ROUND BRILLIANT PROPORTIONS

Proportions
A stone shows the maximum brilliance and fire only when its cutting proportions exactly correspond to those calculated from physical and optical laws.

According to Tolkowsky, the ideal diamond cut has the following proportions (% of stone diameter): Table - 53%, Pavilion depth - 43.1%, Girdle thickness - 0.7%, Crown height - 16.2%, Crown angle (a) -34 1/2 ; Pavilion angle (b) - 403/4 . Actual parameters always deviate from these calculated values, although a diamond-cutter tries to keep the proportions within certain limits. Keeping b (41) close to the ideal value is one of the most important conditions, since this parameter controls the total internal reflection of diamond. For example, the table size may vary, ranging from 55 to 65%, the girdle thickness may range up to 5%, and a may vary between 30 and 40. The variation limits of the cutting parameters may differ in different countries and depend on the stone size and requirements imposed by manufacturers and clients.


Table size evaluation

The table size ranging within 56-62% of the stone diameter is considered ideal by most dealers.

The table size can be measured directly with a transparent micrometric scale, proportionscope or loupe with a micrometric scale. The distance between two opposite vertexes of the table is measured. Thus, four measurements are possible (along the octagon diagonals). It is recommended to accomplish all the four measurements and then derive the mean value. The table size is calculated by dividing the mean table diameter by the girdle diameter and is expressed in percentage.

In addition, there are two methods for rough estimation of table size :

Ratio method

This method can be applied to both loose and mounted diamonds provided the mounting does not hide the girdle of the stone. The distance between the center of the table and girdle is divided by the edge of the table in two at a certain ratio.

This method is based on estimating this ratio. The larger the table, the closer its edge to the girdle. From this ratio and with the examples in figure, the table size can be estimated in percentage accurate to 2-3%.

Important:

A diamond is examined under the microscope or with a loupe to provide accurate measurements;
A stone should be observed face-up at a right angle;
This method does not work if a stone has an off-center table or crown facets are characterized by significant geometric distortion.
Table comparison method

This method is also approximate. It includes two steps:

Step 1. Curvature evaluation.

If the table size is 60%, the edges of the table and star facets appear as two regular squares (see figure). As the table size increases, the lines representing the sides of the squares become broken and convex. From the degree of their convexity or concavity (in case if the table size decreases), the table size can be qualitatively estimated. In this procedure, the examples shown in figure can be conveniently used for comparison.

mizgib.gif (40003 bytes)

Step 2. Correction.

The star facet size is estimated from the distance between the intersection point of five facets and the table edge. If this point falls at the middle between the girdle and table, no correction is needed. If this point is shifted towards the girdle, a few percent is added (up to 7%); if it is shifted towards the table, a few percent is subtracted (up to 7%)

mizgib2.gif (43673 bytes)


Crown angle evaluation

The crown angle typically ranges from 30 to 40. The most accurate estimation of the crown angle can be performed with a proportionscope. However, a rough estimation is needed in some cases, which can be accomplished through the following methods:

Profile examination

Using the angles shown in next figure for comparison, the crown angles can be estimated. A diamond is held table-to-culet , and the angle between the crown facets and tweezers can be easily estimated by eye.

profil.gif (38708 bytes)

If the diamond is so held with tweezers that its crown profile appears broken, it should be slightly turned with a pointer so that one of its bezel facets was on the side. The right positions are shown in Figure.

profil1.gif (19056 bytes)


Examination of pavilion facet reflections

The larger the crown angle, the larger the angle between the table and the bezel facets. It is clearly seen from the breaking reflection pattern of the pavilion facets when a stone is observed face up. Figure demonstrates how the crown angle can be judged from the breaking of a pavilion facet.

Actual diamonds may differ in table size, but have almost the same breaking pattern of the pavilion facets. This can be is seen in next figure, which shows diamonds with different tables.

The closer to the culet the lower-girdle facets, the narrower the pavilion main facets. Hence, this method gives the estimate of the relative rather than absolute widening of a pavilion facet seen through the crown facets.

Important, that the crown facets should be exactly above the pavilion facets. This method is hardly applicable to the diamonds with crown and pavilion shifted relative each other.


Girdle evaluation

Judging by the surface character, girdle can be bruted or faceted. Rough girdle is considered as a disadvantage of polish. The main evaluated parameter of the girdle is its thickness. Evaluation can be accomplished by three methods:

  • estimation of the girdle thickness by comparison to examples in next figure;
  • measurement of the girdle in the narrow zone;
  • measurement of the girdle in the wide zone.
Since the girdle of a common diamond has 16 sections, 16 measurements should be done with subsequent calculation of the mean value. International grading systems suggest that the wide zones of the girdle should be measured. The variation amplitude of the girdle thickness is not evaluated.

The following terms are commonly used in qualitative girdle description:

Extremely thin

With 10x magnification "knife-edge" is visible.
Without magnification is not seen .
 
Very thin

With 10x magnification very thin line is visible.
Without magnification is seen hardly.
 
Thin

With 10x magnification thin line is visible
Without magnification is seen
 
Medium

With 10x magnification the distinct line is visible.
Without magnification thin line is visible
 
Slightly thick

With 10x magnification clearly visible
Without magnification clearly visible
 
Thick

With 10x magnification rather clearly visible.
Without magnification rather clearly visible
 
Very thick

With 10x magnification rough visible
Without magnification rough visible
 
Extremely thick

With 10x magnification very rough visible
Even without magnification rough visible

The average girdle thickness is the thickness value most frequently established for a given stone. Thin to slightly thick girdle is regarded optimal. The diagram in figure can be used for conversion of the percentage girdle thickness into qualitative characteristics and for calculation of weight correction factors.


Estimation of pavilion depth

The pavilion depth is interrelated with the pavilion angle B. It is believed that any deviation of B from 41 O affects badly the stone appearance and deteriorates its brilliance and fire. Hence, international grading systems always deal with pavilion depth rather than pavilion angle. The Tolkowsky ideal diamond has a pavilion depth of 43.1%, however, that of actual stones may vary between 40% and 50%. With a loupe and tweezers, the pavilion depth can be roughly estimated from the size of table reflection in pavilion facets (see figure). The diamond is examined face-up at the right angle. The reflection of the table in pavilion facets appears as a dark fringe. For more effective picture, the stone should be held somewhat below its ordinary position and should be examined at a greater distance from the lamp and against light background. Quantitative grading is performed with master cards (figure). When using this method, one should take into account the geometric distortions of crown facets, which certainly affect the diameter of the table reflection. This can bring about erroneous estimates of the pavilion depth: the more significant the deviations of the crown proportions from ideal parameters, the greater the error.

Estimation of culet size

Only recently cutting technologies has enabled making a pointed culet. Almost all old-cut diamonds have large culets, which on face-up examination, appear as dark spots. The dark spots are due to the loss of light which enters the diamond crown and does not undergo total internal reflection. Therefore, a good culet is that not visible by unaided eye.

The following culet grades are used:

Culet

Description

None (pointed) No culet present (culet appear as dark spots on face-up examination)
Very small Very difficult to see under 10x magnification
Small Difficult to see under 10x magnification
Medium Easily visible under 10x magnification, but not visible with naked eye
Slightly large The octagon contour is seen under 10x magnification. Culet is distinct to the naked eye
Large Visible to the naked eye
Very large Visible to the naked eye as black stain in table
Extremely large Octagon contour is seen with naked eye

Very small, small, or medium culets are best suited for diamonds. If a diamond has pointed culet, "no culet" is often written in the worksheet. Culet is the most fragile part of a diamond, hence it can be chipped off or abraded in the course of cutting, transportation, or mounting of the stone.


Effect of proportions on stone price

To derive a proportion grade and estimate the stone price, one should understand how proportions determine the appearance and appeal of diamond. Opinions differ; some purchasers prefer diamonds with a large table, others - those with a small table. Some diamonds are very attractive in spite of significant deviations from the Tolkowsky ideal diamond parameters. For this reason, many grading systems involve only measurement but not grading of stone proportions.

Calculated parameters of some ideal diamonds are presented in the following table: (Source: Verena Pagel-Theisen "Diamond Grading ABC")

Proportions Ideal brilliant 1926 Parker brilliant 1951 Tolkowsky Brilliant 1919 Practical Fine Cut 1939 Scand. Standard Brilliant 1969 Brilliant Cut Eulitz 1972
Crown Height, in % 19.2% 10.5% 16.2% 14.4% 14.6% 14.45%
Girdle Diameter - - - - - 1.50%
Pavilion Depth 40.0% 43.4% 43.1% 43.2% 43.1% 43.15%
Table Diameter 56.1% 55.9% 53.0% 56.0% 57.5% 56.50%
Crown angle 41.1 25.5 34.5 33.2 34.5 33.36
Pavilion Angle 38.7 40.9 40.75 40.8 40.75 40.48
Ratio of Crown Height / Pavilion Height 1:2.07 1:4.13 1:2.66 1:3.00 1:2.95 1:3.00