(original text - much provided by footnotes in this annotated version)

Tolkowsky starts off good but becomes decreasingly thorough as he progresses. This happens often in research work, due to an urge to hasten completion - usually imposed by management. The fact that the theory agreed with the already-known answer was probably considered sufficient by all concerned.

Tolkowsky's omissions would have had insignificant effect on the answers. His error in using the intensity lost from the right oblique group would result in a bezel angle of 34.3^o by calculation. The fact that he got 34.5^o by graphical layout indicates the accuracy of his graphical method.

It is humorous to note that the pavilion angle of 40.75^o was developed to send the average rays ( q₁=0^o) back to the table at q₃=17^o for optimum dispersion and brilliance, yet, after restricting the table size, less than 11% of the rays following such a path hit the table! Every other calculation is based on this pavilion angle which, in the final analysis, does not achieve its purpose! In analyzing the central group of rays, Tolkowsky assumed that none of them hit the table and apparently missed the significance of this assumption.

A 34^o bezel angle would give Tolkowsky the 17^o angle to these rays that he was looking for to produce dispersion, yet he developed this angle on the basis of maximum brilliance with zero dispersion! Something is contradictory.

Is Tolkowsky's theory valid or does it just happen to agree with the best results obtained by trial-and-error? I wish he was alive today so that we could discuss this.

 Editors note 1: When Tolkowsky have entered this it was one of his biggest logic errors. Below it is shown that there are two basic light directions: 17 and 70^o. Bezel facet at 35 will not be preferable for both light beams. What we have lost for 17^o beam by taking 35^o bezel facet we will not compensate from 70^o beam. Would it better to place 17^o bezel facet? No.
To illustrate this one can consider two equal beams: 0^o and 180^o. Will it better to take 90^o bezel facet? No.

 Editors note 2: Author is suggested to subtract 10.8%. But the nailhead effect can have even more influence. If the observer's head obscure the part of this light then the intensity of such light will be less and can not be measured. These calculations are incorrect for crown angle measuring.