A method is developed from first principles for finding the average illumination on any surface of a rectangular room due to the luminances of the other surfaces. This method depends on the Hisano “room index,” k, and an associated function Pk, derived from the work of Yamauti, which is tabulated for a range of values of k. Illustrative examples show how it may be used to determine the direct flux required to produce a predetermined luminance pattern, or to reverse this procedure. Some comparisons are made between the results obtained by this method and by others, including direct measurement, and the agreement is shown to be generally satisfactory.
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