402 HANDBOOK OF PHOTOGRAPHY 



To illustrate the use of this equation, suppose we wish to reduce the amount 

 of hypo to 1/50,000 of its initial value before stopping washing. Then (Mo — M) is 

 1/50,000 of Mo, so that (Mo) /(Mo - M) = 50,000. If we choose k =0.1, then the 

 time, in minutes, required for washing will be 



t = 23.0259 X 4.6990 = 108 min. (11) 



Similarly, if a given negative has 1 g. of hypo on it initially, and we wish to carry out 

 washing until the amount of hypo finally remaining is 0.0001, then 



t = 23.0259 logic ( q qoqi ) = 23.0259 logic 10,000 = 23.0259 X 4 = 92 miu. (12) 



It should be realized that the results given by these equations depend upon the 

 assumptions that the rate of diffusion is an exponential function of time and that the 

 photosensitive material is thoroughly agitated in the continuously flowing wash water. 

 The first assumption is generally well fulfilled in practice, so that the degree to which 

 the above expressions represent actual conditions depends upon the degree to which the 

 second assumption (which is under the control of the photographer) is fulfilled. For 

 practical applications it may be said that the above equations represent favorable 

 limiting conditions and that in any practical case the wash time may be increased 

 advantageously over that given in the above equations. 



Multiple-hath Washing. — -In the multiple-bath system of washing, the removal of 

 sodium thiosulphate (or other solute) is a slightly more complicated process. In any 

 given wash, the amount of solute is removed continuously with agitation of the nega- 

 tive in the wash water until the final limiting value is reached. This limiting value is 

 • that for which the amount of solute in the wash water is in equilibrium with that 

 remaining in the negative, i.e.. the concentration of solute in the negative is equal to 

 the concentration of the wash water. The negative is then removed to another bath 

 where the amount of solute removed progresses continuously until another equilibrium 

 of lesser concentration is reached. Except for the instant when the film is initially 

 introduced into a fresh wash bath, it is always immersed in a bath which is contami- 

 nated with hypo which this bath has removed from the film. Because the film is 

 immersed in water containing hypo, only that amount of solute (hypo in this case) can 

 be removed which will bring to equilibrium the solute in the gelatin with that of the 

 wash water. There is no possibility of removing more solute from the film after the 

 equilibrium condition has been reached no matter how long the material is washed 

 beyond this point. For each bath, therefore, a time is reached beyond which the bath 

 is no longer effective in the removal of solute, and further washing can be attained 

 only by removal of the film to a fresh bath. 



Following the method of the previous section, equations may be developed for the 

 effect of each of a number of baths, as well as the over-all or net effect of several baths. 

 The essential feature in multiple-bath washing is the number of baths required to 

 reduce the original concentration of the solute to some definite and small fraction of 

 its original value. This case has been treated by Warwick. ^ If n is the number of 

 wash baths, all of which are similar, \/A is the fraction of the solute left after n wash- 

 ings, V is the volume of the wash water in each bath, and v is the volume of solution 

 on the surface of the film and carried over into one bath as a contamination from the 

 preceding bath, then the number of baths required is given by 



^ ^ (13) 



' Warwick, A. W., Scientific Washing of Negatives and Prints, Am. Phot., 11 (No. 6), 317-327 

 (1917). 



