many angles. This factor further highlights the need to reevaluate Tolkowsky's results, and to recalculate the effects of a diamond's proportions on its appearance aspects. ... Another important point to consider is that Tolkowsky did not follow the path of a ray that was reflected more than twice in the diamond. However, we now know that a diamond's appearance is composed of many light paths that reflect considerably more than two times within that diamond. Once again, we can see that Tolkowsky's predictions are helpful in explaining optimal diamond performance, but they are incomplete by today's technological standards. Tolkowsky's guidelines, while revolutionary in their day, are not a definitive solution to the problem of finding the optimum proportions of a round brilliant cut diamond. In the 1970s, Bruce Harding developed another mathematical model for gem design. Since then, several groups have used computer models and specialized scopes to design diamond cuts. The world's top diamond cutting and polishing center is India. It processes 11 out of 12 diamonds in jewelry worldwide. The sector employs 1.3 million people and accounts for 14% of India's $80 billion of annual exports. Its share in the world polished diamond market is 92% by pieces and 55% by value. Theory In its rough state, a diamond is fairly unremarkable in appearance. Most gem diamonds are recovered from secondary or alluvial deposits, and such diamonds have dull, battered external surfaces often covered by a gummy, opaque skin—a comparison to "lumps of washing soda" is apt. The act of polishing a diamond and creating flat facets in symmetrical arrangement brings out the diamond's hidden beauty in dramatic fashion. When designing a diamond cut, two primary factors are considered. Foremost is the refractive index (RI) of a diamond, which, at 2.417 (as measured by sodium light, 589.3 nm), is fairly high compared with that of most other gems. Diamond's RI is responsible for its brilliance—the amount of incident light reflected back to the viewer. Also important is a diamond's dispersive power—the ability of the material to split white light into its component spectral colors—which is also relatively high, at 0.044 (as measured from the B-G interval). The flashes of spectral colors—known as fire—are a function of this dispersion, but are, like brilliance, only apparent after cutting. Brilliance can be divided into the definitions external brilliance and internal brilliance. The former is the light reflected from the surface of