Sunday, 30 April 2017

The lost treasure of Joseph Pâris Duverney

Here is a curious little story of grave robbers and mysterious lost treasure - sadly there are no Knights Templar or lost bloodlines, otherwise it could have been made into a bestseller...

Jean-Baptiste II Le Moyne,       
bust of Pâris Duverney,  
Musée de Brunoy
On 17th June 1770 Joseph Pâris Duverney, intendant of the 
École militaire, and the last of the four great financier brothers Pâris, died at his hôtel in the rue Saint-Louis in the Marais.  He was 86 years old. The funeral service took place at his parish church of Saint-Gervais.  Duverney had stipulated in his will in 1766 that he wanted to be buried in the cemetery of the École militaire, "if burials had been authorised by the time of his decease".  In accordance with his wishes, his body was transported to the École and on 20th June it was laid to rest, not in the cemetery but in the crypt of the public chapel, still under contruction at the time. On this occasion the priest of Saint-Gervais, the abbé Bouillerot, delivered a funeral oration before the clergy of the Hôtel Royal.  A further service took place in the private chapel of the cadets on 9th August. On the anniversary of Duverney's death, on 17th June 1771 a full memorial service was also held, again in the pupils' chapel.  In 1773 Duverney's body was joined in the crypt by that of the chevalier Jacques René Croismare, the former governer of the École.  No monument was ever erected to either man, perhaps it was still intended at some point to transfer the bodies to the cemetery, which did exist but remained much smaller than had originally been planned (Laulin (1933) p.133-4; 137)

In the years after his death Duverney's name was kept in the public eye by the protracted and well-publicised legal battle which ensured between his heir,  the Comte de La Blâche, and his protégé, Beaumarchais. Unsurprisingly, there was speculation his estate was worth far more than had been openly declared. 

Here is the account of subsequent events, taken from a publication of 1860:

The Chapelle Saint-Louis today 
A great deal of astonishment  was caused by Duverney’s modest legacy [1,500,000 livres] for public opinion held that he was worth 20 million livres.  People wondered what had become of the immense riches of the great financier, who had always been so fortunate in his speculations.  Strange rumours abounded; there was talk of treasure hidden away for some mysterious purpose. However, interest died away in the turbulent years of the Revolution and  Duverney was so thoroughly forgotten that, even fifteen years ago, his name was unknown in the École militaire which he had founded.

A chance event  brought back to mind both his name and his treasure.

In 1846, during repairs to the floor of the chapel of the École militaire, an old lady reported that she had heard from her father, a sacristan before the Revolution, that there existed close to the altar, a crypt containing coffins.  This claim seemed unlikely, for there was no monument or inscription in the chapel,  nor any sign that one had ever existed.  However, investigations revealed that one of the stone slabs to the right of  the altar concealed  the entrance to the crypt that the old lady had described.  The investigators went down and the engineer in charge found two coffins.  One belonged to Duverney:  a copper plaque attached to it bore an inscription to him].

The two coffins were in a state of perfect preservation, as if they had been put there only yesterday.  In the earth could be seen clearly the footprints of the last priest or friend who had left, eighty years previously, after paying their final respects. The coffins were left as they had been found; all that was done was to replace the stone  slab with one of a different colour to mark the spot.

One would have supposed that such a minor event would have gone unnoticed.  But in certain circles news spread and memories of the mysterious hidden treasure were revived, though in whose  mind we do not know.  All seemed forgotten when  in 1848 a general who boasted one of the most illustrious names of the First Empire  appeared at the École militaire with authorisation to look for treasure.  All the buildings were searched with great care...but to no avail.  

That is not all.  Last year [towards the end of 1859] an unknown person, who imagined himself better informed, took advantage of the absence of the  chaplain insinuate his way into the chapel at night , lift up the stone into the crypt and conduct a thorough survey.  No doubt frustrated by his lack of results, this man seems to have fallen prey to a kind of madness and  imagined suddenly that Duverny must have with him, in his very hands perhaps, a paper  or sign which would provide the searcher with some clue. Without hesitation he took a sacrilegious hand to the coffin, broke it open  and rifled thoroughly through the clothes of  the body.  The cadavre kept its secret.

Several days later, when the violation of the sepulcre was notice, a judicial enquiry was began, which we are assured is still ongoing at this time (May 1860)
Adolphe Rochas, Biographie du Dauphiné, vol.2 (1860), p.222

There are certainly strange goings-on here; but the identity of the general, and the information the intruder was acting on remain a mystery.

A detailed history of the chapels and clergy of the École militaire, which was published in the 1933,  adds only that the judicial enquiry was abandoned.  In 1901 the Commission du Vieux-Paris once again rediscovered the crypt and noted the inscriptions on the two coffins. In Spring 1929  a party accompanied the architect responsible for Historical Monuments on an inspection.  They lifted up two flagstones, and decended by an iron ladder.  They were impressed by the dryness of the earth and the perfect state of the walls and vault. The two oak coffins rested on iron tressles and were still open.  Both contained inner anthropomorphic lead coffins; Duverney's still showed signs of the damage which had been inflicted on it and was resoldered (Laulin (1933) note, p.157-8).

In 2015 as part of a programme in the series" L'Ombre d'un doute", the inside of the crypt was filmed for the first time.  The presenter here is Marc Cheynet de Beaupré, successful banker and author of a two volume biography of Joseph Pâris-Duverney.  It is quite moving to see the two coffins exactly as described:



Adolphe Rochas, Biographie du Dauphiné, vol.2 (1860), p.222

R.Laulan, "Les chapelles de l'École militaire et la vie religieuse dans l'ancien hôtel royal", Bulletin de la Société de l'histoire de Paris et de l'Ile-de-France, 60, 1933. p.108-185.

L'ombre d'un doute - "Louis XV, l'homme qui aimait trop les femmes" broadcast 5th January 2015

Here is small relic of Joseph Pâris Duverney, a altar bearing his arms which he presented to the parish of Nogent on the occasion of his reception as Seigneur of Plaisance in 1721.  After being in the museum in Nogent since 1959, it was recently restored to the parish church of Saint-Saturnin.  The château de Plaisance itself survived the Revolution only to be demolished in 1818. Only a small pavillion remains, today part of the  maison de Santé, 30 rue de Plaisance.

Château de Plaisance, Nogent on the website for the exhibition, "Madame Du Châtelet:  La femme des Lumières"(2011)

"L'autel de Pâris-Duverney de retour à Saint-Saturnin", Nogent-sur-Marne website

Friday, 28 April 2017

Shock and Awe: the Marly experiment

BBC Four is currently repeating Jim Al-Khalili's documentary,  "Shock and Awe: the Story of Electricity",  which was first broadcast in 2011.  The first episode is devoted to 18th-century discoveries.   Catch it if you can, before it disappears from i-player as it is a brilliant programme - the camera work is stunning throughout.  There is no gimmicky docudrama, just Jim recreating the original experiments in a load of unusual locations: Charterhouse and the Royal Society in London, Leiden and the University of Bologna.

One of the most satisfying of the early experiments in electricity took place in France at Marly-la-Ville.  How could it be proved that lightning, most awe-inspiring of God's wonders, was really an electrical phenomenon?  Easy.... Stick a long metal rod in a wine bottle and wait for the storm.....!   Here is Jim on the very spot (on location in someone's back garden):  


Franklin had first outlined his experiment in 1751, in a letter to the Royal Society in which he had also advocated the use of lightning rods.  The Royal Society had refused to include his speculations in its transactions, so Franklin printed the letter himself in a book entitled Experiments and Observations on Electricity (Philadelphia 1751)

Buffon was not particularly interested in electricity, but when Franklin's little book fell into his hands, he saw an opportunity to score against his enemy Réaumur whose protegé the abbé Nollet, had opposed Franklin's theories.  Buffon's schoolfriend and collaborator, the botanist Thomas-François Dalibard translated the book into French with an insolent Avertissement attacking "hack physicists". The two hired a public demonstrator in "experimental philosophy" called Delors to repeat Franklin's earlier experiments.

On 3rd February 1752 Louis XV himself was invited to a demonstration, hosted by the duc d'Ayen at St Germain-en-Laye. The monarch was so appreciative that it "excited in Messieurs de Buffon, d'Alibard and De Lor, a desire of verifying the conjectures of Mr. Franklin, upon the analogy of thunder and electricity".

Plate from Expériences et observations sur l'électricité 2nd, ed. 1756, vol.2
Dalibard had previously installed a small laboratory in the grounds of the house in Marly where he lodged and it was here that he set up his insulated pole in early  May 1752. On 10th May it thundered in Marly. The former dragoon charged with the experiment, whose name was Coiffier, ran to the pole and presented to it a brass wire stuck into a glass handle; he was the first man ever to see a spark drawn intentionally from the sky.  Coiffier alerted the curé, Raulet, who repeated the experiment "at least six times in a period of four minutes, each trial lasting as long as "a pater and an ave".

On 13th May Dalibard reported the Marly test to the Academy of Science. 
Dalibard's house and garden in Marly-la-Ville
There was now no doubt that lightning was indeed electricity.  News of the triumph spread rapidly. The furious Nollet, who had not heard of Franklin, thought at first that the great man was Buffon's malicious invention.

In June 1752 Franklin himself famously (though possibly apocryphally) confirmed the findings by flying a kite in a storm, with a key attached to it by a silk ribbon. Once the ribbon became wet, he was able to generate a spark and charge a Leyden jar from the key.  Although Franklin now diverted his attention to politics, his lightening rods were soon set up in Philadelphia and Boston.  Nollet was forced to give up his attacks on Franklin, who was accepted by the Academy of Sciences and became the darling of French society.

Letter of Father Raulet to Dalibard 

 I can now report, Monsieur, the news that you have been waiting to hear: the experiment has been carried out. Today at twenty past two in the afternoon, thunder was heard directly over Marly; it sounded quite strong. My desire to serve you, and  my own curiosity, took me away from my armchair where I had been reading;  I hurried to Coiffier's house, meeting on the way a child whom he had already dispatched to fetch me.  I redoubled my pace in a torrent of hail. 

I arrived at the place where the bent rod had been placed, and advanced slowly towards it with the brass wire.  When I was an inch and a half away, the rod emitted a small blue column of fire which smelled of sulphur; it hit the end of the wire with some force, making a sound as if the rod had been struck with a key.  I repeated the experiment at least six times in a period of four minutes, in the presence of several people, and each test lasted the the time it took to recite a pater and an ave. I tried to continue but the effect diminished gradually; I approached closer, but produced only a few sparks, and finally nothing at all.

The thunder which had started events was not repeated;  a heavy storm of hail brought an end to the proceedings.

In the course of the experiment I received a shock on my arm just below the elbow;  I was too preoccupied with what I was doing to be able to say whether it came from the rod or the wire. I did not complain at the time, but since the discomfort continued, on my return I uncovered my arm in the presence of Coiffier. We observed bruising right around it as though my naked arm had been struck by a blow from a brass wire.  Leaving Mr Coiffier, I met the Vicaire, M. de Milly and the Schoolmaster, to whom I reported what had happened.  All three were  certain that they smelt an odour of sulphur which grew stronger as they approached me. I still had the smell about me when I arrived home;  my servants pointed it out without me mentioning it to them.

Such, Monsieur, is my account. It is written in haste, but I vouch for its veracity and will testify to the events whenever I am called upon to do so.  Coiffier was the first to perform the experiment and he repeated it several times;  it was only afterwards that he sent for me to come.  If other witnesses are needed besides him and me,  I am sure  you will find them.  Coiffier is anxious to leave. 
 I am yours, respectfully, Monsieur,

Raulet, Priest of Marly.  10th May 1752.


BBC Four: Shock and Awe - programme website

Papers of Benjamin Franklin, Founders Online (U.S. National Archives): 
“Thomas-François Dalibard: report of an experiment with lightning, 13 May 1752,”
Jean-Antoine Nollet: Letters on Electricity
Various documents collected and translated by Robert A. Morse as part of a course at Tufts University:

See also:
 J. L. Heilbron, Electricity in the 17th and 18th century (1979), p.348-50.

Thursday, 27 April 2017

St Petersburg paradox

Pierre-Louis Dumesnil, Interior with Card Players, c1752 , Metropolitan Museum, N.Y.
The "St  Petersburg Paradox" is a classic problem in probability theory first formulated in the early 18th century by the Swiss Mathematician Nicolas Bernoulli.  It first came to widespread attention in 1738 when Daniel Bernoulli, another of the Bernoulli dynasty, presented it to the Imperial Academy of Sciences in St. Petersburg.  D'Alembert described it in the Encyclopédie article "Croix ou pile" in 1754 and returned to it repeatedly in later writings. Buffon claimed to have been introduced to it independently as early as 1730 by the Genevan professor Gabriel Cramer and come to conclusions similar to those of Daniel Bernouilli.

The paradox concerns the "expected value" of a game of chance, that is  the likely winnings and the amount one might reasonably pay to participate.  This is calculated as the sum of (probability x winnings/loses) for all possible outcomes. This formula had been proposed in the 17th century by Fermat and Pascal and was well-known to the 18th-century theorists. The St Petersburg scenario describes a game where the "expected value" computes as infinite.  A player is offered the chance to win money on the toss of a coin.  The initial payout is 2 ecus and this doubles every time a head appears;  the game stops as soon as tails are flipped. This gives a 1-in-2 chance of winning 2 ecus, 1-in-4 of winning 4 ecus. a 1-in-8 chance of winning 8 ecus and so on ad infinitum. What is such a game worth?

The appeal to experience

In practice, the chances of winning soon become so remote that the amount of money on offer is irrelevant; as d'Alembert observed,  "no reasonable man"  would prefer a 1% chance of 99,000 coins over a 99% chance of 1,000 coins, even though they yielded an equivalent theoretical value. The sums involved become so huge as to make the figures meaningless - as Buffon picturesquely noted, even 29 consecutive throws represented  "as much money as exists perhaps in the whole kingdom of France".

Buffon suggested that very small probabilities - less than a hundredth of one percent - could reasonably be regarded as zero.  D'Alembert agreed, though he pointed out that any cut-off point was necessarily arbitrary. 

D'Alembert himself recalculating the "expected value" in the light of his theory of recurrent events.  In his view, having thrown one head, it became marginally less likely than 50:50 that the next throw would also yield a head. Even though no absolute figures could be assigned, by factoring in this "law of nature", it was possible to reconstruct the EV as an infinite series which approached zero.

Buffon tried to resolve the problem empirically by having a child in his employ repeatedly toss coins. Out of 2048 games played only six resulted in eight consecutive heads.  The "expected value" based on Buffon's experimental data came out at only 9.82 ecus, leading him to conclude a stake of five and-a half ecus was about right

Modern computer simulations tend to corroborate Buffon's findings. The EV of the game increases with repetition, but  remains comparatively modest.  In one experiment the game was repeated times 226 (268 435 456 million) times, and the EV computed at 17.02 dollars / ecus. This suggests to some mathematicians that the paradox is miscast and infinity could never be reached.
See, for instance, Vivian Robert William, "Ending the myth of the St. Petersburg Paradox", SAJEMS, 16(3) 2013:

The theory of utility

According to Gabriel Cramer and Daniel Bernouilli, the essential problem is that EV calculated in this way cannot form the basis of a general decision theory since it does not conform to the behaviour of real gamblers. "Moral expection" or perception of risk, is not based on absolute monetary value but utility.  This varies according to individual fortunes:  "there is no doubt that a gain of one thousand ducats is more significant to a pauper than to a rich man though both gain the same amount".  Bernoulli to proposed a calculation based on diminishing marginal utility: the higher the payout the less it was worth. This enabled him to recast the EV of the St Petersburg game as an incrementing series with a finite value.

Most modern theories represent refinements of this approach:
See: Wikipedia, "St. Petersburg Paradox"

18th century sources in English:

D. Bernoulli, “Exposition of a new theory on the measurement of risk"  Econometrica, 22 (1954), 23–36.

Georges-Louis Leclerc de Buffon's "Essays on Moral Arithmetic"

Jean Le Rond d'Alembert on probability and statistics

See also: 
L. J. Daston, "D'Alembert's critique of probability theory", Historia Mathematica 6 (1979), p.259-79.

Wednesday, 26 April 2017

D'Alembert loses at roulette...

Our experience and understanding of the laws of nature teach us that the same event never happens many times in a row, and it is by virtue of this acquired knowledge that we dismiss the repetition of "heads" or "tails" many times consecutively.
(d'Alembert, Opuscules mathématiques, 1780, p.48)

If Google hits are anything to go by, d'Alembert is remembered chiefly today as the author of a codified gambling staking plan.  Although there is no documentation, the d'Alembert System probably dates from the late 18th or early 19th century and was not "invented" by d'Alembert at all, though it is loosely based on his speculations on the mathematics of probability.

The system is associated particularly with outside bets in Roulette, but applicable to any game of chance based on 50-50 probability. It relies on the idea that prolonged runs of a single outcome are less likely than an even distribution of outcomes. The strategy is simple: the player always bets on the same outcome; if he loses he increases the stake by one chip, if he wins he take away one chip. As  the table shows, if he succeeds in returning to his original bet, he will have made one chip for every winning coup.  Provided the game lasts long enough to approximate to mathematical probability, the result is will be a modest gain. (The Martingale system is similar but the number of chips are doubled for each loss making the risk much higher).


See "d'Alembert system",

So where does d'Alembert fit in?

 Catherine Lusurier, Portrait of d'Alembert, 
1777,   musée Carnavalet, Paris
The betting plan is named for d'Alembert since his work on probability supported the theory that a consecutive run of similar events (for example repeated tosses of the same side of a coin) was inherently unlikely.

D'Alembert's position is based on  a distinction between what is "metaphysically possible" (the mathematical laws of probability)  and the "physical possible" (what can actually occur),   No event can be precisely duplicated in nature; indeed, observation shows that long sequences of identical events can never happen purely by chance:
...In the ordinary course of nature, the same event (whatever it might be) happens only rarely twice in succession, more rarely three or four times, and never 100 consecutive times.(Opuscules mathématiques, 1761, p.10)

 D’Alembert famously considered the problem: “When a fair coin is tossed, given that heads have occurred three times in a row, what is the probability that the next toss is a tail? He  insisted  the probability of a fourth tail must “obviously” be greater than 1/2: 

However I ask if ... if the number of times that heads has already successively occurred by the hypothesis, does not make it more likely the occurrence of tails on the fourth time? Because after all it is not possible, it is even physically impossible that tails never occurs. Therefore the more heads occurs successively, the more it is likely tail will occur the next time.  If this is the case, as it seems to me one will not disagree, the rule of combination of possible events is thus still deficient in this respect. (p.14)

Despite the elegance of the formulation - and sadly for exponents of the d'Alembert system - this is really just the classic "gambler's fallacy" recast.  There is no mysterious "law of nature" governing repeated events in games of chance and a series of identical outcomes is as mathematically probable as any other pattern. Here is the verdict of the Merriam-Webster's Guide to Everyday Math:

Perhaps fortunately, d'Alembert himself was not optimistic that mathematicians made effective gamblers. In the Encyclopédie article "Géomètre" he takes issue with Diderot's dismissive comparison of the two: granted, both compute and calculate; but a good gambler operates by instinct and  seizes his opportunities without lengthy reflection.  If the evidence of experience is anything to go by, great geometers are poor gamblers - a truth which d'Alembert claims to have learned from bitter experience.
See Hankins, Jean d'Alembert (1990), p.93:


Prakash Gorroochurn, "Errors of probability in historical context", The American Statistician, 65(1), 2011 p. 246-54  [reprint]

On the early history of Roulette, The online Guide to traditional games

Monday, 24 April 2017

Winning the lottery of life - the tontines

Mercure 1726:  24th February, Charlotte Bonnemay, widow of Louis Barbier, died in Paris aged 96 years old.  She alone remained of all the Rentiers who comprised the 13th Class of the first Tontine, and the 14th of the second; at the time of her death she enjoyed an annity of  73,500 livres of income from an subscription of 300 livres in the two classes.

Mercure historique et politique 1762: Mr. Christophle de Beaud, native of Pontarlier, former Chaplain to the nuns of Chaillot and Confessor to the late Queen of England, wife of James II, has just died in his parish of Doux, aged 97 years.  He was the last shareholder of his Division in a Tontine; thus in the last two years of his life, he enjoyed 10,400 livres in rentes

Madame Barbier's obituary, with details of her marvellous annuity, was repeated in journals, dictionaries and books of anecdotes, both French and English, throughout the 18th and early 19th centuries. The source of her wealth was a  "tontine", a form of life annunity with benefit of survivorship, which was occasionally issued alongside ordinary annuities by the French government.

19c book illustration - Tonti is the plump bewigged gent on the left
The "tontine" takes its name from the Italian banker Lorenzo Tonti, who first proposed the scheme to Mazarin in 1652.  Although his plan was initially rejected, the French government later resorted to tontines on a considerable scale.  Ten French tontines were issued in all, starting in 1689 and ending in 1759. They were strictly a wartime expedient:   ten thousand persons contributed 6.5 million livres during the War of the Grand Alliance, twenty-five thousand contributed 26 million livres during War of the Polish Succession; a similar number thirty million in the War of Austrian Successson, and in 1759 nearly fifty thousand  contributed 47 millions in the Seven Years War in a single tontine.

Royal Edict creating the tontine of 1744

French tontines were divided into 14 age classes with different rates of return, and the intial investment was normally set at 300 livres. Payments could be made contingent on the subscriber's own life, or that of a third-party nominee, typically a child.  The crucial difference from an  ordinary life annuities was  that payments did not cease on the death of an individual but were divided between the rest of  shareholders, and continued until the death of the last survivor in each class.  Hence the huge gain of a few lucky (but aged) individuals.
Tontine agreement from 1736, with nine ms. signatures
Unsurprisingly tontines were widely recognised as a desperate measure forced on a reluctant government.  According to the Encyclopof all financial expedients, tontines are perhaps the most expensive for the State". The entry in Savary's Dictionnaire universelle de commerce notes that  f all expedients they were the most burdensome due to their  high interest rate and because they took "about a century to extinguish"
Savary, Dictionnaire universel de commerce (1762 edition)

Tontines: list of trustees and payment agents, Almanach royal, 1764
It was often supposed that finance ministers had foolishly underestimated the longevity of the subscribers.  This view was lent credence by the Antoine Deparcieux's Essai of 1745 in which he contructed  life-tables based on 9,000 nominees from the first two tontines and compared them with records of deaths from religious houses;  to everyone's surprise the tontine-holders achieved the greater life-expectancy;  it was "a false prejudice" Diderot admitted, to suppose that religious lived longer than gens du monde.  The American economic historian David Weir estimated that  the expected age at extinction of  a class in the French tontines was in fact about 92, but notes that a few extra years was not that significant in terms of additional cost;  tontines at least had the advantage   that commitment could be more easily calculated than for ordinary life annunities, since it depended mostly on numbers in each class (Weir, "Tontines", p.112)

David Weir compared the outcome of  tontines in France with the situation in England, where they were also used in the 18th century, but with notably less success. The terms offered by the  French government were much more favourable, and were particularly advantageous in the older age classes, whereas almost all English tontines were taken out on children (p.113)  Contemporaries often regarded tontines as a form of lottery but, as David Weir comments,  it takes a very long time to "win" the gamble of a tontine.  In practice, like individual life annuities, they appealed mainly to pension seekers.  The initial investment tarif was set slightly above price of life annuities to reflect the advantageous terms, but both life annuities and tontines paid well over 7% interest.(Weir, p.112-3)  

Dr Weir emphasised that the annuities played a political role in cementing the allegiance of the urban bourgeoisie who did not benefit from tax exemptions and privilege. The inviolability of tontine income in particularly was emphasised in strongest terms.  Nonetheless, in November 1763 a royal edict banned any future government tontines, citing their enormous expense. In 1770 the abbé Terray froze tontine payments and converted them to life annuities, thereby transferring the future benefits of survivorship to the State.  The subscribers still enjoyed advantageous terms, since flat-rate 10 percent annities were  applied to all tontine classes, but there was a widespread sense of betrayal and fear of default was heightened among other annuity holders.  At a crucial juncture royal government alienated an important sector of support, without realising substantial financial gain.


David R. Weir, "Tontines, public finance, and revolution in France and England, 1688-1789
The Journal of Economic History, 1989, 49(1): p. 95-124 [article on JStor]

The idea of winning out through longevity at least had a certain amusement value. In 1708 Alain-René Lesage offered the Comédie-Française a one-act farce entitled "La Tontine".  A physician hoping to raise the funds to give his daughter a dowry, buys a tontine on the life of an elderly peasant, whom he then strives to keep alive. The play was  not performed until 24 years later, in February 1732, and finally appeared in print in the Oeuvres of 1739.    The tontine featured only as a device, but the preface to the collection maintained - without foundation - that the play had been suppressed for "reasons of State".

See:   Christelle Bahier-porte, "Dans l'atelier de Lesage : l'histoire de La Tontine, des manuscrits au livre (1708-1739)". Revue d'histoire littéraire de la France, 2011. 111,(4), 837-850.

Saturday, 22 April 2017

The "Thirty Maidens of Geneva"

The famous “Thirty Maidens of Geneva” were real little girls who, by a curious twist, became the centre of an elaborate and highly lucrative financial strategy to take advantage of  life annuities issued by the French government in the 1770s and 1780s.  To revolutionaries like Jean-Pierre Cambon, the scheme constituted a damning indictment of the financial incompetence of the ancien regime, the "imbecillity of our old government "(note 33) .  It modern  historian described it as the epitome of "rococo finance" (Herbert Lüthy,  La banque protestante en France, 1959, p.469)

Life annuities (rentes viagères) had become  the “financial instrument of choice” for the management of French public debt in the last seventy years of the monarchy.  It is reckoned that between 1730 and 1789  1.4 billion livres was raised in life-contingent debt, of which around 1.1 billion was still outstanding at the time of the Revolution.(p.244)   The principal was simple.  Subscribers paid a lump sum  and received in return a given percentage of their investment  as a payment each year.  This continued until their death,  at which time the capital  was retained by the state coffers. The longer the rentier lived, the more he stood  to gain.

It was well understood in the 18th century that life annuities could only be made cost-effective if rates were varied according to the age of the subscriber.  In the first half of the century the French government issues had consistently applied the age-banding principle and in 1746 the mathematician Antoine Deparcieux was employed to refine practice further. His “Essay on the probability of human life-expectancy”, based on statistical analysis of longstanding life-annuity issues,  was a pioneering tour-de-force of actuarial science. Yet in 1757 the government began issuing flat-rate life annuities; the Controller-general of finance responsible was Jean de Boullongne,  the very official to whom Deparcieux had dedicated his book.  The practice became standard; after dismissal of Turgot in 1776. "uniform rate" for a life annuity issue was always "10 per cent on one head, 9 or 8.5 on two, 8 on three or four" 10% was reckoned to be a fair price for an adult of age fifty and thus it was  extremely generous as a general rate. 
The move was not simply "imbecility", but a response to a pressing need to attract more speculative capital. 
As Necker, the leading purveyor of flat-rate annuities, implicitly admitted, it was a bad deal made by a desperate government (Oeuvres, vol. 5, p.491)   Age-related life annuities appealed almost exclusively to pension-seekers; the typical subscriber profiled as between forty and sixty, in search of  a secure return for their capital.   rentiers that Mercier sin 1757atirised.  Investors in this age-bracket could usually count on  between 9% and 10%, and the outcome is reckoned to have been viable for the  government too (see Velde and Weir, p.30-1)  The problem was that the pool of pension-seekers was too limited. The shortfall had to be made up from speculators investing in annuities issued against third-party lives.  Such investors  wanted competitive rates of interest and, in order to compensate for the risk that their third-party nominees would die prematurely, they inevitably demanded an above-market rate of return. 
Life annunity: 10 percent on a single head,. issue of November 1778
Offered for sale by Alpes Collections

Seine - Paris - Louis XVI - Rente viagère à 10% pour l'emprunt royal de 1778
- Emprunt royal de 1778 signé Joseph MICAULT D'HARVELAY
- Date : 31 décembre 1778
- Achat d'une rente perpétuelle : valeur 1620 livres
- Signé au verso du Contrôleur Général des Finances
- Daté du 8 avril 1779
- Dimension : 325 x 245 mm
In 1757 with flat rate annuities of 10% the government was able to raise twice the amount of any previous issue. In the years 1757 to 1787 the government garnered 1.1 billion livres on flat-rate annuities, only about a quarter of which was accounted for by pension-seekers.  The rest were third-party annuities. In order to simplify the verification process and to make the annuities more marketable, annuities were sometimes  placed on public figures - when Louis XVI died on the scaffold, 400,000 livres in rentes died with him.   By far the majority, however, were taken out on the lives of children and young people.  It is here that the "Thirty Maidens of Geneva" fit in.
The scheme began as the exclusive domain of the Genevan banks through their branches in Paris;  though the initiative was later extensively emulated elsewhere, roughly a third of all third-party annuities after 1775 continued to be held in Geneva.  The organisation was the brainchild of the banker Jacob Bouthillier Beaumont, who set up his first investment syndicate  for the annunity issue of 1763, refined in 1771 into the so-called "Syndicat de Trente Demoiselles".  The idea was to take out a large number of annuities on different "heads" (the most common number being thirty), then place them into a common investment pool.  Not only did this reduce the risk represented by premature deaths, but, since the annuities were not tied to a particular life, they  could be be packaged much more easily into negotiated assets.  Bankers increased their profit by parcelling small amounts of their pool for resale, and by restructured the dividends into other investments. 

The ridiculous element was,  of course,  that all this complex finance still depended on the life-expectancy of otherwise insignificant young people,  most commonly  little girls. They were selected for preference from aristocratic or monied backgrounds, most often from the families of the investors themselves.  A random selection yields two daughters and a son of Jean-Louis Pictet, Syndic, the two daughters of Philibert Cramer, Trésorier-Général, the two daughters of  Alexandre Sarasin, Syndic, "des Diodati, des Gingins d'Eclepends, des Rilliet, des De la Rive, des Thelluson,etc." (Cramer, p.115). An elaborate procedure ensured their continued survival.  They were required to report for inspection by the French Resident in Geneva every week.  Doctors were employed to draw up the initial shortlists of nominees and the associates paid for their medical care.  Reports on their health even appeared in the Genevan newspapers. Before 1774 nominees had to be over seven so as to be beyond the risk of premature death from smallpox.   Later, after the successful introduction of vaccination, the minimum age dropped to four  (Louis Odier, the Genevan apostle of vaccination, was himself father of one of the "demoiselles").  According to Cambon, boys were sometimes paid small allowances in exchange for a commitment not to leave the country or opt for dangerous careers, like military service abroad.
How did they fare?

There were a certain number of well-publicised misfortunes The operations of 1780-82 saw several premature deaths.  Little Jeanne Pictet, with  164,469 livres on her head, died at the age of only four and in July 1788 Pernette Elizabeth Martin, took with her to her grave no less than 212, 197 livres in rentes, more than the 200,000 livres thought to have been riding on Marie-Antoinette herself.  On the whole, however, diligent care and the pure Swiss air worked their magic.  Of the first "thirty demoiselles", twenty-five were still alive at the end of twenty years and another early syndicate achieved an average life span of sixty-three years, far in excess of that predicted by the actuarial information available at the time. Of twenty-two heads assured in 1778, fifteen were still alive in 1820 and two lived to over eighty - this despite living through turbulent times.  

More difficult to assess, is the toll of the annuities on French public finances.  According to James Macdonald, resale of shares in the Genevan syndicates made only a modest mark-up, suggesting that expected rates of return on life-annuities were roughly in line with other forms of government loans.  The real problem for the French government was not so much the form of French debt - or even the total owed - but the high rate of servicing borrowing (according to modern estimates  7.3% after 1726 as opposed to just over 3% in Great Britain).  It would seem this was as much more to do with fear of default and failure of  public confidence - and the perceived as much as the real "imbecillity" of  Royal financial policy.


Marc Cramer, “Les trente Demoiselles de Genève et les billets solidaires”, Swiss Journal of Economics and Statistics (SJES), 1946, vol. 82(2),  p.109-38.

François Velde and David Weir, “The Financial market and government debt policy in France, 1746-93,” Journal of Economic History, Mar.1992, p.1-39 [on JStor]

James Macdonald, A Free Nation Deep in Debt (2006), "The Dilemma" p.239ff.  [Extracts on Google Books] 


Mercier, Tableau de Paris, LXXVI:"Rentiers" 

This is the name given to those who have placed their capital in life annuities, making the King their sole heir and selling out their posterity  for 10 percent.  They have disinherited brothers, nephews, cousins, friends, and sometimes even their own children.  They don't marry, but just sit around waiting for their payout, congratulating themselves each morning that they are not yet dead.  Every six months they go to the corner Notary and sign to certify that they are still alive.

Whatever money they make, they immediately reinvest, so that capital which could have fed commerce and sustained industry, languishes forever in the royal coffers....

Pierre-Joseph Cambon,  Report to the National Convention on public debt in the form of life annuities (1794)

....Based on these observations, one may put [life annunities] among the class of ruinous loans made by the former government; at a flat rate of 10 per cent on all heads, it was in everyone's interest to choose young heads; it is to this cause, at least in part that the disorder of French finances must be attributed.

These loans were made even more disadvantageous by the refined speculation of certain financiers in the final years of the monarchy.  They chose, in a clean country, in a little Republic sheltered from the ravages of war, children of five to six, that they had innoculated and on whom they lavished the greatest care;  boys were given a small pension not to leave their country or engage in a dangerous profession.  Since the repeated observations of human life expectancy had shown that women in every country live longer than men, speculators prefered to take out their life annuities on the heads of little girls.  In this way the flat rate annuities issued by the former government between 1779 and 1787 were made very advantageous to lenders and very onerous to the state. 

There were some companies who pushed their speculation further. Seeing that mortality of the women and girls of geneva, of whom the sound constitution, healthy lifestyle, the wealth and stablility of their country are the most probable.  They assembled together with the doctors to chose yooung girls who, having passed the dangers of infant disease, seemed to have the best constitution;  all the recommendations of the doctors were put together to form a list from which, for each new issue, they chose thirty heads.They drew   up for each one a certain number of contracts, to unit annual income and life anueties, and then divided them equally between all the participants.

It was thus that they played on the imbecility of our former government, and that enormous fortunes were acquired, without paying penny, but  simply by lending credit.