Font size

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 â€”

about 15Â° to the horizontal â€” 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 " â€” as consequent from the great

dispersion of the rays of light â€” will be

slightly diminished, the "life" â€” 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 â€” ^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 = 40Â° 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) : â€”

Diameter A B . . .100

Table D E . . . . 53-0

Total thickness M C . . 59-3

Thickness above girdle MM' 16-2

â€ž below â€ž M'C . 43-1

â€¢ 7

98

DIAMOND DESIGN

Fig. 36 shows the outline of a brilliant

with these proportions.

These proportions can be approximated

as follows : â€”

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) : â€”

102

DIAMOND DESIGN

Table I

a .

4or

4or

40Â°

41Â°

41Â°

^ â€¢ .

35Â°

35Â°

34r

33Â°

34Â°

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 : â€”

Table II

a

40fÂ°

4or

40Â°

41Â°

41Â°

40^42'

40^45'

i8 .

35Â°

35Â°

344Â°

33Â°

34Â°

34Â° 18'

34Â° 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.

lÂ»Sl.2!r CONGRESS

0^003 455 912

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 â€”

about 15Â° to the horizontal â€” 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 " â€” as consequent from the great

dispersion of the rays of light â€” will be

slightly diminished, the "life" â€” 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 â€” ^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 = 40Â° 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) : â€”

Diameter A B . . .100

Table D E . . . . 53-0

Total thickness M C . . 59-3

Thickness above girdle MM' 16-2

â€ž below â€ž M'C . 43-1

â€¢ 7

98

DIAMOND DESIGN

Fig. 36 shows the outline of a brilliant

with these proportions.

These proportions can be approximated

as follows : â€”

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) : â€”

102

DIAMOND DESIGN

Table I

a .

4or

4or

40Â°

41Â°

41Â°

^ â€¢ .

35Â°

35Â°

34r

33Â°

34Â°

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 : â€”

Table II

a

40fÂ°

4or

40Â°

41Â°

41Â°

40^42'

40^45'

i8 .

35Â°

35Â°

344Â°

33Â°

34Â°

34Â° 18'

34Â° 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.

lÂ»Sl.2!r CONGRESS

0^003 455 912