## Abstract

Wave-lengths have been calculated for use in the thirty selected ordinate method for computing the visual reflectance or transmittance of colored materials illuminated with radiation from black bodies at the temperatures: 2000°K, 2200°K, 2360°K, 2600°K, 2848°K, 3000°K, 3200°K, and 4000°K. Each ordinate of any one of these sets is displaced by an almost constant wave-length interval from the corresponding ordinate of any other set. The average value of this displacement is given very accurately (±0.10m*μ*) by the formula:

where the two sets of wave-lengths correspond to black-body illuminants having the Kelvin temperatures, *T*_{1} and *T*_{2}, between 2000°K and 4000°K. The numerical constant of the above equation is proportional to the value of the constant (*C*_{2}=14,330) adopted for use in Planck’s formula. Table XVII of the *Handbook of Colorimetry* gives the wave-lengths of the thirty selected ordinates for the I.C.I. illuminant “A” (2848°K) and the I.C.I. “visibility” function,
$\overline{y}$. These wave-lengths increased by the constant given by the following formula, can be used for any black-body illuminant having the temperature *T* between 2000°K and 4000°K:

A. C. Hardy has suggested the use of a transparent plate ruled along the wave-lengths of the selected ordinates for 2848°K when placed over a spectrophotometric curve drawn on some standard size graph paper. Such a plate, displaced toward longer wave-lengths by the amount given by the above formula will serve for the selection of the ordinates for any temperature *T* between 2000°K and 4000°K. The resulting wave-lengths will have an average error of less than 0.5m*μ*, and the largest error, occurring at the shortest wave-length, will not be greater than 3.0 m*μ*. Errors exceeding 1m*μ* occur only for the first one and the last two ordinates, and only within a few hundred degrees of the limits of the temperature range. The effects of such errors are quite negligible for the types of spectrophotometric curves commonly encountered. The selected ordinates for the I.C.I.
$\overline{x}$ and
$\overline{z}$ functions for general colorimetric computations do not conform with sufficient accuracy to any law of the above form to justify the labor of evaluation of the corresponding constants.

© 1938 Optical Society of America

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