466 Messrs. S. E. Sheppard and C. E. K. Mees. [Dec. 20, 



proportionately, the ratio of the densities due to any two exposures 

 is constant, and independent of the time of development. 



Hurter and Driffield showed that if a geometrically increasing series 

 of exposures be given to a plate over a certain range, the density 

 increased arithmetically. Over this period of " correct exposure " the 

 following equation holds : D = y log E/i, where E is the exposure, 

 iis a characteristic constant of the plate, termed the inertia, and y is 

 a constant depending upon the development, and called the develop- 

 ment factor. The magnitudes i and y are obtained graphically as 

 follows : the densities due to nine successive exposures are plotted as 

 ordinates, and the logarithms of the corresponding exposures as 

 abscissae. A curve is obtained which, for a certain period, is practi- 

 cally a straight line. The point where this cuts the exposure axis 

 gives log i, and if be the angle of inclination, y = tan 9. Analyti- 

 cally, the value of y may be deduced as follows : for two exposures, 

 EI and E 2 , we obtain the densities DI and D 2 , the equations being 



Dj = y logEi/i, D 2 = y log E 2 /* 

 eliminating i, D 2 - DI AD .* 



' ~ log E 2 - log EI . A log E ' 



y is therefore independent of the absolute exposure, and only depen- 

 dent on the E 2 /Ei which is fixed by the sector wheel. t 



In order to test the constancy of the density ratios, two plates were 

 exposed simultaneously in the sensitometer to avoid errors due to 

 light inconstancy, and developed for different times. The values [of 

 y were obtained from the curves in the graphic manner described. 

 Each plate was allowed 100 c.c. of developer. 



FeSo 4 Mol. 8-0 c.c. + K 2 C 2 4 Mol. to 100 c.c. 



The logarithms of the exposures are given on an arbitrary scale, 

 putting logE 9 = 1-0, as the absolute value is unimportant. A typical 

 table is given below : 



Table X. Tj = 2 mins., T 2 = 6 mins. 

 No. Log E. Density Tj. Density T 2 . Eatio 



1 3-30 



2 3-012 0-876 2-563 2-935 



3 2-72 0-759 2-230 2-900 



4 2-42 0-685 1-995 2'920 



5 2-14 0-499 1-491 2'983 



6 1-80 0-332 1-096 3-330 



7 1-575 0-234 0-716 3-050 



8 1-360 0-128 0-329 2'680 



Mean ... 2-957 



* Or D = 7 k?J, hence y= dl) 



, 

 t dlog E 



f For calibration of sector-wheel v. loc. cit., p. 2. 



