Equations are developed which give values for the optimum optical densities at which to run spectrophotometric analyses. Calculations made on a range-of-error basis show that the optimum optical density is 0.5553 (27.84 percent transmission); on a probable error basis the optimum optical density is 0.4816 (32.99 percent transmission). However, the precision of measurement is about the same for optical densities from 0.3 to 0.9 (or transmissions from 50 percent to 12.5 percent). The treatment is presumably valid for any type of single-beam spectroscopy in which the receiver (including amplifier) has a limit of precision (dI) which is independent of the size of signal received. Thermopiles and photoelectric cells are in this class. Where the intensity is detected by visual comparison, dI/I is independent of the size of signal, and the treatment is not valid.
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