IT IS ONE OF THOSE RARE halcyon days when I'm feeling serene and Eila is at rest. I sit in the cockpit with a beer, sundown on the way. It has been a hard day.
A fish jumps about half a mile away breaking the calm atoll lagoon. With the binoculars I take a better look. It’s not a fish at all, but a dolphin – I can see its arching back glinting in the low sun.
Vicki grabs the snorkelling gear. I pull out my camera case and we pile into the dinghy. Planing, we cover the distance in no time. We stop the motor at a discreet distance and I snap on a 300mm lens with the idea of taking “dolphin barrel-rolling against the sunset” pictures.
Not that unlikely since we can see it is a spinner dolphin. But where are the others? Spinners are intensely social animals usually living in groups of 30 or more.
Vicki rows the dinghy towards the dolphin who seems curious about us, moving closer with each pass. I slip into the water, naked except for snorkelling gear. Suddenly, there it is, streaking past at the limit of visibility, about 20m away.
Instead of swimming towards the sleek animal, I feign some indifference, snorkel-diving down, doing barrel-rolls of my own, keeping a watch from the corner of my eye. With my palate I make sequences of clicking sounds, mumbo jumbo to the dolphin, but conversation nevertheless.
When I can see the dolphin, I half look away in appeasement, to show in the universal language of animals that there is nothing to fear.
I swim dolphin-style, neither towards nor away. Within minutes she is swimming past, just a dolphin length between us. Vicki joins us in the water. It is only a few metres deep with a few coral heads. The sand between them reflects what little remains of the light.
The dolphin's behaviour is reminiscent of a puppy – pleased to see us after a long absence. (The dolphin no doubt describing our behaviour as reminiscent of a couple of lunatics.) She swims away only to come skidding back, veering away at the last moment, bombarding us with clicks and whistles, tossing her head as though sniffing out a clearer sonic view.
Finally, as the colours become muted with the end of the day, a grey reef shark appears. I am hoping to see the much written about “dolphin kills shark” scenario where the dolphin ruptures the shark’s internal organs with its beak.
This may happen in the confines of an aquarium but in the ocean, as elsewhere in nature, animals usually establish hierarchies without resorting to violence. The dolphin and shark are indifferent to one another; the shark more interested in the aliens – us.
Cold and the gathering dusk persuade us to leave. Not wishing to shatter the calm, we row back to Eila, the dolphin leading the way by a dinghy length.
This, we think, is the conclusion of a unique encounter. In fact it is just the beginning.
We hadn’t intended to come to Apataki at all. But the frenetic trade blowing when we left Takaroa easily persuaded us that Toau would be a grim slog to windward.
I love the freedom to change plans at a moment's notice, so we declined the challenge and chose Apataki instead.
This rectangular ring of coral 15 miles long has a single village of 250 people at the south-west corner. Elsewhere are miles of uninhabited, palm-covered motus encircling the lagoon.
There are two passes, one by the village and another near the north-west corner. There we found anchorage off the motu of Rotoava. Not a soul; just the birds, terrestrial crabs, a shallow brackish lake among the palms and Coenobita terrestrial hermits on the lagoon sand.
The next day we explore the motus further afield, taking the dinghy a couple of miles east across the calm lagoon. Of the dolphin, which Vicki has named Bojangles on account of her ragged dorsal fin, there is no sign.
Later, I spend long interludes up the mast searching the glassy lagoon surface for telltale activity.
At about four in the afternoon, we take the dinghy down towards the pass. Vicki catches a glimpse of something – Bojangles has returned.
Again we stop the motor and row close. I slip into the water, this time with the camera in its underwater housing. The light is poor and the flashguns seem to disturb the dolphin, so I return it to the dinghy. She leads us into shallow water, a sandy bottom 5m deep, studded with beautiful coral heads reaching towards the surface.
Here she plays games with us for half an hour. Dark falls and she is gone, but as we plane back to Eila, Bojangles appears alongside; her low, powerful leaps effortlessly matching our 14 knots.
In the morning we take the dinghy to the pass again, thinking perhaps she spends the night outside, feeding in deep water in the usual spinner fashion on small fish and squid. Although it is calm and easy to see any surface disturbance, there is no sign of her at all. Not until mid-afternoon do we find her, among the same pretty coral heads as yesterday.
This time we are able to spend two hours with her, sometimes just an arm’s length apart.
Often Vicki and Bojangles swim leisurely circles side by side around one particular coral head. They drift towards one another till almost touching. Bojangles seems entranced, her eyes closing. Then her eyes pop open and she thrusts forward, only to slip back into the same mesmerised torpor.
Vicki runs her pendant along her chain necklace and Bojangles goes crazy, rushing away to throw herself half out of the water a few times, then zooming back, as if to make sure we are still there.

WHEN VICKI IS COLD she sits in the dinghy, gleaning what little warmth remains in the low sun. She whistles and talks to Bojangles who swims very slowly, blowhole and head high out of the water for long periods. I quietly take pictures with natural light.
When I am cold Vicki and I change places.
I talk to Bojangles too and whistle a Maori tune we learned in New Zealand. It feels good and reassuring to watch this communion of two species.
When, finally, we both leave the water, Bojangles does back-flips and rushes around the dinghy. We return to Eila for film, intending to take some topside shots of her barrel-rolling against the sunset. But she is sedate now and not inclined to play games to order. The evening is perfectly calm, the interface of sky and lagoon absolutely seamless.
After dark she comes to visit Eila; we can easily hear her breathing from down below. We go outside to talk with her, thinking the chat itself is more important than what is said.
In the past we have had good responses from dolphins with Bach, so we try the double violin concerto on the cassette-player. This time her behaviour seems unchanged.
During the night Bojangles visits us three more times; each time I feel obliged to go outside for a chat, to show her that she hasn’t been forgotten.
In the morning we spot her at about 9.30. At last this is the kind of light I need for reasonable pictures. We make her acquaintance in her usual spot.
Today her behaviour is more playful, more intimate. Often as she swims past she shits a muddy jet-plane vapour trail. Thus we can see the anus right next to the ventral slit which allows us to sex her. Male cetaceans have a gap between the anus and ventral slit.

WE SPEND TWO-AND-A-HALF hours with her, just frolicking in the shallows.
Often she shows us her ventral surface, often throws herself half out of the water and dashes away only to return. I try peek-a-boo with her but she gives no response.
I use a wetsuit this time, and scuba gear intermittently. Surprisingly the bubbles don’t upset her; underwater exhalations are sometimes used as warnings by cetaceans.
Then, there is the leaf. An old leaf the size of a hand, drifting on the surface. Suddenly it is caught on her flipper. Now it is adrift. I grasp the leaf, swim with it and release it. Bojangles glides up to the leaf, nods at it with her beak and it is caught on her flipper again.
Vicki and I exchange elated smiles behind our masks – which instantly flood! Four times the dolphin catches and releases the leaf.
At last we are cold, out of film and emotionally frazzled. We return slowly to Eila, the dolphin following all the way. She does a couple of circuits around Eila and returns to the shallows.
After lunch and changing films we return, finding her in a different place, where the water around the coral is turbid with zooplankton.
She seems reluctant to interact at first and is more sedate now. Often she swims out towards deeper water, but the dinghy is anchored and we are reluctant to follow. She returns each time and passes close by as if to ask "Why?"
Finally she disappears into deeper water and does not return. On our way back to Eila we see no sign of her. The wind, however, almost absent over these past four days, has begun – the south-east trade. We have no protection here from the south-east and 10 miles of fetch across the lagoon is too much for comfort so we prepare ourselves for leaving.
As a last farewell, she visits us that night – just once – and we go outside to say our goodbyes.
By morning the anchorage is marginal.
I take the dinghy to her favourite coral heads but I cannot see her. I motor reluctantly back to Eila against the chop kicked up by the new trade. Vicki and I are silent as we stow the outboard below and the dinghy on deck, exchanging long glances to which words would be a precarious addition. By mid-morning we are under sail, on our way to Tahiti.
At dawn, against a backdrop of grey cloud, I watched the air-brush green, purple and orange colour the east. To the south-west, the first touch of colour and relief came to Tahiti.
While in Papeete I was able to correspond with Wade Doak in New Zealand, a leading authority on extended encounters between humans and cetaceans and the author of numerous books on whales and dolphins.
Although there have been interlocks with groups of spinner dolphins in Brazil, this is the first extended interaction with a solitary spinner dolphin of which he is aware.

Polynesia – An Ocean Realm
Find out more about the 242pp eBook Polynesia – An Ocean Realm: Underwater Exploration in the South Pacific by Pete Atkinson at www.peteatkinson.com, or download it via iBooks. The price is US $9.99. A limited number of hardback versions are available at £57.