As generalized equations for expressing the steady state of interreflection, a linear equation and an integral equation are formulated which are capable of representing interreflection in systems of non-diffusely reflecting surfaces having arbitrary configuration and arbitrary emission characteristics. Methods of solving these equations are considered and as for the integral equation the significance of applying the successive substitution method is pointed out. This method is successfully applied to some substantial systems, giving clear physical interpretation and useful mathematical expression of their state, namely, (1) the superposed state of emission and multiple reflections, (2) the thermodynamic equilibrium in completely closed cavities of uniform wall temprature.(3) departure from the thermodynamic equilibrium, effective emissivity, effective absorptivity and effective reflectivity of incompletely closed cavities of non-uniform wall temperature are analysed. Relation of the present work to the previous ones, especially those of Buckley, Yamauti, De Vos, Nakaji, Sparrow and Kelly is discussed

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Many studies of interior interreflections have hitherto been made, but they have remained a mathematical analysis of integral equations under various conditions.
The analytical formulation of the lighting system has been described by P.F.O'Brien in terms of the equivalent network. A new network method i n nonclosed surface has been published by Hiroshi Bo. Instead of using Shape Modulus F_i-1, Transfer Factor C_i is used for decreasing the number of surfaces in case of the nonclosed surfaces. Use of computers in design and analysis of luminaires has been reported by B. F. Jones. In case of a symmetrical luminaire, halving the number of surfaces required for calculation, the authors already have carried out calculation by a luminous analogue computer and digital computer.
In this report, instead of a circular cylinder of fluorescent lamp, hexagonal cylinder with infinite length is used for analyzing characteristics of luminaires. Computer may be employed for the solutions of the simultaneous linear equations which describe lighting systems.
This paper is a report on the luminaire efficiency and the luminous emittance ratio of idealized luminaires.

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