The problem defined in the title has partially been addressed by various studies, in a complicated manner, without providing sufficient details or in ways that are to some extent confusing. For these reasons the basic equation governing the operation of the cell-reciprocal integrating nephelometer (CRIN) has been deduced by a comprehensible and didactic approach in this work. A comparison of this equation with the respective one for the cell-direct integrating nephelometer (CDIN) has been undertaken. An introductory review analysis of the equation and its first and second corrections, due to the so-called truncation error and light extinction error, respectively, has been performed. An indication of how they can, in theory, be minimized is given. The essential CRIN-calibration procedure has been described with special emphasis on the convenient use of a monodisperse, non-absorbing and spherical aerosol as a calibration substance instead of using toxic and environmentally damaging gases. However, in this respect, some comments on fundamental technical problems and possible errors arising in generating, sampling and operating an aerosol of this kind for calibration purposes have been added. For the various aspects analysed in this work it is shown that the CRIN-calibration procedure is a very difficult task to accomplish, especially when an aerosol is used.