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 member or possible specification in every color system can be reduced to such excitation values, and hence can be assigned a certain position on the color-mixture triangle. In this way the data of separate systems can be definitely intercompared, and can be interconverted in so far as the representations of the several systems overlap; with the obvious restriction that peculiarities of the stimulus—such as spectrophotometric details—which determine no characteristic excitation values, are necessarily lost.

It would therefore appear that the first step in our task is to provide means for transforming the data of each colorimetric system into elementary excitation values, and where possible, means for the reverse transformation. When such transformations have been made, it will be easy to determine the equivalents of one system in terms of any other system. The general principles underlying these computations have already been outlined briefly in our presentation of the excitation curves (vide supra). The spectral energy distribution of a given standard stimulus is required if the latter is to be dealt with directly, but can be dispensed with as soon as its combination with the elementary excitation curves has provided a specification of the stimulus in terms of the elementaries.

A. .—Spectrophotometric data are usually given in the form of spectral transmission or reflection curves. Such curves require combination with a certain energy distribution—representative of the particular source by which the object is viewed—in order that they should become determinative of a definite color. The process of reducing any given spectrophotometric specification to excitation values is therefore as follows. (a) Multiply each of the ordinates of the transmission or reflection curve by the corresponding ordinates of the energy distribution curve of the source. (b) Multiply each of the ordinates of the resulting curve by the corresponding ordinates of each of the color excitation functions as given in (under “Excitations’’), this being a separate operation for each of the three excitations, yielding three separate curves which represent the respective excitation values for each wave