To measure size distributions of submicrometer aerosols with an electrical differential mobility analyzer (DMA) requires an inversion procedure. The Knutson (1976) and the Hoppel (1978) inversion procedures were numerically investigated for the case of log-normal aerosol size distributions. It was found that the Hoppel procedure converges to the same result as that given by the Knutson procedure. The computational range for geometric mean diameter (χg) was 0.025-0.25 μm, and for geometric standard deviation (σg) was 1.1-2.4. The inversion error was found to be greater than 10% in certain"forbidden zones” of χg and σg values. For the case of an ideal DMA having no lower mobility limit, only one forbidden zone exists, this consisting of small σg values. The boundary of this forbidden zone intercepts the computational range boundaries at σg = 1.25, χg = 0.025 μm and σg = 1.62, χg = 0.25 μm. These results also apply to an actual DMA when the size distribution of particles larger than the DMA singly charged mobility limit is available a priori. If such information is not available, the concentration of these larger particles is assumed to be zero in performing the inversion. This assumption adds a second forbidden zone, consisting of large σg values and having the intercepts σg = 2.44, χg = 0.025 μm and σg = 1.50, χg = 0.25 μm. The first forbidden zone remains nearly the same. © 1982.