraminophenols was especially 
studied and additional relations are shown. In addition to 
those already stated the following may be given: 

In the case of nuclear methylation (one methyl group only) 
the energy is increased, but the increase depends on which 
position the methyl group occupies with respect to the other 
groups. (See paramino-orthocresol and paramino-metacresol. 
The latter has undoubtedly greater energy.) 

Paraminocarvacrol has a much lower potential than para- 
minophenol, which would indicate that further methylation 
or increase in the size of the molecule in that direction is 
undesirable. Benzyl paraminophenol gives a result which 
may be questioned, and which should therefore be studied 
further. (The energy is lowered by the substitution of a 
phenyl group in the amino group.) 

Introduction of another amino group greatly increases the 
energy. 

Chlorination of paraminophenol appears of doubtful 
advantage. 

Simultaneous nuclear and side chain methylation (one 
methyl group for each) appears to give greater energy than 
either substitution alone. 

Change to a glycine lowers the potential, as does also the 
introduction of a — CH2OH group. 

These results apply to the groups only in the positions 
shown. Present data do not warrant further deductions, 
especially in view of the fact that the influence of the position 
of the groups is not yet known. 

Many fallacies in the published results of previous investiga- 
tions have come to light during the present investigation. It 
is now quantitatively proved that while developers differ in 
their action, and some have objectionable features, there is a 
considerable number of developers which when properly used 
are capable of giving identical results. It is very often true 
that a greater change in results may be brought about by 
altering the relative concentrations of the ingredients of the 
developing solution than by using a different reducing agent. 

177 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

The action of bromide has been dealt with at length, and 
some of its practical applications have been pointed out. If 
bromide is used in accordance with the principles recorded 
above, there is no doubt of its being of real advantage for 
much photographic work. 



178 



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HCbl, a., Entwicklung. (Knapp, Halle a. S., 1901.) 

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THE CONSTITUTION OF DEVELOPING AGENTS AND THEIR 
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179 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

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schwefliger Saure. Jahrb. Phot. 21: 473. 1907. 

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180 



V 



THE THEORY OF DEVELOPMENT 

VoTECEK, E., Ueber das Verhalten der Hydrazine zu dem photographischen 
Lichtbilde. Phot. Korr. 35: 458. 1898; Arch. wiss. Phot. 1: 73, 
1899; Jahrb. Phot. 13: 98, 515. 1899. 

Waterhouse, J., Amines as accelerators. Brit. J. Phot. 45: 846. 1898. 

Watkins, a.. Some developers compared. Phot. J. 40: 221. 1900. 

THEORY OF REDUCTION POTENTIAL AND EFFECT OF BROBilDES 

Abegg, R., Zur Frage nach der Wirkung der Bromide auf die Entwickler. 

Jahrb. Phot. 18: 65. 1904. 
Armstrong, H. E., The chemical changes attending photographic opera- 
tions. I. The theory of development in relation to the essentially 

electrolytic character of the phenomena and the nature of the photo- 
graphic image. Brit. J. Phot. 39: 276. 1892. 
Bancroft, W. D., The effect of bromide. Brit. J. Phot. 59: 878. 1912. 

Ueber Oxydationsketten. Zeits. physik. Chem. 10: 387. 1892. 
BoGiscH, A., Reductions und Entwicklungsvermogen. Phot. Korr. 37: 

89, 272. 1900. 
Bredig, G., Die electromotorische Scala der photographischen Entwickler. 

Jahrb. Phot. 9: 19. 1895. 
Frary, F. C, and Nietz, A. H., The reaction between alkalies and metol 

and hydrochinon in photographic developers. J. Amer. Chem. Soc. 

37: 2273. 1915. 
, — ., , — ., The reducing power of photographic developers 

as measured by their single potentials. J. Amer. Chem. Soc. 37: 

2246. 1915. 
HuRTER, F., and Driffield, V. C, The action of potassium bromide. 

Phot. J. 38: 360. 1898. 
Lumi£:re, a., and L., and Seyewetz, A., Wirkung von Chinonen und 

ihrer Sulfoderivate auf photographischen Silberbilder. Chem. Ztg. 

34: 1121. 1910. 
LCppo-Cramer, Die verzogernde Wirkung der Bromide in den photo- 
graphischen Entwicklern als kolloidchemischer Vorgang. Koll. Zeits. 

4: 92. 1909. 
, Ueber den Einfiuss der Bromide im Entwickler auf 

die topographische Verteilung des Silbers im Negativ. Phot. Korr. 

49: 383. 1912. 
Luther, R., Die chemische Vorgange in der Photographie. (Knapp, 

Halle a. S., 1899.) 
Matthews, J. H., and Barmeier, F. E., The electro-potentials of certain 

photographic developers and a possible explanation of photographic 

development. Brit. J. Phot. 59: 897. 1912. 
Sheppard, S. E., Gegen Dr. Luppo-Cramer's Auffassung der verz6gernden 

Wirkung der Bromide in den photographischen Entwicklern als 

kolloidchemischer Vorgang. Koll. Zeits. 5: 45. 1909. 
, — ., Reversibility of photographic development and the retarding 

action of soluble bromides. J. Chem. Soc. 87: 1311. 1905. 
, — ., Theory of alkaline development, with notes on the affinities 

of certain reducing agents. J. Chem. Soc. 89: 530. 1906. 



PHOTOGRAPHIC THEORY 

Abegg, R., Eine Theorie der photographischen Entwicklung. Arch. wiss. 

Phot. 1: 109. 1899. 
, — ., Theorie des Eisenentwicklers nach Luther. Arch. wiss. 

Phot. 2: 76. 1900. 

181 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Andresen, M., Zur Theorie der Entwicklung des latenten Lichtbildes. 

Phot. Korr. 35: 445. 1898. 
Banks, E., The theory of development. Brit. J. Phot. 43: 677. 1896. 
Bennett, H. W., Control in development. Phot. J. 43: 74. 1903. 
Bloch, O., Plate speeds. Phot. J. 57: 51. 1917. 
Bothamley, E. H., Remarks on some recent pa{>ers concerning the latent 

photographic image and its development. Phot. J. 39: 123. 1899. 
Desalme, J., The chemical theory of development. Brit. J. Phot. 57: 

653. 1910. 
Dbiffield, v. C, Control of the development factor and a note on s{>eed 

determination. Phot. J. 43: 17. 1903. 
Friedlaender, J. H., Zur Theorie der Entwicklung. Phot. Korr. 39: 

252. 1902. 
KiNGDON, J. C, On the causes of the variation of the Watkins factor for 

different developers. Phot. J. 58: 270. 1918. 
Krohn, F. W. T., The mechanism of development of the image in a dry 

plate negative. Brit. J. Phot. 65: 412. 1918. 
LuMiiiRE, A. and L., and Seyewetz, A., Distinguishing by means of 

development between images in chloride and bromide emulsion. Brit. 

J. Phot. 58: 299. 1911. 
, — ., , — ., On the comparative reducing power of the prin- 
cipal developers. Brit. J. Phot. 56: 627. 1909. 
LCppo-Cramer, Ueber die Veranderung der Kornform der Bromsilbers 

bei der Reduktion und die Nahrkornertheorie der Entwicklung. Phot. 

Korr. 48:547. 1911. 
, Zur Theorie der chemischen Entwicklung. Phot. Korr. 

35: 266. 1908. 
Luther, R., Physical chemistry of negative Processes. Phot. J. 52: 

291. 1912. 
Mees, C. E. K., Time development. Phot. J. 50: 403. 1910. 
, , and Piper, C. W., The fogging power of developers. Phot. 

J. 51:226. 1911; 52: 221. 1912. 
Piper, C. W., The application of physico-chemical theories in plate-testing 

and experimental work with developers. Brit. J. Phot. 60: 119. 1913. 
Renwick, F. F., The physical process of development. Brit. J. Phot. 

58: 75. 1911. 
ScHAUM, K., Zur Theorie des photographischen Prozesses. I. Das latente 

Bild; II. Der Entwicklungsvorgang. Arch. Wiss. Phot. 2: 9. 1900. 
ScHiLOW, N., and Timtschenko, E., Physikalisch-chemische Studien an 

photographischen Entwicklern. III. Hydrochinon als Induktor. Zeits. 

Elektrochem. 19: 816. 1913. 
ScHWARZ, J., Exposition und Entwicklung. Jahrb. Phot. 12: 145. 1898; 

13: 259. 1899. 
Sheppard, S. E., and Mees, C. E. K., Some points in modern chemical 

theory and their bearing on development. Phot. J. 45: 241. 1905. 
, — ., and Meyer, G., Chemical induction in photographic devel- 
opment. J. Amer. Chem. Soc. 42: 689. 1920. 



sensitometry 

AcwoRTH, J., Exposure and development. Phot. J. 35: 361, 1895; 20: 

48. 1895. 
Driffield, V. C, Control of the development factor. Phot. J. 43: 17. 1903. 
Edwards, B. J., Control in development. Brit. J. Phot. 41: 789. 1894. 
Ferguson, W. B., and Howard, B. F., Control of the development factor 

at various temperatures. Brit. J. Phot. 52: 249. 1905. 

182 



THE THEORY OF DEVELOPMENT 

HuRTER, F., and Driffield, V. C, An instrument for the measurement of 
diffuse daylight, and the actinograph. J. Soc. Chem. Ind. 9: 370. 1890. 

y — ., , — ., Exposure and development. Phot. J. 35: 372. 1895. 

, — ., , — ., On the accuracy of the grease spot photometer, etc. 

J. Soc. Chem. Ind. 9: 725. 1890. 

-, — ., y — ., On the range of light in photographic subjects. 



Phot. J. 36: 134. 1895-6. 
, — ., , — ., Photochemical investigations and a new method 

of determination of the sensitiveness of photographic plates. J. Soc. 

Chem. Ind. 9: 455. 1890. 
Jones, L. A., A new non-intermittent sensitometer. J. Frankl.Inst. 

189: 303. 1920. 
Mees, C. E. K., and Sheppard, S. E., New investigations on the study of 

light sources. Phot. J. 50: 287. 1910. 
, — ., , — ., On instruments for sensitometric investigations, etc. 

Phot. J. 54: 200. 1914. 

— , — ., On the sensitometry of photographic plates. Phot. 



J. 54: 282. 1914. 
Sheppard, S. E., and Mees, C. E. K., On the development factor. Phot. 

J. 43: 48. 1903. 
, — ., — — , — ., On the highest development factor attainable. 

Phot. J. 43: 199. 1903. 
Sterry, J., Exposure and development. Phot. J. 35: 371. 1895. 
, — ., Exposure and development relatively considered. Phot. 

J. 35: 288. 1895. 

, — ., Light and development. Phot. J. 51: 320. 1911. 

-, — ., The separation of development into primary and secondary 



actions. Consequent effect upon the correct rendering of light values, 
and theory of the latent image. Brit. J. Phot. 51 : 315. 1904. 

WatkiNs, A., Control in development. Brit. J. Phot. 42: 133. 1895. 

, — ., Development. Brit. J. Phot. 41 : 745. 1894. 

, — ., New methods of speed and gamma testing. Phot. J. 52: 

206. 1912. 

chemistry of developing SOLUTIONS 

Frary, F. C, and Nietz, A. H., The reaction between alkalies and metol 
and hydroquinone in photographic developers. J. Amer. Chem. Soc. 
37: 2273. 1915. 

Luther, R., and Leubner, A., The chemistry of hydroquinone develop- 
ment. Brit. J. Phot. 59: 632, 653, 673, 692, 710, 729, 749. 1912. 

Sheppard, S. E., and Mees, C. E. K., Investigations on the theory of the 
photographic process. (Longmans, London, 1907.) 

PLATE speed determinations 

Bennett, H. W., Control in development. Phot. J. 43: 74. 1903. 

Bloch, O., Plate Speeds. Phot. J. 57: 51. 1917. 

Driffield, V. C, Control of the development factor. Phot. T. 43: 17 

1903. 
HuRTER, F., and Driffield, V. C, Exposure and development. Phot 

J. 35: 372. 1895. 
, — ., ; , — ., Photochemical investigations and a new 

method of determination of the sensitiveness of photographic plates 

J. Soc. Chem. Ind. 9: 455. 1890. *- k . 

, — ., , — ., The latent image and its development. 



Phot. J. 30: 360. 1890. 

183 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Jones, L. A., A new non-intermittent sensitometer. J. Frankl. Inst. 

189:303. 1920. 
KiKGDON, J. C, New methods of speed and gamma testing. Phot. J. 

52: 206. 1912. 
, — ., On the causes of the variation of the Wat kins factor for 

different developers. Phot. J. 58: 270. 1918. 
Krohn, F. W. T., The mechanism of development of the image in a dry 

plate negative. Brit. J. Phot. 65: 412. 1918. 
LxTTHER, R., Die Nomenclature fur die charakterischen Grdssen eines 

Negatives. Jahrb. Phot. 15: 586. 1901. 
Mees, C. E. K., Time development. Phot. J. 50: 403. 1910. 
, — ., and Sheppard, S. E., New investigations on the study of 

light sources. Phot. J. 50: 287. 1910. 

-., On instruments for sensitometric investiga- 



tions, etc. Phot. J. 44: 200. 1904. 

, — ., On the sensitometry of photographic 



plates. Phot. J. 44: 282. 1904. 
Piper, C. W., The application of physico-chemical theories in plate testing 

and experimental work with developers. Brit. J. Phot. 60: 119. 1913. 
Reiss, R., Photographischen Bromsilbertrockenplatte. (Knapp, Halle 

a. S., 1902.) 
ScHWARZ, J., Exposition und Entwicklung. Jahrb. Phot. 12: 145. 1898; 

13: 259. 1899. 
Sheppard, S. E., and Mees, C. E. K., Investigations on the theory of the 

photographic process. (Longmans, London, 1907.) 

, — ., , — ., On the development factor. Phot. J. 43: 48. 1903. 

, — ., , — ., On the highest development factor attainable. 

Phot. J. 43: 199. 1903. 
Sterry, J., Exposure and development. Phot. J. 35: 371. 1895. 
, — ., Exposure and development relatively considered. Phot. 

J. 35:288. 1895. 

, — ., Light and development. Phot. J. 51: 320. 1911. 

, — ., Standard plates and some causes of apparent alteration in 

rapidity. Phot. J. 35: 118. 1895. 
Watkins, a., Control in development. Brit. J. Phot. 42: 133. 1895. 

, — ., Development. Brit. J. Phot. 41: 745. 1894. 

, — ., Photography, its principles and applications. (Van Nostrand, 

New York, 1911.) 

y — ., Some developers compared. Phot. J. 40: 221. 1900. 

-, — ., Time development. Variation of temperature coefHcient 



for different plates. Brit. J. Phot. 58: 3. 1911. 



VELOCITY OF DEVELOPMENT 

Abegg, R., Theorie des Eisenentwicklers nach Luther. Arch. wiss. Phot. 

2: 76. 1900. 
Bloch, O., Plate speeds. Phot. J. 41: 51. 1917. 
Brunner, E., Reaktionsgeschwindigkeit in heterogenen Systemen. Zeits. 

phys. Chem. 47: 56. 1904. 

CoLSON, R., Einfluss der Diffusion der Bestandteile des Entwicklers bei 
der photographischen Entwicklung. Arch. wiss. Phot. 1:31. 1899. 

Gu6bhard, a., Diffusion im Entwicklerbade. Jahrb. Phot. 30: 515. 1899. 

Hurter, F., and Driffield, V. C, Photochemical investigations and a 
new method of determination of the sensitiveness of photographic 
plates. J. Soc. Chem. Ind. 9: 455. 1890. 

184 



THE THEORY OF DEVELOPMENT 

Lehmann, E., Zur Theorie der Tiefenentwicklung. Phot. Runds. 50: 

55. 1913. 
Li) ppo- Cramer, Photographische Probleme. (Knapp, Halle a. S., 1907.) 
Luther, R., Chemische Vorgange in der Photographie (Knapp, Halle 

a. S., 1899.) 
Mbes, C. E. K., Time development. Phot. J. 50: 403. 1910. 
Piper, C. W., The application of physico-chemical theories in plate-testing 

and experimental work with developers. Brit. J. Phot. 60: 119. 1913. 
Renwick, F. F., The physical process of development. Brit. J. Phot. 

58:75. 1911. ' 
ScHAUM, K., Zur Theorie des photographischen Prozesses. Arch. wiss. 

Phot. 2:9. 1900. 
ScHiLOW, N., and Timtschenko, E., Physikalisch-chemische Studien an 

photographischen Entwicklern. HI. Hydrochinon als Induktor. 

Zeits. Elektrochem. 19:816. 1913. 
Sheppard, S. E., Reversibility of photographic development and the retard- 
ing action of soluble bromides. J. Chem. Soc. 87: 1311. 1905. 
, — ., Theory of alkaline development, with notes on the affinities 

of certain reducing agents. J. Chem. Soc. 89: 530. 1906. 

— ., and Mees, C. E. K., Investigations on the theory of the 



/ / f * ^^ 

photographic process. (Longmans, London, 1907.) 

-, — ., On some points in modern chemical theory 



and their bearing on development. Phot. J. 45: 241. 1905. 

— ., The chemical dynamics of photographic 



development. Proc. Roy. Soc. 74: 457. 1904. 

-., The theory of photographic processes. Part 



IL Phot. J. 45: 319. 1905. 

— ., and Meyer, G., Chemical induction and photographic 



development. J. Amer. Chem. Soc. 42: 689. 1920; Phot. J. 60: 12. 

1920. 
Vanzbtti, B. L., Diffusion of electrolytes. Chem. Abst. 9: 406. 1915. 
WiLDERMANN, M., Ueber die Geschwindigkeit der Reaktion vor voll- 

standigem Gleichgewichte und vor dem Uebergangspunkte, u. s. w. 

Zeits. physik. Chem. 30: 341. 1899. 



185 



Index of Authors 



Abegg, R., 22, 23 

Andresen, M., 16, 18, 175 

Armstrong, H. E., 22 

Bancroft, W. D., 15 

Bloch, O., 84 

Bredig, G., 15 

Colby, 79 

Driffield, V. C, Hurter, F., and 

, 22, 25, 30, 32, 33, 59, 

60, 61, 64, 73, 78, 80, 82, 110, 
141, 162, 165 

Eder, J. M., 14 

Frary, F. C, 29, 147 

, and Mitchell, 147 

, and Nietz, A. H., 29, 57 

Hurter, F., and Driffield, V. C.t 
22, 25, 30, 32, 33, 59, 60, 61, 
64, 73, 78, 80, 82, 110, 141, 162, 
165 

Jones, L. A., 26 

Leubner, a., Luther, R., and 
, 29, 167 

LuMifeRE, A., 16, 18, 175 

LuMifiRE, L., 16, 18 

Lufpo-Cramer, 150, 153 

Luther, R., 22 

, and, Leubner, A., 29, 167 

Mellor, 84 



Mees, C. E. K., and Piper, C. W.„ 
136, 137, 139 

, and Sheppard, S. E., 26 

, Sheppard, S. E., and 

, 18, 25, 29, 30, 32, 33, 80, 

81, 82, S3, 124, 165, 166 

Meyer, G., Sheppard, S. E., and 
, 77, 153 

Mitchell, Frary, F. C, and 
,147 

Nernst, W., 15, 78, 107 

Nietz, A. H., 92 

-, Frary, F. C, and ,. 



29,57 

ostwald, w., 15 

Perley, 147 

Piper, C. W., Mees, C. E. K., and 
, 136, 137, 139 

Seyewetz, a., 16, 18 

Sheppard, S. E., 18, 19, 23, 24, 
25, 32, 36, 57, 78, 79, 82, 92, 
126, 150, 166 

, and Mees, C. E. K., 18, 

25, 29, 30, 32, 33, 80, 81, 82, 83, 
124, 165, 166 

, and Meyer, G., 77, 153 

-, Mees, C. E. K., 26 



Waterhouse, J., 147 
WiLSEY, R. B., 92, 125 



186 



Index of Subjects 



Abegg's theory of bromide restraint, 22 

plan for measuring reduction potential, 23 

Alkyl groups, substitution of, in developer, 17, 18, 176 
Ammo groups, substitution of, in developer, 17, 18, 176 
Apparatus used in developing test plates, 27, 28 

Bloch's method of solving velocity equations, 84 

Bromide, Abegg's theory of restraining action of, 22 

abnormal effect of soluble, on developer, 150 

advantages of, in developer for speed determination, 69, 178 

chemical effects of, in developer, 22, 23, 24 

effect of soluble, on maximum contrast, 119, 169 

, on density, 19, 24, 32-58, 113, 122, 150, 160-164, 

173 

, on fog, 68, 69, 144, 146, 152, 173 

— , on maximum density, 113-118, 169 

, on plate curves, 39, 450, 160-164 

, on reduction potential, 109 

• , on time of appearance of image, 32, 125, 170 

, on velocity, 112, 113, 124, 126, 130, 169, 170 

• , on velocity constant, 124, 170 

Bromide concentration and density depression, 19, 24, 32-58, 122, 160-164, 
173 

Bromide concentration giving same maximum density for different emul- 
sions, 116-118, 169 

Carbonate, effect of variable quantities in developer, 72, 156, 157 

Chemical fog, 134, 135, 171 

Contrast, 31 

effect of fog on, 101, 143, 166 
maximum, determination of, 100 

, effect of bromide on, 119, 169 

, relation of, to reduction potential, 102, 109 

, variation of, with developer, 102-109, 168 

Density, concentration of bromide required to give same maximum, for 
different developers for same emulsion, 116-118, 169 
definition of, 26 
growth of, with development, 31 

, with exposure, 31 

maximum equation, 78, 79, 83, 88, 97, 165 

, variation with concentration of bromide in 

developer, 113-118, 169 

, variation with develop)er, 113-118, 169 

— ' — ' , variation with exposure, 99 

, variation with reduction potential, 102-105, 167 

measurement of, 30 
Density depression, due to bromide, 32, 36, 37, 41, 49, 122, 130, 160-164 

a measure of the shift of the equilibrium, 122, 170 
method of measuring reduction potential by, 19, 24, 

32-58, 160-164 
rate of, 38, 52, 163 
relation to bromide concentration, 38, 41, 49, 163 

187 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Developers, abnormal effects of bromide in, 150, 173 

classification of, according to fogging velocity, 140, 142 

, according to maximum fog, 142 

, general, 14 

; —, structural, 16, 174, 175 

depression with different ■ — , in relation to- bromide 

concentration, 49 

effect of changes in constitution of, 72, 155 

carbonate in, 72, 156, 157 

hydroquinone in, 72, 156, 157 

neutral salts in, 150, 153, 154, 173 

potassium iodide in, 153, 173 

sulphite in, 72, 156, 157, 158, 168 

enerp^y of, 18, 58, 175 

fogging velocity of, 138, 172 

formulae of, used for test plates, 28 

induction p)eriod of, 77 

reduction potential of, 15. 19, 22, 32, 54, 58, 175 

, chemical theory of method of deter- 
mining, 19 

; , table of relative, 56, 58, 175 

relation of concentration of ingredients of, to speed, 72, 165 

different to speed, 67, 69, 70, 71, 165 

relation to fogging, 68, 140, 141, 172 

structure of, and relation to photographic properties, 16, 
174, 176 

substitution of alkyl groups in, 17, 18, 176 

; — ; ammo groups in, 17, 18, 176 

variation of maximum contrast with, 102-109, 168 

maximum density with, 102-109, 167 

Development, method of, for standard conditions, 26 

velocity of, 15, 76 
Dichroic fog, 136 

Emulsion, effect of, on value of density depression, 54 

Emulsion fog, 134, 171 

Emulsions used for experimental work, 29 

Energy of developer, 58, 176 

increase of, 18, 176 
Exposure of photographic plates for quantitative measurement, 25 

importance of method of, for speed 

determination, 59 
variation of maximum density with, 99 

Fog, chemical, 134, 135, 171 

dichroic, 136 

distribution over image, 69, 141, 144-147, 149, 171 

emulsion, 134, 171 

nature of, 134-137, 171 

relation of bromide to, 68, 69, 144, 146, 152, 173 

relation to reduction potential, 68, 136, 137, 172 
Fogging action of thiocarbamide, 136, 147, 172 
Fogging power, 137-141, 171 
Fogging velocity, expression for, 138, 172 

of different developers, 140, 141, 142 

Glycine, effect of change to, in developer, 17, 18, 177 

188 



THE THEORY OF DEVELOPMENT 

Hurter and Driffield's method for determining the speed of emulsions, 60 

sensitometric work, 25, 30, 80 

work on velocity, 78, 80, 165 
Hydroquinone, effect of variable quantities of, in developer, 72, 156, 157 

Induction period of developers, 77, 155 

Latent image, development of, 109, 168 

curve for, 109-111 

Maximum contrast, determination of, 100 

effect of bromide on, 119, 169 
relation of, to reduction potential, 102-109 
variation of, with developer, 102-109, 168 
Maximum density, equation, 78, 79, 83, 88, 97, 165 

variation of, with concentration of bromide in devel- 
oper, 113-118, 169 

, with exposure, 99 

, with reduction p>otential, 102-109, 167 

Neutral salts, effect of, in developer, 150, 154, 173 

Nietz's equation for velocity of development, 88, 92, 97, 165 

Potassium bromide, abnormal effect in developer, 150, 173 

Potassium citrate, effect in developer, 154 

Potassium ferrocyanide, effect in developer, 154 

Potassium iodide, effect in developer, 153 

Potassium nitrate, effect in developer, 154 

Potassium oxalate, effect in developer, 154 

Potassium sulphate, effect in developer, 154 

Reduction potential of developers, 15, 19, 22, 32, 54, 56, 58, 107, 108, 113' 

175 
Abeg^'s plan for measuring, 23 
chemical theory of method of determining, 19 
definition of, 15, 19 
determination of, by density depression method, 19, 

24, 32, 33-58, 122, 160-164 
, by maximum density method, 113- 

118, 169 

, by Sheppard's method, 32 

— , by velocity method, 107, 108, 168 

effect of bromide on, 109 
relation to chemical structure, 176 

fog, 68, 136, 137, 172 

maximum contrast, 102-109 

maximum density, 102-109, 167 

photographic properties, 174 

^ speed, 70, 72, 165 

sensitometric theory of determining, 30 
Sheppard's method of measuring, 19, 24, 32 

Sensitometry, 25, 31, 80 

Sensitometric theory of method of determining reduction potentials, 30 

Sheppard's method of measuring reduction potential, 19, 24, 32 

velocity equation, 78 
Sheppard and Mees' work on velocity of development, 81, 82, 124, 165 

sensitometric work, 25, 30, 80 

189 



MONOGRAPHS ON THE THEORY OF PHOTOGRAPHY 

Speed of emulsions, 59, 164 

definition of absolute, 65 

determination of, 59, 62 

determination by Hurter and Driffield's method, 60 

, precision of method of, 73 

effect of bromide on, 68, 165 

changing ^concentration of ingredients of 

developers on, 72, 165 

different developers on, 67, 69, 70, 71, 165 

contrast, 64 

reduction potential of developers, 70, 72, 165 

relation to exposure, 59 

variation with different emulsions, 66 
Sulphite, effect of variable quantities in developer, 72, 156, 157, 158, 168 

Thiocarbamide, fogging action of, 136, 147, 172 
Time of appearance of latent image, 32 

effect of soluble bromide on, 32, 125, 170 

Velocity of development, 76 

Bloch's method of solving equations for, 84 

offog, 138, 172 

determination of, 76, 80 

, reduction potential by, 107, 

108, 168 

effect of diffusion on, 78, 83 

soluble bromides on, 113, 124, 126, 130, 

170 

two successive reactions on (Mellor), 84 

equations, 78, 79, 83, 88, 97, 165 

Nernst's theory for reaction , 78 

Nietz's equation for, 88, 92, 97, 165 

Sheppard's equation for, 78 

Wilsey's equation for, 92 
Velocity curves, depression of, 130, 170 

effect of bromide concentration on, 126, 170 

Wilsey's equation for velocity of development, 92 



190 



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