Skin colour segmentation is important for human face tracking. An often used approach is to approximate the skin chromaticity distribution with a statistical model, e.g. with the distribution's covariance matrix. The advantage of this approach is that it is invariant to size and orientation and fast to compute. A disadvantage is that it is sensitive to changes of the illumination colour.This paper investigates how accurately the covariance matrix of facial skin chromaticity distributions might be modelled for different illumination colours using a physics-based approach. Results are presented using real image data taken under different illumination colours and from subjects with different shades of skin. The eigenvectors of the modelled and measured covariances deviate in orientation about 4o. This seems to be within a useful range for skin colour segmentation, and hence allow the statistical model to adapt to illumination changes.