Using graphical tools, the potential multi-modality of } mixtures is demonstrated; in particular it is shown that the number of modes may exceed "n" and that the modes may not be coincident with the component means. For two components they develop a graphical tool for analysis by instead solving the aforementioned differential with respect to "w"1 and expressing the solutions as a function Π("α"), so that the number and location of modes for a given value of "w"1 corresponds to the number of intersections of the graph on the line . This in turn can be related to the number of oscillations of the graph and therefore to solutions of formula_15 leading to an explicit solution for a two component homoscedastic mixture given by