Ideally, the material in a spot on a two-dimensional chromatogram forms a bivariate normal distribution in which the base of the figure corresponds to the dimensions of the circular spot and the height of the curve is a function of the maximum absorbance. Using a paraboloid as an approximation of the Gaussian figure, it has been possible to construct a mathematical model of a series of chromatographic standards over a five hundred-fold range of values and to define mathematically deviant “spots” which were more compact or more diffuse than the standard series. The model has been used to evaluate the various empirical techniques of direct chromatographic analysis including: spot length, area, maximum absorbance, (area) (maximum absorbance), total absorbance and slit scanning with fixed and fixed-ratio slit length. It was found that slit scanning where the length of the slit is a constant fraction of the spot diameter is probably the best technique for mono-dimensional chromatograms while for two-dimensional chromatograms the product of (spot area) × (maximum absorbance) appears to be the best method.
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