Journal of the Society of Motion Picture and Television Engineers (1950-1954)

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(T+(A (18) (T+v-tvY" (19) When solved for Z), this equation then appears as: _A A D = AC° TA~B ~C(T + (A ~ B)f)A~B A A (T + (A B)f)A~B TA~B (20) In tanks where the film is dry when it enters, the differential equation takes the form: dW -WE df "= Y^Bj D (21) This may be solved as follows: dW B df "h T Bf W + ^-ITpf W = -D (22) T-Bf 1*2** (23) When solved for Z), the equation then appears as: <• b) In those tanks where the rate of gain of liquid exactly equals the rate of loss of solution (so that A = B), the differential equation is: dW _ -WE df " -? (27) and may be solved by the following steps: dW WE + TD = (28) I WB+TD -f B ln W0B + TD T W ^L (30) Or when solved for D, this equation is expressed as: D = B (C0e CXI e (31) Values of D may be obtained by methods similar to those used in determining A and B. The solution is analyzed for a constituent, both before and after a known amount of film is processed. Values of tank volume (F), concentration (C and C0), footage (/), carry-in rate (A), and carry-out rate (B) are then substituted in the appropriate equation — whichever one applies for the particular tank — and the equation is solved for D. A summary of the equations which may be used in calculating D for this type of chemical is listed in Fig. 2. Determination of Reaction Rates (Chemicals Added) When film passes through processing solutions, certain constituents are added to the solutions, rather than withdrawn, as a result of chemical action. Potassium bromide, silver thiosulfate, and potassium ferrocyanide are the most prominent examples of the chemicals showing this type of behavior. The differential equations for such constituents may be set up, and solved, in the same way as for constituents depleted by chemical action, except that in this case D may be considered to have a negative sign. Values of D for these January 1954 Journal of the SMPTE Vol. 62