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The key to understanding this short paragraph (just one sentence) is of course to know what La Buse meant by 'Turkish dog' (CHIEN TURQ, a slight mis-spelling of chien turc, understandable in the sense that in French the female form for 'Turkish' is 'turque' and because 'turq' is phonetically correct).

My first instinct was to find out what particular breeds of dog are specific to Turkey, and whether there was any plausible connection between them and pirates. I learnt that there is a breed of Turkish dog was is remarkable for its huge size - it must be one of the biggest dog breeds on the planet! It's called the kengal: 

But my research indicated that pirates rarely kept animals on board except maybe a cat to catch any mice or rats that might have been present. Pirates did not even keep parrots on board!

After doing some more research, I became aware that for a while the term 'sea dog' was used to mean sailors, and then it became a generic slang term for pirates. So I thought the sentence might be a reference to pirates. But why Turkish dog? Some further research taught me that there was collaboration between Turkish and English pirates against their common enemy, Catholics, but this collaboration was, I think, only along the Barbary coast (the coast of north Africa) so this is probably not relevant to the story of La Buse. 

Ultimately I rejected those lines of enquiry in favour of a solution which I am certain is the correct one. I found several text which give the same explanation for the meaning of 'chien turc' (Turkish dog). For example, this passage from 'The Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, par une Société de Gens de lettres' which was published under the direction of Diderot and d'Alembert between 1751 and 1772:

Chiens sans poil. Le chien Turc est le seul que nous connoissions qui n'ait point de poil : il ressemble beaucoup au petit Danois : sa peau est huileuse.

Hairless dogs. The Turkish dog is the only one we know of which has no hair : it strongly resembles  the little Danish : its skin is oily.

The following extract also speaks of 'the hairless dogs popularly known as Turkish dogs' ('Les chiens sans poils qu'on appelle vulgairement chiens Turcs...').

This quote above is from ' Histoire naturelle générale et particulière: Concordance et table alphabétique des noms pour les animaux quadrupèdes, Volume 13' published by Imprimerie Royale in 1770.

The quote below is similar but more detailed:

In this last quote we read again about the 'hairless dog, called a Turkish dog' ('chien sans poil, appelé chien turc') . The above quote is from 'Œuvres complètes de Buffon: 2: L'homme, Les quadrupèdes' published by Garnier frères in 1853.

So it is very clear that at that time 'Turkish dog' ('chien turc') was a slang term used to refer to hairless dogs. The above passages say that hairless dogs are in fact not found in Turkey but rather in hotter climates, but further research told me that is wrong, for there used to be a breed of almost-hairless dog that was specific to Turkey. We have a very prestigious witness of this: Charles Darwin. This page says 'Hairless dogs across the world have been recognized since the time of Darwin, who wrote (in 1859) about naked Turkish dogs with defective teeth (Darwin C. 1859. Origin of species by means of natural selection. London, UK: John Murray). While many hairless dogs have reportedly existed over time, many are now extinct and no more than half a dozen are recognized around the world today.'

This page confirms that the Turkish hairless dog is now extinct. It says 'Some extinct hairless breeds include the African Elephant dog, African Sand dog, Ceylon hairless dog, Egyptian Hairless dog (a relative of the African Sand dog), Guatemalan Hairless, Indian Hairless dog (a naked sighthound breed), Mayan hairless dog, Nubian dog, Small African Greyhound, Thai Hairless Boran Dog and Turkish Hairless dog'.

Thanks to the work of Georges-Louis Leclerc Buffon, the author of the extract above, I can even show you a picture of a Turkish Hairless dog, from 1755. Source: Bibliothèque nationale de France.

Having established that 'chien turc' was a slang term used to refer to dogs with little or no hair, why would La Buse have had any interest in hairless dogs?

I found the answer on this page, which says: 

'This is not what is lacking on Réunion island… dogs that are tired, skinny and too often without hair wander through the streets.'

'Ce n’est pas ce qui manque à La Réunion… Des chiens fatigués, maigres et trop souvent sans poils errent dans les rues.' 

Source of this photo: zinfos974.com

What's going on? Why are there so many hairless dogs in this part of the world? (Recall that Réunion, then called Bourbon Island, was the island where La Buse captured his greatest haul of treasure, and also where he was hanged.) The answer is clear from this site: these dogs have lost a lot of hair because they suffer from canine scabies (sarcoptic mange). And this site refers to present-day Réunion – 300 years ago veterinary care would obviously have been far worse than today, and these dogs would have been in an even worse state than the dog in the photo above.  

These sick dogs are repugnant to look at and people would be especially perturbed by their proximity if their illness is contagious to humans – is that in fact the case? Yes! According to the same site, (translated into English)

Dog Scabies

If there is a disease that everyone has already heard of, it is indeed scabies ...

Mangy dog, black sheep ... So many expressions that reflect the popular disgust and the sensation of itching felt at the simple evocation of the name of this historical skin disease. ... Scabies is a parasitic skin disease … This parasite lives permanently on the surface or in the thickness of the dog's skin. The mite is a parasite quite specific to the dog. Man, cat, ferret and fox can also be infested by this parasite. Contamination is mostly by contact with a mangy dog, more exceptionally with a cat, a ferret or an infected fox. However, indirect transmission is possible, to a lesser extent, by the external environment and accessories (carpet, brush, etc.). Contagiousness is very important since 50% of exposed dogs develop the disease.

Some animals, however, are more receptive than others, such as young animals and those whose health is already impaired.

Doctor, I am also itching…

The mites responsible for canine scabies can infest humans. Human infestation is manifested by the appearance of very pruritic papules on the zones of contact with the infested animal (often on the forearms). The infestation resolves itself without treatment, for the parasite can not have a complete development in man, which is called an epidemiological cul-de-sac. Like scabies, other skin diseases are transmissible from dog to man.

On this page you have learnt that

Now we are ready to see an interpretation of this one-line paragraph which is very faithful to the original symbols of the cryptogram while at the same time being very plausible in terms of what we have learnt (my interpretation is copyright May 2017).

Removing the unexpected characters that could represent the next level of clues to the location of the treasure:

Pour faire filer un chien turq, flenké de la merde bien sèche desu.

Correcting the spelling errors made by La Buse:

Pour faire filer un chien turc, flanquez de la merde bien sèche dessus.

In English:

To make a Turkish dog run away, throw some dry shit at it.

It makes perfect sense that no one would want to be approached by a 'Turkish dog' (mangy dog, in the context of the cryptogram) since one could temporarily catch the mange from it and suffer terrible itching for weeks, so throwing something at it to make it run away would make sense. I don't know why La Buse would recommend 'dry shit' in particular. On the other hand, I know that if someone threw dry shit at me I would certainly not want to approach that person! We also have to recognise that throwing dry shit is a more practical proposition than throwing wet shit!

Let's return to the deeply philosophical question: "why poop?". A friend of mine pointed out that dogs do in fact have the reputation of often eating poop. Could it be that La Buse was suggesting throwing poop with the intention that the dog would eat it? I imagine that pirates had a coarse sense of humour and might be amused by the sight of a dog eating dog poop. Next philosophical question then: 'why eat poop?' The same friend provided this link and this link to possible answers.  We read 'Some dogs will start eating poop when they aren’t absorbing enough nutrients, they have parasites, or they have issues with their pancreas' and 'There is also evidence that dogs that aren’t getting enough of certain nutrients will resort to eating poop'.  It's clear, then, that unhealthy dogs are especially likely to eat poop, so throwing dry poop at a mangy dog is quite likely to result in the amusing (for a pirate) sight of the dog eating the poop. Reinforcing this interpretation of paragraph 4 of the La Buse text, I read in a dictionary dating from 1771 that at that time the French word 'piler' could be used as slang to mean 'eat well'. 

PILER signifie figurément bien manger. Mandere. Les écoliers ont toujours bon appétit & pilent bien. Ce mot en ce sens est bas & burlesque.

PILER figuratively means eating well. Mandere. Schoolchildren always have good appetite and eat well. This word in this sense is low and burlesque.

Not only that, but 'piler' is closer than 'filer' to the letter sequence 'PITER' in the cryptogram. For this reason, I myself actually prefer the correction 'piler' rather than 'filer'.

As I understand it 'piler' is never used to mean 'eat well' in modern French so you are unlikely to find such a suggestion on sites that are less-well researched than this one!

Here, then, is an alternate interpretation of the sentence:

Removing the unexpected characters that could represent the next level of clues to the location of the treasure:

Pour faire piler un chien turqu, jetez de la merde bien sèche desu.

Correcting the spelling errors made by La Buse:

Pour faire piler un chien turc, jetez de la merde bien sèche dessus.

In English:

To make a Turkish dog eat well, throw some dry shit at it.

In this version the suggestion is that trying to make a mangy dog eat shit could have amused La Buse, who was after all a pirate, no doubt with a coarse sense of humour and little moral sense. After all, this is the same man who ordered the burning of the Duchesse de Noailles in December 1721 while hundreds of slaves were trapped on board.

In this alternate interpretation I have also replaced the word 'flenké' (meaning 'flanquez' or 'throw') with 'jetez' which is a less familiar and more common French word also meaning 'throw'. A problem with the 'flanquez' version is that I was unable to find evidence in old French dictionaries that 'flanquez' could be used at that time to mean 'throw'. Which do I prefer: 'flenké' or 'jeter'? I prefer 'flenké' because the 'jeter' interpretation seems to force me to use the spelling 'chien turqu' instead of 'chien turq' but 'chien turq' is definitely the spelling used elsewhere in the cryptogram, so that would be an inconsistency.

Of course it is also possible to make variations of the interpretation that would include 'piler' and 'flanké' or 'filer' and 'jeter'.

Ultimately, as treasure hunters, we are not interested in the silly main text of the cryptogram, we are only interested in the embedded clues that could lead us to the treasure. As you can see in the above interpretations, the choice of 'flenké' or 'jeter' does affect which embedded character appears, whereas the choice of 'piler' or 'filer' does not.

Notes

Charles de La Roncière made it clear in his 1934 text that he thought this part of the cryptogram included 'de la merde sèche' though he avoided actually mentioning the word 'merde' which is somewhat offensive in French, just as 'shit' is in English. But many other people, seeking desperately to identify geographical landmarks in the text, have suggested that the text could instead include the word 'mer', meaning 'sea'. But in order to make a plausible sentence using the word 'mer' these people are forced to distort the letters of the cryptogram much more than I have done.

My interpretation is in fact very faithful to the original cryptogram (most of the chevrons are green, meaning my suggested corrections correspond to symbols that are only slightly different to the originals) but there are two words that are less satisfactory (with red chevrons): PITER becoming filer or piler and NLENEN becoming flenké or (8)jeter.

I looked hard for a better correction for PITER but for me either FILER or PILER is a good compromise between fidelity and plausibility. PITER actually is a word in French, though not a common one. It means 'to take the bait' or 'to bite the hook' which does not seem plausible in this context. 'Filer' can mean 'to run away' which works very well here. 'Piler', which at that time could mean 'eat well' also works very well.

I 'corrected' NLENEN to 'flenké' which in French would be phonetically equivalent to 'flanquez' so again La Buse has used an incorrect but phonetically valid spelling. 'Flanquer' is certainly a commonly used word in French, a familiar expression which can mean 'to throw suddenly', the example given by the Larousse dictionary being 'Flanquer une assiette à la tête de quelqu'un.' or 'To throw a plate at someone's head'. It's true that the word 'prenez' ('take') would actually be a correction that is more faithful to the original symbols, but it does not work well in the context of the sentence:   To make a Turkish dog run away, take some dry shit on it.

According to my interpretation, La Buse spelt Turkish in French as 'Turq' whereas the correct masculine spelling is 'Turc'. The spelling 'Turq' is phonetically correct and it could be that La Buse obtained this spelling from the feminine form, which is 'Turque'. But in that case he could also have spelt the word as 'Turqu', especially since the next letter in the cryptogram is a 'u'. That would mean that the 'u' should not be interpreted as one of those special embedded symbols which may represent the next level of clues. My assumption in my interpretation is that he wrote 'Turq' and that the next symbol is indeed an embedded symbol, one of the next level of clues.

I don't believe that Charles de la Roncière would have been aware of the full significance of 'chien turq' in the cryptogram especially since it involves two steps: knowing that 'chien turc' is slang for 'hairless dog' AND knowing that hairless dogs were a particular problem in and around the island of Réunion due to the prevalence of canine scabies (sarcoptic mange). Therefore I take this interpretation to be further evidence that the cryptogram is NOT a fake that was created by De La Roncière, but is more likely to have its origins in the area around Madagascar and Réunion where La Buse operated (though this does not prove that the cryptogam was made by La Buse).