A form of mathematical analysis that permits an extended analysis of l
imiting dilution assays under conditions in which accessory factors or
cells are limiting is presented. This is in contrast to the tradition
al form of analysis that permits only a single limiting parameter. Bot
h make use of in vitro experiments to determine the number of antibody
-producing cell precursors; the traditional form of analysis requires
that all accessory cells or their factors be present in saturating con
centrations, whereas in the analytic method employed here, not only B
cells, but accessory cells (macrophages) or their factors are limiting
. Analysis under nonsaturating conditions permits greater elucidation
of the mechanisms of intercellular interaction.