Why do pirates bite gold coins they are given?

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Why do pirates bite gold coins they are given?
Arnaud Manas
March 31, 2017
Abstract — In this paper I investigate whether it is true and to what extent
pirates determined the fineness of gold coins by biting them. I use the classic
beam theory to model coin bending. I bite five discs made of different gold alloys
and conclude that while fine gold is softer than alloyed gold, pirates biting coins
is almost certainly a Hollywood myth.
R´esum´e — Dans de nombreuses oeuvres litt´eraires et cin´ematographiques,
des pi`eces d’or sont mordues pour d´eterminer leur authenticit´e. Pour ´evaluer
les fondements ´eventuels de cette pratique, un mod`ele physique de la torsion
des disques m´etalliques est propos´e. Une exp´erience men´ee sur cinq disques
d’alliages diff´erents permet de conclure que si l’or pur est plus mall´eable que les
alliages mon´etaires, mordre les pi`eces est tr`es certainement un clich´e hollywoo-
dien sans r´ealit´e historique.
Keywords: tensile strength, beam theory, Vickers hardness, gold alloy, coun-
terfeited coins, pirates, Hollywood movies
Mots cl´es: r´esistance `a l’´etirement, th´eorie des poutres (resistance des mat´eriaux),
duret´e Vickers, alliage mon´etaire, fausses pi`eces, pirates, films hollywoodiens
Introduction
Biting a coin to determine whether it is genuine or counterfeit is a widespread
clich´e. It is depicted in many movies (Young Lincoln,Gunsmoke and countless
pirate movies...), the most famous being Charlie Chaplin’s film (see fig. 1).
It also appeared in several books as Sutter’s Gold (L’or, 1925) from Blaise
Cendrars and Berthold Brecht’s play Mother Courage (1938), set during the
Thirty Years’ War of 1618-1648. Olympic champions also ritually bite their
gold medals.
The rationale for such practice was the supposed widespread dissemination in
the 19th century of gold plated lead coins.1Since lead is much softer than gold,
biting the coins is a sensible test for counterfeiting. Nevertheless, this type of
counterfeiting was rare and the coin’s weight was the most discriminating factor
(see [12]). For instance, a genuine 20 franc gold coins (21 mm diameter, 1 mm
1“If you can leave teeth marks in a gold coin, it’s almost certainly a fake. People who’ve
watched too many old pirates movie think that, because gold is a soft metal, the way to prove
a gold coin is genuine is by biting into it. While this theoretically works with a pure gold
coin it ignores that all ’gold’ coins minted for circulation in the UK and America since Tudor
times have contained copper. This made them more durable (and hard to bite).” [11], p.73
1

Figure 1: Waiter biting the coin of Chaplin’s character, The Immigrant, 1917
thickness of gold .900 fineness) weighs 6.45 g while a coin of the same size made
of lead and plated with a gold foil would weigh 4.2 g. This could be recognized
without biting the coin. Silver coins (5 F coin : 25 g of .900 Ag) were also
widely counterfeited2with tin and lead alloys that were close to genuine coins
in terms of hardness, sound and colour. Only the “rawest novice counterfeiters”
used pure lead.3Hence hardness seems to have played no role in detecting false
coins in the 19th and 20th centuries.
The origin of the tradition must therefore be older. In medieval times gold
coins were made of the purest gold possible for both prestige and practical
reasons (see [4] on hammer striking). The coins were thin, and relatively soft.
It was also known that adding a different metal to gold had a hardening effect.4.
The standard medieval gold coin was Florence’s florin made of fine gold (24 K5
3.5 g, 20 mm diameter) and minted using the same method from 1252 until
1523. Most of the gold coins created in Europe in the 13th and 14th centuries
were modelled upon the florin. In 1290, the King of France, Philippe-le-Bel
(1268-1314) had “standard” gold florins (“petits royaux” 3.5 g 24K 20 mm)
minted. These coins had the same intrinsic value as the Florentine coins. Later
he minted double gold florins (“grands royaux”) weighing 7 g ans measuring 31
mm. They came in two issues: standard 24 K (pure gold) and “substandard” 22
K (alloyed gold) with a slightly different design. These coins were also named
“masse” or “chaise” because of their design in which the King was depicted
seated on a chair and holding a mass (see fig. 2).
These changes were perfectly lawful,6and publicized, according to Leblanc
[10]. Nevertheless, they prompted a public outcry particularly in Italy and Flo-
2See Baudelaire, La fausse monnaie, Le spleen de Paris, XXVIII
3R.-A. Reiss, Manuel de Police scientifique, t. 1, Payot, 1911, p.306
4The German monk Theophilus (Roger of Helmarshausen), who wrote De diversis artibus
(c. 1110–40), mentions explicitly that if gold is alloyed with a base metal, its malleability is
reduced and striking it with a hammer could give an indication of its purity ([?] p.140)
5Karats (K) measure the parts of pure gold per 24 parts of metal, so that 18 karat = 18/24
= 75% and 24 karat gold is 100% (fine) gold.
6See Registre des deux ais, De Saulcy, p.28.
2

Figure 2: Philippe-le-Bel’s 24 K “masse”
rence, where money changers undoubtedly took advantage of this little known
specificity to defraud unsuspecting travelers and merchants. As a result of this
unorthodox, deceitful practice, Philippe Le Bel was named the “Counterfeiter
King”. The practice entered posterity when the Florentine Dante wrote about
Philippe-le-Bel, who died while he was hunting,“There they shall see the sorrow
brought upon the Seine by one who falsifies his country’s coin and who will die
assaulted by a boar.” (Paradiso XIX, 118-120). Dante also placed the counter-
feiters in the 8th circle of the Inferno (the Malebolge), next to traitors like Judas
and Brutus. Apparently, the favoured way of determining the type of “royaux”
(24 K or 22 K) was to test their hardness. In his work L’Encyclop´edie7in the
18th century, Diderot mentions that the 22 K “royaux” were called “royaux
durs” (hard royals) while the 24 K were just called “royaux”.
This practice could explain the clich´e and give both historical and physical
grounds to coin biting. In this paper, I attempt to test whether or not it is
possible to detect alloyed gold coins by biting them. It is divided into three
parts: in the first part I use a simple classical beam model and the Vickers
protocol to model the bending and indenting of coins that occurs in biting ;
in the second part, I estimate the parameters, such as the strength of the arm
and jaw and the hardness of monetary gold alloys) ; in the third part, I perform
tests on five different gold alloy discs having the same size as the Philippe-le-Bel
“royaux”.
1 Tooth and Metal
1.1 Coin as a cantilever beam
The bending of a coin can be analysed within the framework of the classical
beam theory. Classic, i.e. disc-shaped coins (see below for rectangular coins),
have rectangular cross sections (non-constant) and are made of homogeneous
7“Masse ou Chaise (Monnoy.) monnoie d’or, Philippe-le-Bel fit faire des chaises [...] qu’on
appelloit aussi royaux durs. Cette monnoie n’´etoit qu’`a 22 karats & pesoit 5 deniers 12 grains
tr´ebuchans. Elle fut appel´ee masse, `a cause que roi y tenoit une masse de la main droite.
[...] Enfin on donna `a cette esp`ece le nom de royal dur, parce que n’´etant qu’`a 22 karats,
elle ´etoit moins pliable que les monnoies d’or fin.” (Masse [literally Mass] ou Chaise [literally
Chair]: gold coin, Kink Philippe-le-bel minted chaises that were also named hard royals of
22K weighing 5 deniers 12 grains. They were also named masses because the king wielded a
mass. [...] Eventually, they ware named hard reals because as they were only 22K they could
not be bent as easily as fine gold)
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metal. Intuitively, a pirate would put the coin’s edge in his mouth, grip it
between his molars and pull the opposite edge down with his finger.
Figure 3: Using finger and teeth to bend a coin
The coin can be considered as a cantilever beam of thickness hand length
a. One end is clamped by the molars and the opposite is free and pulled down
by the finger with force F. At distance ax, the moment is Mx=F a(x−s), for
s≤x≤r, and the normal tensile stress σx(parallel to the coin) is maximal on
the top edge (dot on fig. 4): σx=Mx
Ix
h
2where Ixis the moment of inertia of
the rectangular cross section of width bxand height h. For rectangular coins,
such as Aruban ones (see fig. 5), bxis constant.
F
r a
a/2
h/2
x a
s a
Figure 4: The coin as a clamped cantilever beam
For classic disc-shaped coins, the stress is maximal when x=r(see fig. 6).
Its value is:
σmax =3
h2
r−s
pr(1 −r)F(1)
Note that Aruban coins are less stressed.8The coin should bend on or break
8σx=3
h2(x−s)F
4

Figure 5: Aruba 50 cents, coin (Ni)
apart close to the top molar. The shear stress, which is maximal in the middle
of the coin and nil at the surface can be ignored.
0.3
0.4
0.5
0.6
0.7
0.8
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Figure 6: Stress (s=r=0.2), round (upper blue curve) and square coins (lower
purple line)
1.2 Indenting the coin
Another way to determine the hardness of a coin is to indent it. As one may
suppose, pirates did not carry specialized tools with them. They could use their
teeth to indent the coins and visually determine the softness of the metal by
considering the size of the mark. The commonly used Vickers test determines
hardness by pressing a small pyramid with a force Tonto the material. The
pyramid’s side makes an angle of 22 degrees with the horizontal plane. The
surface area resulting from the indentation Ais then measured. The Vickers
hardness (Hv) is then determined by calculating the ratio between the force T
5

and the area9A. A pirate’s lower canine makes an angle of approximately 25-30
degrees and could to some extent be considered as an indenter (see fig. 7). The
length (diameter) of the mark dis therefore given by the formula:
d= 0.4348rT
Hv
(2)
22°
T
Figure 7: Canine and Vickers indenter
2 Estimating the parameters
2.1 Coin’s parameters
The hardness of the soft and hard “royaux” depend theoretically on several
factors.
At the atomic level, the crystal lattice depends on the structure, which is
determined by the type of atom. Gold and silver form face-centered cubic (f.c.c.)
crystal. With pure gold, the crystal lattice is regular. In binary alloys (Au-Ag or
Au-Cu), a number of gold atoms are replaced in the crystal by the other metal
(silver or copper). This leads to a distortion of the lattice and a roughness in the
planes, which limits the sliding of the crystal planes. This increases the hardness
and the tensile strength. As it depends on the energy needed to disrupt a pair
(Au-Ag or Au-Cu), it is maximal when the number of this pair is the largest
(i.e. when the metals are in equal atomic proportions):10 for gold-silver, this
means a 15.5 K alloy (64.5% gold and 35.5% silver) and for gold-copper a 18.1
K alloy (75.7% gold and 24.3% copper). Gold alloyed with copper is harder
than gold alloyed with silver (see table 2.1).
In the 1930s, Sachs and Weerts studied the hardness of gold-silver alloys.
They found that the hardness, critical shear stress and ultimate tensile strength11
9T
gA (the factor gcomes from the fact that when the test was devised forces were measured
in kilogram-forces kgf).
10As the atomic mass are respectively for the different metals : mAu = 196.9, mAg = 107.8
and mCu = 63.5, q=kmAg
mAu+k(mAg −mAu )
11Zugspannung an der Fließgrenze σsin kg/mm2: Tensile stress at the yield point σsin
kg/mm2; Kritische Schubspannung τsin kg/mm2: Critical shear stress τsin kg/mm2
6

depended on the concentration and followed a quadratic law,12 and confirmed
that the maximum was reached for a 50% concentration (see fig. 8).
Figure 8: Maximal hardness of gold-silver alloys, from Sachs and Weerts (1930)
[14]
The rationale for lowering the gold content of the coin is economic, silver and
copper are much cheaper than gold. Alloying changes not only the hardness of
the metal but also the colour. Adding silver gives a greenish tint, while copper
gives a reddish one. When mixing in approximately equal proportions silver
and copper, the alloy keeps its yellow color, and this practice was common in
the Middle-Ages [1], which explains the ternary nature of alloys of that time
(Au-Ag-Cu).
There are other factors influencing hardness. Cold working creates disloca-
tions at the crystal level in the lattice structure, which makes the metal harder
and less ductile. The size of the grains (i.e. crystals) also matters. Smaller
grains make the metal harder [2]. These factors depended on the “industrial
process” used by the coin manufacturer under Philippe-le-Bel [1]. It is reason-
able to suppose that these factors did not change with the type of “royaux”.
Based on information from diverse sources,13 the gold alloys’ characteristics
were as shown in table 2.1.
Hence, the parameters can be measured or estimated14 (see Table 2.1) for
the alloys that should have been used under Philippe-le-Bel: h= 0.5 mm and
a= 31 mm.
2.2 Pirate’s parameters
The two main parameters for the pirate are the strength of his grip and the size
of his teeth. A third parameter that should be taken into account is his level of
12σs=qσAg + (1 −q)σAu +q(1 −q)4σ0
13Corti [2], Velde [17], Grimwade [7]. These measuring are not always consistent due to
different protocols.
1424 K: see Table 2.1, 23 K : linear interpolation between 24K and 22 K, 22K: Average
value between 22K alloys Hv(138-142) and TS (390-463), 21 K : below 190 and 650, 18 K :
see Table 2.1
7

K Au Ag Cu Hv(GPa) Hv(GPa) TS (N/mm2) TS (N/mm2)
%wt %wt %wt Annealed Worked Annealed Worked
24 K 100.0 0.0 0.0 20 48 124 216
99.7 NA 0.0 0.3 52 NA NA
22 K 91.7 8.3 0.0 67 NA 157 NA
91.7 0.0 8.3 NA 139 NA NA
91.7 5.5 2.8 52 138 220 390
91.7 3.2 5.1 70 142 273 463
90.0 0.0 10.0 NA 147 NA NA
21 K 87.5 4.5 8.0 100 190 363 650
87.5 1.75 10.75 123 197 396 728
18K 75.0 12.5 12.5 150 212 520 810
75.0 4.5 20.5 160 227 550 880
Table 1: Gold alloys’ parameters
% Au (wt) Hv(GP a)T S(N/mm2) Source
24 K 48 216 Measured
23 K 100 320 Estimated
22 K 140 425 Estimated
21 K 180 600 Estimated
18 K 212 810 Measured
Table 2: Theoretical values for gold cold worked alloys
intoxication. Unfortunately, while its effect is well known this important data
is rather undocumented.
It can be assumed that pirates could be compared to U.S. Navy personnel
(for their strength). According to NASA which conducted extensive studies
on Human Performance Capabilities [13], finger grip strength is at least 90 N
(F= 90N) for its weakest sailors. The distance between two cusps in a molar15
is 8-10 mm. An extra millimetre should be allowed to avoid the coin to slip (9-11
mm). For the finger, the pressure is exerted by the bone that ends approximately
at the middle of the third phalanx, at 6-8 mm from the coin’s edge. The stress
produced by the weakest modern sailor should be between16 720 and 1,170
N/mm2. Therefore it should be at least 1,000N/mm2for a “normal” pirate.
This value is above the ultimate tensile strength of the hardest 18 K gold alloy
(see table 2.1).
Regarding indenting, other muscles are involved. Unfortunately, NASA did
not conduct surveys on the sailors’ biting capabilities. Nevertheless, the jaw
muscles can produce a force up to a 500N [9]. Pirates probably did not exert
full pressure on the coins as they did not not want to ruin their teeth. A 100-
300 N force seems reasonable. The pirate’s tooth mark should therefore range
between 0.4 mm and 0.9 mm as it depends on the square root of the Vickers
hardness and there is a fourfold increase between the softest (24 K) and the
15See [9] for tooth size
16r≈10/31 and s≈10/31 implying σmax between 8Fand 13F
8

hardest (18 K) alloys. Estimating the size of the tooth mark with the unaided
eye is difficult.
3 Testing the coins
A professional jeweler made five discs of the size of Philippe-le-Bel’s “royaux”
(31 mm diameter, 0.5 mm thickness, 24 K, 23 K, 22 K, 21 K and 18 K, see fig.
9). They were made of five different gold alloys with the same proportion of
silver and copper (50% Ag - 50% Cu). The first one was made of 24 K gold
(.9999). It must be stressed that medieval fine gold (24 K) was .99 fine gold
(23.75 K based on modern estimates [1]). Monetary alloys were always higher
than 22 K (.916) until the French Revolution, when the decimal system was
introduced and standard fineness was set at .900. The last one (18 K, .750) was
the hardest and served as a benchmark.
The coins were disinfected with cognac.17 All the disks could be bent without
much difficulty and without exerting full strength. The first one (24 K) was very
easy to bend while the last one (18 K) was significantly harder to bend. In a
second experiment, the five discs were ranked by hardness in a blind test. Except
for the hardest (18 K) and the softest (24 K), it was not possible to determine
the right order. In trying to bite them. marks were made on all five discs but,
except for the 18 K alloy, it was very hard to estimate their relative sizes (see
fig. 9). This uncertainty comes from the difficulty in controlling the strength of
the jaw.
At this stage, these experiments do not seem very conclusive. Biting does
not provide a clear pass or fail test. Its results relies too much on judgment
and unobservable factors (pirate’s strength and level of intoxication). This lack
of clarity comes from the fact that all coins can be bent and indented with
reasonable strength. This would not be the case for thicker coins, like today’s.18
A doubled thickness produces a fourfold increase in resistance to tensile stress,
allowing only the softest coins to be bent. For thin coins, the moment must be
reduced to provide clear-cut test results. A different test might be considered,
in which the thumb presses the centre of the coin which is held by the index
and middle fingers (see fig. 10).
The stress is lower,19 and should be in the order of magnitude of 300N/mm2
which above the tensile strength for 24K and close to 23K limit. By pressing very
hard the 23 K coin can be bent, while the 22 K one does not yield. This simple
test could explain why many medieval gold coins are bent (or have bending
marks) in the middle.
17Rum would have been more appropriate but I did not have a bottle to hand while I did
have an old bottle of cognac. Whisky is a suitable alternative (see the “Whiskey turkey recipe”
http://www.jokeindex.com/joke.asp?Joke=626 for an interesting alternative protocol).
18Before the French monetary reform of 1640, thin coins (.5 mm) were hammer-struck and
24 K or 23 K gold (except in some cases like Philippe-le-Bel’s) was used. After the reform,
thicker coins (1 mm) were minted using a screw press and harder 22 K alloy was used.
19The stress of 3F r/h2corresponds to r= 1/3 and h=.5 and a force of 60-90 N to 240-360
N/mm2.
9

Conclusion
In conclusion, Jack Sparrow and movie pirates may bite coins on camera to
check for their gold content but real pirates probably never did it. Biting is not
precise enough, since all thin coins can be bent and indented.
Since coin biting is not referenced by pirates’ contemporaries, it is very
likely that it is just a Hollywood clich´e. This clich´e was reproduced by writers
like Cendrars or Brecht. Brecht based his play Mother Courage on Grimmel-
hausen’s Courage [6]. The book, published in 1670, makes many references to
coins, money, ducats and pistoles but at no time is a coin bitten to determine
whether or not it is genuine. One must conclude that Brecht and Cendrars
merely invented the scene of biting the coin, taking inspiration from Hollywood
movies.This clich´e might find its origin in the crude testing method used by
American prospectors during the 19th century gold rush. They bit the gold
nuggets they found to be sure that they were not fool’s gold (i.e. yellow pyrite
crystals of iron sulfide FeS2). Gold nuggets are very soft and have a Mohs’ index
of 2.5 (Hv= 30 −34), while pyrite’s is between 6 and 6.5 (Hv= 1,505 −1520).
The difference is quite significant: pyrite cannot be indented and is brittle while
teeth marks can be made in gold.
Acknowledgements
The author wishes to thank Fran¸cois de Coustin and Jean-Renaud Lefeuvre for
their help and their suggestions and an anonymous referee for his very helpful
and stimulating comments. The disks were made by Olivia Bevernage, 3 Rue
Dornaldeguy, 64500 Saint-Jean-de-Luz
(http://www.oliviabevernage-joailliercreateur.com/).
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Figure 9: Discs before and after testing
12

Figure 10: Bending with fingers
13