In this paper an attempt is made to show how certain empirical relationships observed in an analysis of air pollution data can be interpreted using extreme-value theory. In order to accomplish this, it was necessary to determine the limiting distribution of the maximum term of a random series from the lognormal law. Since an explicit development of this limiting distribution including a determination of the normalizing constants, is not available in the literature to the knowledge of this author, an appendix has been devoted to it. Potential applications of the extreme value theory to problems of air quality are pointed out.