348 HANDBOOK OF PHOTOGRAPHY 



developers of ammonium chloride in relativelj'- high concentration. This was sug- 

 gested in 1904' with concentrations of 150 to 200 g. per 1. mentioned. The U. S. Pat. 

 2053515, issued in 1936, covers a fine-grain photographic developer comprising 

 metol-hydroquinone as developing agent and ammonium chloride in amount sufficient 

 to produce a fine-grain image. 



In all attempts at fine-grain development, full advantage should be taken of all 

 conditions tending toward that end. Some workers have concluded that fine grain is 

 nothing but low gamma. This appears an oversimplification, but it is very generally 

 true that low contrasts contribute to fine grain. Similarly, overexposure usually 

 tends to increase graininess. Thus for minimum graininess negatives should be 

 developed to as low a gamma as consistent with the work, and the exposure should be 

 the minimum necessary to give the detail required. 



Development Quantitatively Considered. — Quantitative studies of development 

 have been made to establish a basis for its theoretical consideration and for the very 

 practical purpose of control of processing. In using any new emulsion or developing 

 formula, it is necessarj- to choose a developing time which, under the conditions of 

 use, will give the contrast desired. Thus the quantitative study of development is 

 of basic theoretical and practical interest. This study may be carried out through 

 measurements of growth of either gamma or density as development proceeds. 



When the study is based upon gamma, the attempt is made to determine the 

 relationship between gamma and time of development. It is usually possible to 

 express this relationship approximately through an expression of the form 



T = T«(l - f-^'O (1) 



where y = the gamma produced in the time t; 



■Y„ = the maximum gamma produced on prolonged development; 

 K = the velocity constant, so called. 

 Figure 1 shows this type of equation, represented by the solid line, plotted to approxi- 

 mate actual experimental data shown by O's and the dotted line. It is at once evident 

 that this does not fit exactly and, in general, regardless of values of -/„ and K chosen, 

 only two points can be fitted. A noticeable difference between the two curves always 

 occurs at low values of t as the equation shows finite values of y at times shorter than 

 that actually producing any measurable effects. 



The period before any measurable development occurs is called the "induction 

 period." It has no counterpart in the equation above, but a second, slightly different, 

 equation takes account of it. The equation 



y = y„[l _ f-A-(/-(o)] (2) 



may be made to fit three points of the experimental data and specifically allows for an 

 induction period through the term tn. This insures better fit than with the first 

 equation; but it should be considered as only an empirical representation. 



The equations just given approximate the relationship between 7 and time of 

 development. If, instead of 7, the progress of development of density for a given 

 exposure is determined, the growth of density is found to be quite similar to 

 the increase in gamma. In many cases, the family of sensitometric curves represent- 

 ing the results of different development times have straight-line portions which, when 

 extrapolated, intersect in a point, called the tie point, which may be on or below but 

 rarely is above the D = axis. For the cases where a tie point exists and lies on the 

 D = axis, the growth of density of a point on the straight-line portion of the curve 

 may be represented by equations of the same form as those used for the growth of 



1 LuMifcRE, A.. L. LuMifcRE, and A. Setewetz, Brit. J. Phot, 61, 866-867 (1904). 



