A color space is constructed so that lights that have the same appearance for a given observer map into the same point. As such, a color space is specific to an observer, and a different observer requires a different space to represent the mapping between lights of identical appearance and points. Nevertheless, situations arise in which one would like to consider the properties of one observer with respect to a different observer but in the same space. Some examples include the evaluation of rod excitation in trichromatic color space, the relation between anomalous and normal trichromatic discrimination, the relation between the CIE 1931 and the Judd observers and the relation between human and camera observers. The object of this article is to examine the geometry of such situations.