General Problem of Photographic Reproduction. 735 



be employed to produce the positive. In practice this 

 process (o£ printing) is usually different from that by which 

 the negative was itself made ; but for simplicity we shall 

 suppose that the same process is employed in both operations. 

 This requirement of identity of procedure in the two cases is 

 to be construed strictly, extending, for example, to duration 

 of development and degree of intensification, if any. Also we 

 shall suppose for the present that the exposure is the same. In 

 strictness this should be understood to require that both the 

 intensity of the incident light and the time of its operation be 

 maintained ; but since between wide limits the effect is known 

 to depend only upon the product of these quantities, we may 

 be content to regard exposure as defined by a single quantity, 

 viz. intensity of light x time. 



Under these restrictions the transparency t' at any point 

 of the negative is a definite function of the transparency t at 

 the corresponding point of the original, so that we may write 



f=At), (i) 



/ depending upon the photographic procedure and being 

 usually such that as t increases from to 1, t' decreases 

 continually. When the operation is repeated upon the 

 negative, the transparency t" at the corresponding part of 

 the positive is given by 



l"=f(t') (2) 



Complete reproduction may be considered to demand that at 

 every point t" — t. Equation (2) then expresses that t must 

 be the same function of t' that t 1 is of t. Or, if the relation 

 between t and t' be written in the form 



F(-«, O=0, (3) 



F must be a symmetrical function of the two variables. If 

 we regard £, f as the rectangular coordinates of a point, 

 (.'->) expresses the relationship by a curve which is to be 

 symmetrical with respect to the bisecting line t' = t. 



So far no particular form of /, or F, is demanded ; no 

 particular kind of negative is indicated as ideal. But certain 

 simple cases call for notice. Among these is 



« + «' = !, (4) 



which obviously satisfies the condition of symmetry. The 

 representative curve is a straight line, equally inclined to the 

 axes. According to (4), when t = 0, f = 1. This requirement 

 is usually satisfied in photography, being known as freedom 



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