Now suppose another color y is made from the same three colors ts of x and y z=X+Y=(a+a)A+(b+b)B+(c+c)C.(35.6) It is just like the mathematics of the addition of vectors, where (a, b, c)are the components of one vector, and (a, b, c) are those of another vector, and the new light Z is then the "sum""of the vectors. This subject has always appealed to physicists and mathematicians. In fact, Schrodinger wrote a wonderful paper on color vision in which he developed this theory of vector analysis as applied to the Now a question is, what are the correct primary colors to use? There is no such thing as"the"correct primary colors for the mixing of lights. There may be for practical purposes, three paints that are more useful than others for getting a greater variety of mixed pigments, but Any three differently colored lights whatsoever* can always be mixed in the correct proportion to produce any color whatsoever. Can we demonstrate this fantastic fact? Instead of using red, green, and blue, let us use red, blue, and yellow in our projector.Can we use red, blue, and yellow to make, say, green? By mixing these three colors in various proportions, we get quite an array of different colors, ranging over quite a spectrum. But as a matter of fact, after a lot of trial and error, we find that nothing ever looks like green. The question is, can ve make green? The answer is yes. How? By projecting some red onto the green, then we can make a match with a certain mixture of yellow and blue! So we have matched them, except that we had to cheat by putting the red on the other side ut since we have some mathematical sophistication, we can appreciate that what really showed was not that X could always be made, say, of red, blue, and yellow but by putting the red on the other side we found that red plus X could be made out of blue and yellow. Putting it on the other side of the equation, we can interpret that as a negative amount, so if we will allow that the coefficients in equations like (35.4)can be both positive and negative, and if we interpret negative amounts to mean that we have to add those to the other side, then any color can be matched by any three, and there is no such thing as"the""fundamental primaries. We may ask whether there are three colors that come only with positive mounts for all mixings. The answer is no. Every set of three primaries requi negative amounts for some colors, and therefore there is no unique way to define a primary. In elementary books they are said to be red, green, and blue, but that is merely because with these a wider range of colors is available without minus signs for some of the combinations 354 The chromaticity diagram Now let us discuss the combination of colors on a mathematical level as a geometrical proposition. If any one color is represented by Eq. (35. 4), we can plot it as a vector in space by plotting along three axes the amounts a, b, and c, and then a certain color is a point. If another color is a, b, c, that color is located somewhere else. The sum of the two, as we know. is the color which comes from adding these as vectors. We can simplify this diagram and represent everything on a plane by the following observation: if we had a certain color light, and merely doubled a and b and c, that is, if we make them all stronger in the same ratio, it is the same color, but brighter. So if we agree to reduce everything to the same light intensity, then we can project everything onto a plane, and this has been done in Fig 35-4. It follows that any color obtained by mixing a given two in some pro Except, of course, if one of the three can be matched by mixing the other two