Bull sharks are rarely seen by divers, there are very few photographs of them available, and Ive just shot 10 rolls of film, exclaimed Jeremy Stafford-Deitsch excitedly, as he climbed yet again from the water to reload his camera.
We were at Walkers Cay, a tiny spot in the Abaco chain of the Bahamas. Its a place well known for its chumsicle shark feeds, when up to 200 assorted sharks turn up to feed from a barrel of frozen fish scraps suspended in the water.
This delights watching divers. It makes for fantastic diving, finning around in the company of such predators and in such numbers. But you wont see bull sharks on a chumsicle feed, and this experience of ours was something else again.
With us were Swiss-born Dr Erich Ritter, shark behaviourist from Hofstrar University of New York but based in Miami, and Gary Adkison, shark enthusiast and manager of Walkers Cay marina and diving centre. They had discovered that bull sharks congregate in numbers in the murky water next to the islands airstrip, a place now appropriately named Shark Beach.
Jeremy Stafford-Deitsch, author of best-selling books about sharks and founder-trustee of the UK-based Shark Trust, was there to get photographs of bull sharks for his next book, Sharks of the Caribbean.
I remembered that, years ago, dive centres had wrongly thought that the heavier and more bulky female Caribbean reef sharks that turned up for their shark feeds were bull sharks. Arent they just like Caribbean reef sharks but bigger I asked.
The easy way to differentiate between these species is that Caribbean reefs are known as ridgeback sharks, offered Erich Ritter. Bulls-sharks dont have that ridgeback feature. A lot of people call the bigger Caribbean reefs bulls, but theyre wrong.
Wait until you get in and see these animals, Jeremy suggested. Once youve seen a bull shark, youll never forget it. There are more than a dozen big bull sharks here, and we get in and swim with them. Thats almost unknown in the shark world.
Bull sharks typically favour the murky conditions found in river mouths and harbours. Shark Beach consists of grassy sandflats beyond the rocks, and discarded rubble and old iron that have been tipped here. Fishermen have been throwing their fish cleanings here for generations.
The water was so shallow we could stand up in it. A snorkel was all we needed; we slipped off the rocks with our cameras to join the big, dark shapes already splitting the surface with their massive dorsal fins. Erich joined us, armed with a video camera, and ebullient Texan Gary Adkison stood on the shore, ready with a dustbin full of unwanted fish parts, recovered from the marinas fish-cleaning room.
These are the biggest bulls Ive ever seen, exclaimed Erich on first seeing them. I reckon the girls (the big females) must be around 2.5m long and weigh in at 600lb-plus each. Imagine the size of the male that could pin one of these down.
I had never noticed the genitalia of sharks so clearly before. The claspers of these males were bright white, and contrasted strangely with the dark grey of the surrounding skin. The cloacas of the females seemed over-large and gaping.
Then there were their little yellow piggy-eyes...
Each shark had a very broad-based dorsal fin, and virtually no fin markings. But what was most striking was the sheer bulk of their bodies - that tremendous girth.
Bull sharks have the most fearsome reputation for shark attacks, yet you can flick a hand at them and they will retreat, observed Jeremy. The first day, when I was here on my own, I was very cautious. I had to get out of the water when 14 of them starting competing for the bait. It got a bit hectic. I counted a mere 10 on my first day.
Gary carefully lobbed in the bait, so that it was just ahead of our cameras. Would the sharks get stomach aches from eating so much smelly fish Jeremy asked. Erich Ritter explained that the bacteria living permanently in the mouths of sharks were powerful enough to overcome any bugs.
In fact, he went on, if a person were to survive the massive loss of blood from a shark bite, the next problem to be faced would be the massive secondary infection from these powerful bacteria. Gary recalled a shark-bite survivor going down with a life-threatening, pneumonia-like infection.
Fully grown bull sharks are undeniably big. Their girth makes them look ponderous - until, that is, a piece of dead fish would hit the surface and come floating past us. Then they moved like lightning.
I found that if I snorkelled down towards the sinking bait, camera at the ready and careful not to get there before a competing shark, I could get a dramatic photograph, though that oh-so-important moment happened so quickly that I often missed the shot of the open jaws, the shaking head - and those teeth.
Other fish were in there feeding, too. A little needlefish was holding its own, and some octopuses grabbed anything that came within reach and disappeared under cover of the rock- and metal-strewn bottom. One octopus took advantage of a free ride and climbed up my leg, the better to get at the food. Between shark passes, I tenderly tickled him between the eyes, and he seemed quite content to stay with me.
From time to time another species of shark would turn up and compete for the food. A solitary lemon shark looked very scrawny by comparison with the bulls. I always thought nurse sharks had bulk until I saw one in the company of these sumo-wrestlers of the shark fraternity, while a feisty blacktip looked like a pretty little toy next to them.
If you speared a live fish, these giants would go completely bananas, offered Jeremy. You wouldnt get out of the water alive. Theyve learned to recognise the sound of the fish scraps hitting the surface and theyve learned to feed at the surface in the couple of days weve been doing this. Erich is completely fearless, of course.
Dr Ritter, a man whose speech patterns put me in mind of Peter Sellars Dr Strangelove, has many theories, and he was quite prepared to risk his safety to prove them. This included floating closely over a dead fish and allowing a big shark to take it from under him.
I dont do what I do because Im a daredevil, he said. I want to show that you can swim with notorious species. We want to find out what people do to trigger the wrong reaction. We do stupid things like putting fish blood on our hands to test our theories. The shark is a really smart animal. When you lose your fear, you begin to see what it really is.
Does urinating in the water cause shark-attack I asked Erich, after we had been in the water for more than three hours. He looked at me with the whimsical expression of a man who was familiar with the delight of hot urine in a cold wetsuit.
Thats complete rubbish! he replied eventually, with a smile. We are trying to develop a body-language system to build a bridge to the animal, to try to trigger favourable reactions rather than the wrong ones.
We have to do this with species with a known record for attacks - reputed man-eaters. As you have experienced, we can swim with a pack of hungry sharks and do it safely. There really is nothing to worry about.
According to Erich Ritter, a bull shark needs to eat 4 per cent of its own bodyweight in fish each day. That means that some of these animals are eating 20 to 30lb. This bunch probably consumes 200lb between them, he informed us.
Although they can make 30mph, they are very conservative with their energy, he went on.
I had seen the bull sharks working in pairs, even if that meant that only one of them got any of the fish scraps Gary threw in. We think they must be able to communicate in order to co-ordinate their actions, said Erich Ritter. I thought it more likely that they simply found it convenient to hunt in packs, but I wanted to learn more about this communication theory.
First of all, it takes some thought to realise that sharks are not fishes, said Erich. Birds are more closely related to mammals than sharks are to most fishes. If they were related, it was more than 500 million years ago. A sharks brain related to its bodyweight out-ranks that of many mammals.
We are out here in the water every day, and yet we know so little. A shark sees well, it hears well and it has a well-developed sense of smell. It can also pick up differing frequencies of vibration. We think the lateral-line system is used for communication between sharks.
They may not be super-intelligent but there is good evidence to show that they communicate. After 500 million years of evolution, to become the apex predator the shark surely cannot rely only on receiver mechanisms.
I found that if I presented a small frontal area by swimming uncompetitively towards the sharks as they approached a bait, I was better placed to get a good photograph than if I swam vertically, breathing through my snorkel and holding the camera at waist level. This went some way to enhancing my own feeling that animals under water judge size, and therefore threat, by the vertical height of another animal rather than its length.
World shark research started off by trying to develop effective shark-repellents, Erich continued. Most shark scientists study pickle jars because they are afraid to get in the water. They believe old myths.
Its weird when you dont share this fear, because you quickly discover that sharks are not mindless monsters.
Inimitably English gentle giant Jeremy Stafford-Deitsch offered his own point of view.
Erich has a much stronger sense than I that these sharks are not dangerous, period. I was very cautious, but once I saw that their focus was the bait we were feeding them, I quickly realised that in that situation they were not a threat to humans.
However, Erich obviously has not seen them frenzy up the way I did on my first day. In profile, they look a bit like tiger sharks. I find this interesting, because both species enjoy a very generalist diet. They are very catholic in their tastes.
That said, there are many so-called shark-experts who dont get wet. I dont know how you can have any appreciation of animals like these unless you are prepared to go under water and interact with them.
With shark populations being exterminated at a frightening rate, there is a diminishing chance of sharing this sort of underwater experience. You can find out more by going to www.shark.ch or the Shark Trust at www.sharktrust.org

Diving with bull sharks is not normally on the agenda when you visit the Bahamas, but twice a week the dive centre at Walkers Cay organises its famous chumsicle feed.

Walkers Cay is primarily a destination for big-game fishermen, and its fish-cleaning room is used by those visiting the small marina. Scraps and waste from this room are collected in barrels and deep frozen with a wire hawser passing through the resulting block. Its like a giant fishy ice-lolly - or popsicle, as Americans call it.

The dive boat approaches the site, a sandy area around 12m deep, surrounded on most sides by reef but close to the deep water of the ocean. The sound of the engine arouses the expectant sharks.

The divers jump in and wait on the seabed. The chumsicle, anchored at the bottom of the wire and with a float at the surface, is lowered in.

Around 200 sharks regularly turn up to feed from the chumsicle as it defrosts. These are mainly bulky Caribbean reef sharks and nimble blacktips. Sometimes nurse sharks and the occasional hammerhead join the fray, with grouper and many smaller fish chancing their luck for a free meal.

Client-divers are encouraged to get off the sand and swim round with the sharks. As Gary Adkison says: They wont harm you. They think you are another big predator there for the meal.

Divers are discouraged from loitering under the chumsicle, because pieces of bait continually drop from it. The whole thing takes 20 minutes or more. When the final small amount becomes disconnected from the wire, the competing sharks provide a quick demonstration of shark rodeo!

Diving trips which include the chumsicle shark-dive at Walkers Cay can be organised through Divequest (01254 826322). A seven-day trip costs from £1035.