where the formula_16 are eigenvectors of the covariance matrix of the normalized transmission spectra of the ensemble of beers from which the average normalized spectrum (the sum of the two exponential terms in parentheses in the formula_13 formula) was determined and formula_18, formula_19 etc. are obtained as the dot products of the eigenvectors with the normalized transmission spectrum of the beer being characterized. This formula is identical to the one given previously with the exception that it has been augmented by the formula_20 coefficients which encode the deviation of the sample normalized spectrum from the average normalized spectrum. Where the sample beer has a normalized spectrum close to the average the c's are small and it is remarkable how often this is the case. Typically one or two augmentation coefficients are sufficient and they are frequently small enough that one or more can be neglected. For example, an imported ale with SRM equal to 6.8 has coefficients -0.07 and -0.1. Using both these coefficients one obtains color accuracy of less than one L*a*b* space unit (the limit of perception) in up to a 10 cm path under Illuminant C. Using just the SRM for this beer gives a reasonably good description of its color with error of about 4 L*a*b* units. Beers which deviate dramatically from the "average" spectrum are easily accommodated. Thus a sample of Kriek Lambic (Belgian cherry beer), has an SRM of 15.27. Were its color to be reconstructed from just the SRM it would be the color of an "average" beer which will be dark amber not the red of a Kriek. Including 3 coeffiecents (1.8, 0.8 and -0.1) yields color accuracy of less than 1 L*a*b* unit in paths up to 8 cm again under Illuminant C.