Diamond Design Revisited by Bruce Harding
Introduction
In 1919 Marcel Tolkowsky published "Diamond Design" in which he developed the angles and proportions of the brilliant cut which have become widely accepted as ideal.
Copies of this book are hard to find, so Tolkowsky's analysis is reiterated here for those who are curious to know how these 'magic numbers' came about.
This review follows Tolkowsky's logic but uses less awkward and more meaningful mathematics. It shows errors, omissions, and inconsistencies in his work, but none of these have a significant effect on the final results.
Tolkowsky was intimate with diamond-cutting and implies that he knew the answers before developing the theory. This is a common danger in research and it appears that some of his logic is tainted in an effort to arrive at these results.
Tolkowsky's first step involves a compromise of brilliance to get good dispersion, and all subsequent calculations are based on the results of this initial step. For this reason, and others, this method cannot be applied directly to studies of other gemstones; however, it is a good source of concepts for such efforts.
Certain limitations of this analysis must be pointed out:
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- It applies to stones with nearly-constant pavilion and bezel slopes; this excludes step-cut stones.
- It considers only rays in planes parallel to the axis and perpendicular to the facets they hit; this is a small part of all the rays.
- It assumes that such rays have identical facets on opposite sides of the gem; this excludes fancy shape.
5. General method of determining bezel angle
7. Central group of light rays
10. Mean light angle = bezel angle
11. Final angles and proportions
13. Star facets and Comparison to actual cuts