216 HANDBOOK OF PHOTOGRAPHY 



obtain this same opacity with another film having a speed of Weston 24, our equations 

 show that, if the exposure time is the only variable, this must be reduced to Hoo sec. 

 to produce the desired effect. If we had chosen the Wynne system instead of the 

 Weston system in this example, the exposure time in the second case would have been 

 >^oo sec, because in this system doubling the speed number quadruples the exposure or 

 requires only one-fourth the exposure for the same photographic effect. 



Correlation of Factors Affecting Exposure. — We are now in a position to correlate 

 all the factors affecting the exposure of the film. The exposure given to the film in 

 the camera is E = I't where /' is given by Eq. (9). Therefore the exposure of the 

 film in the camera is 



^ = ^'^' == FpiM + irs. (1^) 



which is now related to the exposure It in meter-candle-seconds as given by the H 

 and D characteristic curves. 



If we arbitrarily select some exposure Eo for which we determine the values of 

 exposure meters, exposure tables, or other exposure conditions in terms of other refer- 

 ence values of light intensity 7o, filter factor i^o, lens transmission To, aperture stop /o, 

 magnification Mo, exposure time to, and film speed So, than the reference exposure 

 becomes 



p _ T'f' lokToto 



J^o - loh- FofoHMo + irSo ^^^^ 



In order that identical photographic effects may be obtained, it is necessary that 

 E = Eoso that 



IkTt ^ lokToto 



FP{M + lYKnS FofoKMo + lyS^ ^ ^ 



From this relation we obtain, by dividing by the left-hand side of the equation. 



This relation will be found invaluable for determining the exposure conditions for 

 some unknown conditions when the exposure for other reference conditions are known. 

 This equation can be especially helpful in extending the use of the exposure tables, 

 given in a later section of this chapter, beyond the conditions for which they now 

 apply. In practice Mo<Kl, Fq = 1, and To/T is always 1 for the same lens system. 

 Thus Eq. (17) may be reduced to the more practical form 



' = OS)(T)(t)<T)<'" + "' <''' 



Since Eqs. (17) and (18) are in the form of ratios between known and unknown 

 conditions, it does not make any difference in what units the factors are expressed, so 

 long as both factors in the same parenthesis are expressed in the same system. Thus 

 both S and S^ must be expressed in the same speed system. This may be Weston, 

 H and D, or Watkins. But the equations do not apply if So is expressed in H and D 

 and ;iS in Weston figures. 



The equations may be manipulated by simple algebra to determine any of the 

 other factors which may be desired. 



As a somewhat extreme but complete example of the application of these exposure 

 equations, consider the following problem in which it is assumed that all the 



