Hermann Grassmann (along with William Rowan Hamilton) invented vector and tensor algebra in 1844, but was unable to attract attention to the new method [Sherman 1981]. He subsequently applied the methods of vector analysis to color in order to calculate the outcomes of color mixtures [Grassmann 1854]. In so doing, Grassmann proved that for every spectral color there exists some other opponent color in the spectrum which when mixed with the first color in the correct proportions will produce white light.
Figure 3. Diagram of Grassmann's calculation of color additivity using vectors.
This result agreed substantially with Newton's original observations, but pointed out inconsistencies in the color wheel geometry then current. Grassmann's methods are those which have come to be known as ``center of gravity'' calculations, since they are the same tensor analyses used to calculate center of gravity from measurements of pressure exerted by the legs of a tripod. Most calculations of the positions of colors within a subjective representational space rely on Grassmann's formulation of center of gravity.