The ternary A ndash CN ndash K plot is

Though the above interpretations derived from evaluation of data shown in Fig. 8 are mathematically sound (e.g., Ehlers, 1972), statistical evaluation of such data is inherently difficult and problematical. Such difficulties arise from the fact that chemical compositions are vectors, as for example a = [a1, …, aD], where a1 through aD are the proportions of BMS-303141 oxides in a D-part composition and D is a positive integer ( Aitchison, 1986 and Pawlowsky-Glahn and Buccianti, 2011).