DIAMOND DESIGN
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`Page 1 of 110
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`GIA EXHIBIT 1010
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`GIA EXHIBIT 1010
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`Page 1 of 110
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`GIA EXHIBIT 1010
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`Page 1 of 110
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`GIA EXHIBIT 1010
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` DIAMOND DESIGN
`
`A STUDY OF THE REFLECTION
`
`AND REFRACTION OF LIGHT IN
`
`A DIAMOND
`
`BY
`
`MARCEL TOLKOWSKY
`B.Sc., ‘.‘A.c.G.I.
`
`£VlTH 3?’ [LL USTRA T!0zVS
`
`
`
`E. 8: F. N. SPON, LTD., 57 HAYMARKET, S.W.1
`
`IOHOOII:
`
`1|”-law moth:
`
`SPON & CHAMBERLAIN, 120 LIBERTY STREET
`
`1919
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`i__ __‘
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`‘~13
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`CONTENTS
`
`INTRODUCTION
`
`PART I.—-HISTORICAL
`
`,,
`
`,,
`
`II.'—0PTICAL
`
`III.—MATHEMA-TICAL .
`
`THE ROSE
`THE BRILLIANT
`
`V
`
`.
`
`A. Back
`
`B. From!
`
`_ FACETING
`
`BEST PROPORTIONS OF A BRILLIANT
`
`‘W5
`
`8
`
`20
`
`3
`
`59
`64
`
`64
`
`80
`
`94
`
`97
`
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`DIAMON D DESIGN
`
`INTRODUCTION
`
`THIS book-is written principally for students
`of precious stones and jewellers, and more
`particularly for" diamond manufacturers
`The '
`
`and diamond cutters and polishers.
`author will
`follow the evolution of
`
`the
`
`shape given to a cut diamond, and discuss
`the values of the Various shapes and the
`reason for‘ the discarding of the old shapes
`and the practically universal adoption of
`the brilliant. '
`r
`-
`
`It is a remarkable fact that, although the
`art of cutting a diamond has been known for
`more than two thousand years, it is entirely
`
`empirical, and that, though many keen con-
`temporary minds have been directed upon
`the diamond, and the list of books written
`on that
`subject
`increases
`rapidly, yet
`
`5
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`6
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`DIAMOND DESIGN
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`nowhere} ca11 one find any mathematical
`work determining the best shape for that
`gem. The present Volume’s chief aim is
`the calculation of that shape.
`The calculations have been made as
`
`' simple as possible, so as not to be beyond
`the range of readers with a knowledge of
`elementary geometry, algebra, and trigo-
`nometry. Where, however,
`it was found
`that the accuracy of the results would be
`impaired without the introduction of more
`advanced mathematics,
`these have been
`used, and graphical methods have been
`explained as an alternative.
`The results of the calculations for the form
`
`of brilliant now in use were verified by
`actual mensuration from well-cut brilliants.
`
`The measures of these brilliants are given '
`at the end of the volume both in a tabulated
`
`It will be seen
`and in a graphical form.
`how strikingly near the actual measures are
`to the calculated ones.
`
`The method used in the present work
`will be found Very useful for the design
`of other transparent precious and semi-
`
`Page 6 of 110
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`INTRODUCTION
`
`_ 7
`
`.
`
`. precious stones, although it will be found
`advisable in the case of stones of an agree-
`able colour
`to cut
`the gem somewhat
`thicker than the calculations warrant, so
`
`'
`
`the colour.
`as alto take full advantage of
`The same r_emark applies to diamonds of
`
`some exceptional and beautiful colour, like
`blue or pink, where the beauty or the value
`of the stone increases with the depth of
`
`its colour.
`
`Page 7 of 110
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`Page 7 of 110
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`
`
`I
`
`Part
`
`I
`
`‘HISTORICAL
`
`IT is to Indian manuscripts and early Indian
`literature We turn when we want to find
`the origin of diamond cutting,
`for India
`has always been regarded as the natural
`and ancient home of the diamond.
`It is
`
`there that they were first found: up to
`1728,
`the date of
`the discovery of
`the
`Brazilian deposits, practically the whole
`world’s supply was derived from Indian
`
`sources.
`They are found there in the
`valleys and beds of ~ streams, and also,
`separated from the matrix in which they
`were formed,
`in strata of detrital matter
`
`that have since been covered by twelve
`
`to sixteen feet of earth by the accumula-
`tion of
`later centuries. Diamonds have
`
`existed in“ these deposits within the reach
`of man for many ages, but the knowledge
`3
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`HISTORICAL
`
`9
`
`of the diamond as a gem or as a crystal-
`with exceptional qualities does not
`go
`back in India to the unfathomable antiquity -' 9
`which books on diamonds generally refer.
`,to‘.'
`It was wholly unknown in the Vedic
`period, from which no specific names for
`precious stones are handed down at all.1
`Thme earliest systematic reference appears
`to be in the Artkagastm of Kautilya (‘about
`third century B.(:.), where
`the author
`mentions six kinds of diamonds classified
`
`according to their mines, and describes
`them as differing in lustre and hardness.
`He also writes that
`the best diamonds
`
`should be large, regular, heavy, capable of
`bearing blows? able
`to scratch metal,
`
`az Study in
`1 Berthold Laufer, The Dimnond :
`Chinese and Helfemstic Folklore (Chicago, 1915).
`'
`2 This legend of the indestructibility of the diamond,
`which reappears in many other places, and to which
`the test of the diamond’s capacity of bearing the
`strongest blows was due, has caused the destruc 'on
`of perhaps a very large number of fine stones.
`l‘he
`legend was further embroidered by the remark that
`if the diamond had previously been placed in the
`fresh and still warm blood of a ram, it could then be
`broken, but with great difficulty. This legend was
`
`Page 9 of 110
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`I0
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`DIAMOND DESIGN '
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`refractive and brilliant.
`
`In the MMinda-
`
`(Questions of King Milinda) (about
`}56€’7’3]'l«d.
`first century B.(:.) we read that the diamond
`ought to be pure throughout, and that it
`
`is mounted together with the most costly
`gems. This is the first manuscript in which
`the diamond is classed as a gem.
`It is therefore permissible to estimate
`with a sufficient degree of accuracy that
`
`the diamond became known in India during
`
`the fourth
`the Buddhist period, about
`century B.C., and that its use as a gem
`dates from that period}
`It
`is not known with certainty when
`and where the art of grinding or polishing
`diamonds originated. There is as yet no
`source of ancient Indian literature in which
`
`the polishing of diamonds is distinctly set
`forth, although the fact that diamond is
`used for grinding gems generally is men-
`
`still current in Europe as late as the middle of the
`thirteenth century. The actual
`fact
`is
`that
`the
`diamond, although exceedingly hard (it is the hardest
`substance known), can easily be split by a light blow
`along a plane of crystallisation.
`1 Laufer, Zoo. cit.
`
`Page 10 of 110
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`HISTORICAL
`
`II
`
`tioned.
`
`It is, however, likely that, where '
`the polishing of other precious stones was
`accomplished in that manner,
`that of
`diamonds themselves cannot" have been
`
`entirely unknown. What polishing there
`was must at first-have been limited to
`
`the smoothing of the faces of the crystals
`as they were found. The first description
`of cut diamonds is given by Tavernier}
`a French jeweller who travelled through
`India, and to whom we owe most of our
`knowledge of diamond cutting in India in
`the seventeenth century. At the time of
`his visit (1665) the Indians were polishing
`over the natural faces of the crystal, and
`preferred,
`therefore,
`regularly crystallised
`gems. They also used the knowledge they
`had of grinding diamonds to remove faulty
`places like spots, grains, or glesses.
`If the
`fault was too deep, they attempted to hide
`it by covering the surface under which it
`lay with a great number of small facets.
`It appears from Tavernier’s writings that
`
`1 Tavernier, Voyage an T-urguia, an Parse at am:
`Indes (1679).
`
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`"I2
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`DIAMOND DESIGN
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`in
`also European polishers
`there were
`India at that time, and that it was to them
`the larger stones were given for cutting.
`Whether
`they had learnt
`the art
`inde-
`
`_
`
`pendently or
`
`from Indians and attained
`
`greater proficiency than they, or whether
`they were acting as instructors and teaching
`the Indians a new or a forgotten art,
`is
`uncertain. Both views are equally likely
`in the present state of research upon that
`subject: at the time of Tavernier’s visit,
`
`diamond cutting had been known in Europe
`fortmore than two centuries.
`
`Among the several remarkable gems that _
`Tavernier describes,
`the most noteworthy
`is the one known as
`
`i‘
`
`»
`
`‘
`
`if ’i
`
`I
`
`Great Mogul.
`This diamond was of
`a weight of 280 cts.
`‘ and was
`cut
`as
`
`
`
`I.
`sketched in fig.
`The polishing was
`the work of a Venetian, I-Iortensio Borgis,
`to whom it was given for that purpose by
`
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`HISTORICAL ,
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`1;,
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`its owner, the Great Mogul Aurung Zeb, of -
`Delhi. This kind of cut
`is characteristic
`
`of most of
`
`the
`
`Indian
`large
`stones, such as
`
`the Orlow (fig. 2),
`
`which is now the
`
`
`
`largest diamond
`of
`the Russian
`crown jewels andweighs Igggcts. The Koh-i-
`Noor (fig. -3), now among the British crown
`jewels, was of a somewhat similar shape
`before recutting.
`It weighed then
`186 cts.
`
`
`
`Tavernier also
`
`mentionsseveral
`
`types of
`other
`out which
`he
`
`met
`
`in India.
`
`The Great Table (fig. 4), which he saw in
`1642, weighed 242 cts. Both the Great Table
`and the Great Mogul seem to have dis-
`appeared: it is not known what has become
`of them since the seventeenth century.
`
`Page 13 of 110
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`14
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`DIAMOND DESIGN
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`Various other shapes are ‘described, such
`table stones
`thick stones,
`as point stones,
`— (fig. 5), etc. But the
`
`’‘ chief characteristic
`D
`diamonds have been
`
`remains ':
`
`all
`
`these
`
`cut with one aim con-
`
`FIG. 4.
`
`stantly in view—hoW
`to polish the stone with the smallest
`possible loss of weight. As a consequence
`the polishing. was generally accomplished
`by covering the surface of the
`stone with a large number of
`facets, - and the original shape
`of the rough gem was, as far as
`possible, left unaltered.‘
`It was mentioned before that
`the art of diamond polishing
`had already been known in
`Europe for several centuries when Tavernier
`left for India. We have as yet no cer-
`
`
`
`FIG. 5.
`
`tain source of information about diamond
`
`cutting in Europe before the fourteenth
`century. The first reference thereto 1nen—
`tions that diamond polishers were work-
`
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`HISTORICAL
`
`I 5
`
`l/fig in Nurnberg (Germany) in 1375, where
`they formed a guild of free artisans,
`to
`which admission was only granted after
`an apprenticeship of
`five to six years.1
`We _,do not
`know,
`however,
`in what
`
`shape and (by what method the stones
`were cut. "/
`
`It is in the fifteenth century that Euro—
`
`pean diamond cutting begins to become
`And it .
`more definite, more characteristic.
`
`is from that time that both on its technical
`
`and artistic sides progress is made at a
`
`rate, slow at first, but increasing rapidly
`later.
`
`It is not difficult to find the chief reason
`
`for that change.
`Up to that time, diamonds had almost
`exclusively been used by princes or priests.
`To princes they were an emblem of power
`and wea1th—-in those days diamonds were
`credited with extraordinary powers:
`they
`were supposed to protect the wearer and
`to bring him luck. Princes also found
`them convenient, as they have great value
`
`1 _Iacobson’s Tecimologisches Wdrterbuck (I781).
`
`Page 15 of 110
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`.4!:I
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`I6
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`DIAMOND DESIGN
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`for a verysmall weight, and could easily
`be carried in case of flight. Priests used
`them in the ornaments i of
`temples or
`churches ;
`they have not infrequently been
`
`set as eyes in the heads of statues of
`
`Buddha.
`
`In the fifteenth, century it became the
`
`fashion for women to wear diamonds as
`jewels. This fashion was started by Agnes
`Sorel (about I450) at the Court of Charles
`VII of France, and gradually spread from
`there to all the Courts of Europe.
`This resulted in a very greatly increased
`
`demand, and gave a strong impulse to the
`development of diamond polishing. The
`
`production increased, more men applied
`their brains to the problems that arose,
`and, as they solved them and the result
`of
`their work grew better,
`the increas-
`ing attractiveness of
`the gem increased
`the demand and gave a new impulse to
`the art.
`
`At the beginning of the fifteenth century
`' a clever diamond cutter named Hermann
`
`established a factory in Paris, where his
`
`Page 16 of 110
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`HISTORICAL '
`
`17
`
`work met with success, and where the
`
`industry started developing.
`In or about I476 Lodewyk (Louis) van
`Berquem, a Flemish polisher of Bruges,
`
`introduced‘ absolute symmetry in the dis-
`position of
`the facets, and probably also
`improved the process of polishing. Early
`authors gave credence to the statement
`of one of his - descendants, Robert van
`Berquem,1_who claims that his ancestor
`. had invented the process of polishing the
`diamond by its own powder. He adds:
`“ After
`having
`ground
`off
`redundant
`material from a stone by rubbingrit against
`another one (the process known in modern
`practice as ‘ bruting’ or cutting), he col-
`lected the powder produced, by means of
`
`which he polished the diamond on a mill
`and certain iron wheels of hisinvention.”
`
`1 Robert de Berquem, Les meme-illes des Imies .'
`Tmité des gbierres gbrécienses
`(Paris,
`in-4°, 1669),
`p. I2:
`“Louis de Berquem lfun de mes ayeuls a
`trouvé le premier Pinvention en mil quatre cent
`soizxiante-seize de les tafller avec la poudre de diamant
`meme.
`.Auparavant on fut contraint de les mettre
`en oeuvre tels qu’on les rencontrait aux Indes, c’est-
`2
`
`Page 17 of 110
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`18
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`DIAMOND DESIGN
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`As has already been shown, we know now
`that diamonds were polished at
`least a
`century before Lodewyk van Berquem lived.
`And as diamond is the hardest substance
`
`known, it can only be polished by its own
`powder. VanLBerque1n cannot thus have
`invented that part of the process. He may
`perhaps have introduced some important
`improvement
`like the use of cast-iron
`"polishing wheels, or possibly have discovered
`a more porous kind of cast iron—one on
`which the diamond powder finds a better
`
`hold, and on which polishing is therefore
`correspondingly speedier.
`
`a—dire tout a fait bruts, sans ordre et sans. grace,
`sinon quelques faces an hasard,
`irréguliéres et mal
`polies, tels enfin que la nature les produit.
`I1 mit
`deux diamants sur le ciment et ‘aprés les avoir égrisés
`1’un contre l’.autre,
`il vit manifestement que par le
`moyen de la poudre qui en tombait et a l’aide du
`moulin et certaines roues de fer qu’iJ avait inventées,
`il pourrait venir :21 bout de les polir parfaitement,
`meme de les tailler en telle rnaniere qu’il voudrait.
`Charles devenu duc de Bourgogne lui mit trois grands
`diamants pour
`les
`tailler avantageusement
`selon
`son adresse.
`Il les tailla aussitot, l’un épais, l’autre
`faible et le troisiéme en triangle et .il y réussit si bien
`que le duc, ravi d’une invention si surprenante, lui
`donna 3000 ducats de recompense.”
`
`Page 18 of 110
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`
`HISTORICAL
`
`:9
`
`'
`
`What _Van Berquem probably did ori-
`ginate is, as already stated, rigid symmetry
`in the design of the cut stone. The intro-
`dugtion of the shape known as pendeloque
`or lbfiolette is generally ascribed to him.
`The Sancy and thté7'i'Florentine, which are
`both cut
`in this ‘shape, have been said
`
`
`
`FIG. 6.
`
`by. some to have been polished by him.
`The Sancy (53% cts.) belongs now to the
`Maharaja of Guttiola, and the Florentine
`(fig. 6), which is much larger (I33; cts.),
`is at present among the Austrian crown
`jewels. The history of both these gems
`is, however, very involved, and they may
`
`some period or
`have been confused at
`other with similar stones. That
`is Why
`_it
`is not at all certain that
`they were
`
`Page 19 of 110
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`
`
`20
`
`DIAMOND DESIGN
`
`the work of Van Berquem. At any rate,
`they are typical of
`the kind of cut he
`introduced.
`l
`
`The pendeloque shape did not meet with
`any very wide success.
`It was adopted
`iii the case of a few large stones,‘ but was
`gradually abandoned, and is not used to
`any large extent nowadays, and then in
`a modified form, and only when the shape
`of the rough stone is especially suitable.
`This unpopularity was largely due to the
`fact
`that, although the loss of "Weight
`i11
`cutting was fairly high,
`the play of
`light
`within the stone did not produce sufficient
`
`-
`
`lire or brilliancy.
`About the middle of the sixteenth century _
`a new form of cut diamond was introduced.
`
`It is known as the rose or msezfte, and was
`made in Various designs and proportions
`(figs. 7 and 8).
`The rose spread rapidly
`and was in high Vogue for about a century,
`as it gave a more pleasant effect than the
`
`pendeloque, and could be cut with a much
`
`smaller loss of weight.
`It was also found
`Very advantageous in the polishing of flat
`
`Page 20 of 110
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`Page 20 of 110
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`HISTORICAL
`
`21
`
`pieces of rough or split diamond. Such
`material is even‘noirv frequently cutinto
`roses, chiefly in the smaller sizes.
`
`
`
`FIG. 7.
`
`In the chapter upon the design of
`diamonds it will be shown that roses have
`
`to be made thick (somewhat thicker than
`in fig. 7) for the loss of light to be small,
`
`and that the flatter the
`
`rose the bigger the loss
`
`_
`
`It will also be
`of light.
`seen there that the fire
`
`of
`
`a
`
`rose
`
`cannot be
`
`very high. These faults
`caused the rose to be
`
`superseded by the
`brilliant.
`
`FIG. 8.
`
`We owe the introduction of the brilliant
`
`in the middle of the seventeenth century
`to Cardinal Mazarin—or at any rate to
`his influence. As a matter of fact, the first
`
`brilliants were known as Mazarins, and were
`
`Page 21 of 110
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`Page 21 of 110
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`
`
`22
`
`DIAMOND DESIGN
`
`of the design of fig. 9. They had sixteen
`facets, excluding the table, 011 the upper side.
`
`FIG. 9.
`
`Theyare called double-cut brilliants. Vincent
`Peruzzi, a Venetian polisher, increased the
`number of facets from sixteen to thirty-
`
`
`
`two (fig. I0) (triple-cut brilliants), thereby
`increasing very much the fire and brilliancy
`of the cut gem, which were already in the
`double-cut brilliant
`incomparably better
`
`Page 22 of 110
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`Page 22 of 110
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`HISTORICAL,
`
`23
`
`than in the rose.
`
`Yet diamonds of that -
`
`cut, when seen nowadays, seem exceedingly
`dull compared to modern-cut ones. This
`dullness is due to their too great thickness,
`and to a great extent also to the difference
`in angle between the corner facets and the
`side facets, so that even if the first were
`
`
`
`polished to the correct angle (which they
`were not)
`the second would be cut
`too
`steeply and give an effect of
`thickness.
`Old-cut brilliants, as the triple-cut brilliants
`are generally called, were at first modified
`by,making the size and angle of the facets
`more uniform (fig. II), this bringing about
`a somewhat rounder stone. With the in-
`
`troduction of mechanical bruting or cutting
`(an operation distinct from polishing; see
`
`Page 23 of 110
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`Page 23 of 110
`
`
`
`24
`
`DIAMOND DESIGN
`
`17) diamonds were made absolutely
`p.
`circular
`in plan (fig. 37). The gradual
`shrinking-in of the corners of an old-cut
`brilliant necessitated a less
`thickly cu_t
`stone with a consequent increasing fire and
`life, until »a point of maximum brilliancy
`was
`reached.
`This is
`the-_ present-day
`bri1liant.1
`
`Other designs for the brilliant have been
`
`tried, mostly attempts to decrease the loss
`of weight in cutting without impairing the
`brilliancy of the diamond, but they have
`not met with success.
`'
`
`We may note here that
`the general
`trend of European diamond. polishing as
`opposed to Indian is the constant search
`for greater brilliancy, more life, a more
`
`1 Some American writers claim that this change
`from the thick cut to that of maximum brilliancy was
`made by an American cutter, Henry D. Morse.
`It
`was, however, as explained, necessitated by the absolute
`roundness of
`the new cut. Mr Morse may have
`invented it
`independently in America. But
`it
`is
`highly probable that it originated where practically
`all the world’s diamonds were polished, in Amsterdam
`or Antwerp, where also mechanical bruting was first
`introduced.
`
`Page 24 of 110
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`Page 24 of 110
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`
`
`HISTORICAL
`
`25.
`
`regardless of
`vivid fire in the diamond,
`the loss of weight. The Weight of diamond
`removed by p bruting and by polishing
`amounts even in the most favourable cases
`
`to 52 per cent. of the original rough weight
`for a perfectly cutbrilliant.
`In the next
`chapters the best proportions for a brilliant
`will be calculated ‘without reference to the
`shape of a rough diamond, and it will be
`seen how startlingly near the calculated
`Values
`the modern well-cut brilliant
`‘is
`
`polished.
`
`Page 25 of 110
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`Page 25 of 110
`
`
`
`Part II
`
`OPTICAL
`
`IT is to light, the play of light, its reflection
`and its refraction, that a gem owes its
`brilliancy,
`its fire,
`its colour. We have
`therefore to study these optical properties
`in order to be able to apply them to the
`problem we have now before us:
`the cal-
`culation of
`the shape and proportions of
`a perfectly cut diamond.
`Of the total amount of light that falls
`upon a material, part is returned or re-
`flected; the remainder penetrates into it,
`and cr_osses it or is absorbed by it. The
`first part of
`the light produces what
`is
`termed the “lustre” of
`the material.
`The second part
`is completely absorbed
`if
`the material is black.
`If it
`is partly
`absorbed the material will appear coloured,
`26
`
`Page 26 of 110
`
`Page 26 of 110
`
`
`
`OPTICAL
`
`27
`
`transmitted unaltered it will appear ‘
`and if
`colourless.
`
`The diamonds used as gems are generally
`colourless or only faintly coloured ;
`it can
`be taken that all the light that passes into
`the stones passes "out again.
`, The lustre
`of the diamond is peculiar to that gem,
`and is called adamantine for that reason.
`
`It is not found in any other gem, although
`zircon and demantoid or olivine have _a
`lustre approaching somewhat
`to the ada-
`mantine.
`
`In gem stones of the same kind and of
`the same grade of polish, we may take it
`that the lustre only varies with the area
`of the gem stone exposed to the light, and
`that it isindependent of the type of cut
`or of the proportions given to_ the gem (in
`so far as they do not affect the area) ;
`this
`is why gems Where the amount of light
`that is reflected upon striking the surface
`is great,‘ or where much of the light that
`penetrates into the stone is absorbed and
`
`does not pass out again, are frequently cut
`in such shapes as the cabochon (fig. I2),
`
`Page 27 of 110
`
`Page 27 of 110
`
`
`
`28
`
`DIAMOND DESIGN
`
`so as to get as large a11 area as possible,
`and in that Way take full advantage of
`the lustre.
`
`the amount of light re-
`In a diamond,
`flected from the surface is much smaller
`
`that that penetrating into the stone ; more-
`over, a diamond is practically perfectly ,
`transparent", so that all the light that passes_
`into the stone has to pass out again. This
`
`C3
`
`FIG. 12.
`
`is why lustre may be ignored in the Working
`out of
`the‘ correct shape for a diamond,
`and why any Variation in the amount of
`light
`reflected from the exposed surface
`due to a change in that surface may be
`considered as negligible in the calculations.
`The brilliancy or, as it
`is sometimes
`termed, the “fire” or the “life” of a gem
`
`thus depends entirely upon the play of
`
`light
`in the gem, upon the path of rays
`of light in the gem.
`If a gem is so cut or
`designed that every ray. of
`light ‘passing
`
`Page 28 of 110
`
`Page 28 of 110
`
`
`
`OPTICAL
`
`29
`
`into it follows the best path possible for
`producing pleasing effects upon the eye,
`then the gem is perfectly cut. The whole
`
`art of the lapidary consists in proportion-
`ing his stone and disposing his facets so
`as to ensure this result.
`
`If we want to design a gem or to calculate
`its best shape and proportions, it is clear
`
`that we must have sufficient knowledge to
`be able to work out the path of any ray of
`light passing through it. This knowledge
`comprises the essential part of optics, and _
`the laws which have to be made use of
`
`are the three fundamental ones of reflection,
`
`refraction, and dispersion.
`
`REFLECTION
`
`Reflection occurs at
`
`the surface which
`
`separates two different substances or media;
`a portion or the whole of the light striking
`that surface is thrown back, and does not
`
`cross over from one medium into another.
`
`This is the reflected light. There are dif-
`
`ferent kinds of reflected light according to
`
`the nature of the surface of reflection.
`
`If
`
`Page 29 of 110
`
`Page 29 of 110
`
`
`
`30
`
`DIAMOND DESIGN
`
`that surface is highly polished, as in the
`case of mirrors, or polished metals or gems,
`the reflection is perfect and an image is
`formed. The surface may also be dull
`or matt to a greater or smaller extent (as
`in the case of, say, cloth, paper, or pearls).
`The reflected light
`is then more or
`less
`scattered and diffused.
`'
`
`It is the first kind of reflection that is of
`
`importance to us here, as diamond, owing
`to its extreme hardness, takes a very high
`grade of polish and keeps it practically
`for ever.
`‘
`The laws of reflection can be studied very
`simply with a few pins and a mirror placed
`at right angles upon a flat sheet of paper.
`A plan of the ar_ra11gement is ‘shown in
`fig. I3. The experiment is as follows :—
`I. A straight
`line AB is drawn upon
`the paper, and the mirror is stood on the
`paper so that the plane of total reflection
`(5.3. the silvered surface) is vertically over
`that line. Two pins P and Q are stuck
`anyhow on the paper, one __as near
`the
`mirror and the other as far away as possible.
`
`Page 30 of 110
`
`Page 30 of 110
`
`
`
`OPTICAL
`
`31
`
`Then the eye is placed in _line with P Q at-
`I, so that Q -is hidden by P. Without
`
`two more pins R and S
`moving the eye,
`are inserted, one near to and the other far
`
`from the mirror,
`
`in such positions that
`
`FIG.
`
`1 3.
`
`their images appear in the mirror to lie
`along P Q continued.
`If the eye is now sighted from position
`2 along SR, Q and P will appear in the
`mirror to lie on S R continued.
`
`The mirror is now removed, P Q and S R
`are joined and will be found to intersect
`on AB at _M.
`If-Ha perpendicular MN be
`
`Page 31 of 110
`
`Page 31 of 110
`
`
`
`32
`
`DIAMOND DESIGN
`
`the angles
`erected on AB at that point,
`N M and.N M S will be found equal._
`The above experiment may be repeated
`along other directions, but keeping the pin
`8 at
`the same point. The line of sight
`will now lie on P’ Q’, and the angles
`between P’Q', SR’ and the normal will
`again be found equal.
`'
`In the first experiment S appeared to
`lie on the continuation of P
`in the second
`it appears to be situated on P’ Q’ produced.
`Its image is thus at the intersection of these
`two lines, at L.
`It can easily be proved
`by elementary geometry (from the equality
`of angles) that the image L of the pin is
`at
`the same distance from the mirror as
`
`the pin S itself, and is of the same size.
`II. lf the pins P, Q, R, S in the first
`experiment be placed so that their ‘heads
`are all at the same height above the plane
`sheet of paper, and the eye be placed in a
`line of sight with the heads P, Q, the images
`of the heads R, S in the mirror will be
`
`hidden by the head of pin P.
`The angle NMP (position I)
`
`is called
`
`Page 32 of 110
`
`Page 32 of 110
`
`
`
`OPTI CAL
`
`33
`
`incidence, and the angle N MS '
`a11gle of
`angle of reflection.
`
`The laws of reflection (verified by the
`above tests) can now be formulated as
`follows :—
`
`I. The angle of reflection is equal to the
`angle of incidence.
`,
`
`II. The paths of the incident and of the
`reflected ray lie in the same plane.
`From I it follows, as shown, that
`
`III. The image formed in a plane re-
`flecting surface is at
`the same distance
`from that surface as the object reflected,
`and is of the same size as the object.
`
`REFRACTI ON
`
`When light passes from one substance
`
`into another it suffers changes which are
`somewhat more complicated than in the
`case of reflection.
`‘Thus if we place a coin
`at the bottom of a tumbler which we fill
`with Water, the coin appears to be higher
`than when the tumbler was empty;
`also,
`if we plunge a pencil
`into the Water, 'it
`will seem to be bent or broken at the surface,
`
`'
`
`3
`
`Page 33 of 110
`
`Page 33 of 110
`
`
`
`34
`
`DIAMOND DESIGN
`
`in the particular case when the
`except
`pencil is perfectly Vertical.
`We can study the laws of refraction in
`a manner somewhat similar to that adopted
`
`for the reflection tests. Upon a flat sheet
`of paper (fig. I4) we place a fairly thick
`
`
`
`FIG. _ 14.
`
`its
`rectangular glass plate with one of
`edges (which should be polished perpendi—
`cularly to the plane of the paper) along a
`previously drawn line A B. We place a.
`pin, P, close to the edge AB of the glass
`plate and another, Q, close to the further
`edge. Looking through the surface AB,
`
`Page 34 of 110
`
`Page 34 of 110
`
`
`
`OPTICAL
`
`35
`
`we place our eye in such a position that
`the pin Q as viewed through the glass is
`covered by pin P. Near to the eye and
`on the same line of sight we stick a third
`pin R, which therefore covers pin P. The
`glass. plate is now removed. PQ and PR
`are joined, a perpendicular to AB, MM’,
`is erected at P, and a circle of any radius
`drawn with P as centre. This circle cuts
`PQ at K and RP'at L. LM and KM’
`are drawn perpendicular to MM’, L M and
`
`K M’ are measured and the ratio
`
`LM
`
`KM’
`
`__
`found.
`The experirnent is repeated for different
`positions of P and Q and the corresponding
`L M
`
`K M... calculated.
`
`, It will be found-that
`
`ratio
`
`for a given substance (as in this case glass)
`this ratio is constant.
`It
`is called the
`index to: refraction, and generally repre-
`sented by the letter at.
`Referring to fig. I4, we note that as
`
`P K 2 P L = radius" of the circle,
`
`Page 35 of 110
`
`Page 35 of 110
`
`
`
`36
`
`DIAMOND DESIGN
`
`we can write
`
`L M
`LM _'Ff _ sin RPM
`K M’ ‘ KM’ _ °
`P K
`
`Writing the angle of incidence R P M as 1,,
`
`and the angle of refraction Q P M’ as r, this
`
`equation becomes
`
`or
`
`_ S111 z
`sin 7'
`
`_
`1?, sin 9’ = s1n 1,
`
`(I)
`
`(2)
`
`In this case the incident ray is in air,
`the index‘ of refraction of which is very
`nearly unity. With another substance it
`can be shown that equation (2) becomes
`
`W sin 1* = 72' sin 1}
`
`(3)
`
`where ‘n’ is the index" of refraction of that
`
`substance.
`
`It can be seen easily, and in a way similar
`
`to that used with reflection '(1}.e. sighting
`along the heads of the pins), that, in re-
`fraction ~ also :
`‘
`
`The paths of the incident and of
`refracted ray lie in the same plane.
`
`the
`
`Page 36 of 110
`
`Page 36 of 110
`
`
`
`OPTICAL
`
`37
`
`index’
`Of two substances with different
`qf refraction, that which has the greater
`index of refraction is called optically denser.
`In the experiment the light passed from air
`to glass, which is of greater optical density.
`Let us now consider the reverse case,
`15.6.
`
`MEDIUM I
`
`x
`
`
`
`
`x
`c
`
`/
`
`/
`
`B/
`
`—
`
`A
`
`.
`I
`
`I
`N
`
`~.
`
`c"
`
`\
`
`\
`
`..
`
`A
`
`\BlI
`
`when light passes from one medium to
`another less dense optically.
`Suppose a
`beam of light A0 (fig.
`I5) with a small
`angle of incidence passes from water into
`air. At the surface of separation a small
`proportion of
`it is reflected to A” (as we
`have seen under reflection). The remainder
`is refracted ina direction 0A’ which is
`
`_
`
`Page 37 of 110
`
`Page 37 of 110
`
`
`
`38
`
`DIAMOND DESIGN
`
`more divergent
`than A0.
`
`from‘ the normal N O N’
`,
`
`Suppose now that the angle A O N gradu-
`ally increases. The proportion of reflected
`light also increases, and the angle of re-
`fraction N’ OA’ increases. steadily and at
`a more rapid rate than NOA, until for a
`certain value of
`the angle of
`incidence
`B ON the refracted angle will graze the
`surface of separation.
`It is clear that under
`these conditions the amount of light which
`is retracted and passes into the air
`is
`
`zero.
`
`If
`
`the angle of incidence is still
`
`greater,
`
`as at CON,
`
`there is no re-
`
`fracted ray, and the Whole of the light is
`reflected into the optically denser medium,
`
`or, as it
`
`is termed,
`
`total reflection then
`
`occurs. The angle B ON is called critical
`angle, and can easily be calculated by (3)
`when the refractive indices 77, and M,’ are
`
`known.
`
`It will be noted that when the
`
`critical
`its
`incidence attains
`of
`angle
`value *5’, the angle of refraction becomes
`a right angle, Le.
`its sine becomes equal
`to unity.
`
`Page 38 of 110
`
`Page 38 of 110
`
`
`
`OPTICAL
`
`39
`
`Substituting in (3)
`
`n sin 7 2 7:.’ sin i’
`
`sin 1/ 2 I
`
`S111 7,
`
`._ W,
`
`.
`
`.
`
`Or, if the less dense medium be air,
`
`775:1
`
`.
`.,__i*
`s1nz_
`n,.
`
`.
`
`.
`
`.
`
`(4)
`
`(5)
`
`in
`is Very important
`This formula (5)
`the design of gems, for by its means the
`critical angle can be accurately calculated.
`A precious stone, especially a colourless
`and transparent one like the diamond,
`is
`cut
`to the best advantage and with the
`best possible effect ‘when it sends to the
`spectator as strong and as dazzling a beam
`of light as possible. Now a gem, not being
`in itself a source of light, cannot shine with
`other than reflected light. The maximum
`amount of light will be given off by the gem
`
`* No mention is made here of double refraction,
`as the diamond is a singly refractive substance, and
`it was considered unnecessary to introduce irrelevant»
`Inatt'e1'.
`
`Page 39 of 110
`
`Page 39 of 110
`
`
`
`40
`
`DIAMOND DESIGN
`
`if the whole of the light that strikes it is
`reflected by the back of
`the gem, 12.6. by
`that part hidden by the setting, and sent
`out
`into the air by its front part. The
`
`facets of
`
`the stone must therefore be so
`
`disposed that no light that enters it is let
`out through its back, but that it is Wholly
`reflected. This result is obtained by having
`the facets inclined in such a way that all
`the light that strikes them does so at an
`angle of incidence greater than the critical
`angle. This point will be further dealt with
`in a
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