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The ''star'' facet was probably intro-
duced to complete the design of the brilliant,
which without its use would be lacking in
harmony, but which its introduction makes



96 DIAMOND DESIGN

exceedingly pleasing from the point of view
of the balance of lines.

Let us examine the optical consequences
of the use of '' star " facets.

On the one hand, their inclination —
about 15° to the horizontal — permits a
certain amount of light to leave the stone
without being sufficiently refracted. On
the other, they diminish the area of the
bezels and consequently decrease the leak-
age of light which occurs through the bezel
and the opposite pavilion (owing to the
surfaces being nearly parallel). They also
cause a somewhat better distribution of
light, for they deflect part of the rays
which would otherwise have increased the
strength of the spectra refracted by the
bezels, and create therewith spectra along
other directions ; it is true that, as seen
above, these spectra will be shorter. But
they will be more numerous ; and though
the " fire " — as consequent from the great
dispersion of the rays of light — will be
slightly diminished, the "life" — if we may
term '' life '' the frequency with which a



MATHEMATICAL 97

single source of light will be reflected and
refracted to a single spectator upon a
rotation of the stone — ^will be increased to
a greater degree. And if we take into ac-
count the decrease in the leakage of light,
we may conclude that the, introduction of
the stars, on the whole, is decidedly ad-
vantageous in the brilliant.

Best Proportions of a Brilliant

We have thus as best section of a brilliant
one as given in fig. 35, A B C D E, where

a = 40° 45'

^ - 34' 30'.

D E is obtained from P R in fig. 35.

If we make the diameter A B of the stone
100 units, then the main dimensions are
in the following proportions (fig. 35) : —

Diameter A B . . .100
Table D E . . . . 53-0
Total thickness M C . . 59-3
Thickness above girdle MM' 16-2
„ below „ M'C . 43-1

• 7



98



DIAMOND DESIGN



Fig. 36 shows the outline of a brilliant
with these proportions.

These proportions can be approximated
as follows : —

In a well-cut brilliant the diameter of







/OO'O








S3'0














J

5$


i


y^


\






/













Fig. 36.

the table is one-half of the total diameter,
and the thickness is six-tenths of the total
diameter, rather more than one-quarter
of the thickness being above the girdle and
rather less than three-quarters below.

It is to be noted here that a different pro-
portion is generally stated for the thickness



MATHEMATICAL



99





Fig. 37.



100 DIAMOND DESIGN

above the girdle (*' one- third of the total
thickness''), both in works upon diamonds
and by diamond poHshers themselves. It
is true that diamonds were cut thicker
above the girdle and with a smaller table
before the introduction of sawing, for
then the table was obtained by grinding
away a corner or an edge of the stone, and
the loss in weight was thus considerable,
and would have been very much greater
still if the calculated proportions had been
adopted. With the use of the saw, the loss
in weight was enormously reduced and the
manufacture of sawn stones became there-
fore much finer and more in accordance
with the results given above. It is a
remarkable illustration of conservatism that
although diamonds have been cut for de-
cades with J (approximately) of the thick-
ness above the girdle, yet even now the
rule is generally stated as | of the
thickness.

Stones are still cut according to that
rule, but then they are not sawn stones as
a rule, and the thickness is left greater



MATHEMATICAL loi

to diminish the loss in weight. The
brilliancy is not greatly diminished by
making the stone slightly thicker over the
girdle.

Comparison of the theoretically best
Valuer with those used in Practice

In the course of his connection with the
diamond-cutting industry the author has
controlled and assisted in the control of
the manufacture of some million pounds'
worth of diamonds, which were all cut
regardless of loss of weight, the only aim
being to obtain the liveliest fire and the
greatest brilliancy. The most brilliant
larger stones were measured and their
measures noted. It is interesting to note
how remarkably close these measures, which
are based upon empirical amelioration and
rule-of -thumb correction, come to the
calculated values.

As an instance the following measures,
chosen at random, are given (the dimensions
are in millimetres) : —



102



DIAMOND DESIGN



Table I



a .


4or


4or


40°


41°


41°


^ • .


35°


35°


34r


33°


34°


AB .


7-00


7-o8


6-50


21-07


9-12


MC .


4'12


4-35


3-6i


12-34


5-47


MM' .


i-o8


1-32


0-85


3-31


i-6i



These measures, worked out in percentage
of A B, give : —



Table II



a


40f°


4or


40°


41°


41°


40^42'


40^45'


i8 .


35°


35°


344°


33°


34°


34° 18'


34° 30'


AB


100


100


100


100


100


100


100


MC


587


61-4


55-4


58-5


60


58-9


59-3


MM'


157


i8-6


13-3


157


17-8


l6-2


l6-2


M'C


43-0


42-8


42-1


42-8


42-2


42-6


43-1



In the seventh column the averages of
the measures are worked out, and the eighth
gives the calculated theoretical values. It
will be noted that the values of a, j8, and
M M' correspond very closely indeed, but



MATHEMATICAL 103

that M C and M' C are very slightly less than
they should be theoretically.

The very sHght difference between the
theoretical and the measured values is due
to the introduction of a tiny facet, the
collet, at the apex of the pavihons. This
facet is introduced to avoid a sharp point
which might cause a split or a breakage
of the diamond.

What makes the agreement of these
results even more remarkable is that in the
manufacture of the diamond the pohshers
do not measure the angles, etc., by any
instrument, but judge of their values en-
tirely by the eye. And such is the skill
they develop, that if the angles of two
pavihons of a briUiant be measured, the
difference between them will be in-
appreciable.

We may thus say that in the present-day
well-cut brilHant, perfection is practically
reached : the high-class brilliant is cut as
near the theoretic values as is possible in
practice, and gives a magnificent brilliancy
to the diamond.



104 DIAMOND DESIGN

That some new shape will be evolved
which will cause even greater fire and life
than the brilliant is, of course, always
possible, but it appears very doubtful, and
it seems likely that the brilliant will be
supreme for, at any rate, a long time yet.



(PR. 1605.)



PRINTED IN GREAT BRITAIN BY NEILL AND CO., LTD., EDINBURGH.



l»Sl.2!r CONGRESS



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Online LibraryMarcel TolkowskyDiamond design → online text (page 4 of 4)