There remain some important issues related to the von Kries model which have not been clarified up until now. This article discusses fundamental mathematical characteristics related to one of the issues of the model. The important issue which have not been clarified and will be discussed in this paper is what is the conditions in the wavelength range for the best von Kries model fitting? Because of the multiplication between illuminant spectrums and object spectral reflectances, the conditions in the wavelength range give various resultant tristimulus values though the von Kries model is a model with only three parameters. In the removal of colored illuminants, the model fitting has uncertainty. As the result of this paper, it is shown that the simplest von Kries model provides the best chromatic adaptation for sets of illuminant spectrum and object spectral reflectance which generate the centroid tristimulus values in the tristimulus region corresponding to the uncertainty.