I know that my University of York colleagues regard my trip as the academic wheeze of all time. Round-the-world, ten countries, cruising conditions etc, etc. All true. But - and I expect no sympathy or quarter for this - the teaching is hard. Let me explain.

We teach every day at sea, ignoring real time, and function on a two-day teaching week: days A and B. I teach two courses on A day (race/ethnicity and history of sport) one on B (slavery), then back to A on the third day. There are 30-plus students in each 75-minute class. The end result is a remorseless shipboard regime. We all moan about the load and about the inescapability of students - it is like living in college but all at much closer quarters.

But that is only part of the story. The real difficulties for all of us are posed by the physical circumstances of teaching at sea. I was really concerned about my fitness for sea - I have always been a notoriously bad sailor. But thanks to a regime of pills, wristbands, prayers and incantations, so far, so good.

The ultimate fear is of throwing up in front of a class. Any credibility you might have with students would vanish along with your most recent meal. For their part, students quickly depart from class whenever they feel unwell. At the time of writing, no member of staff will admit to that experience, though some have come close.

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Initially I found it hard standing upright on a pitching, rolling ship. Worse still, the lectern also tends to move. Just when I thought I was anchored to the spot, I realised that the lectern and I were listing, in an ungainly embrace, at an alarming angle. Even when the sea isn't rough, life at sea is tiring. You spend the whole day, balancing and counter-balancing, swaying and bracing in what becomes, in effect, a day-long aerobics class that, inevitably, takes its physical toll.

One of my classrooms looks onto the ocean, chopping past at a stately 15 knots. This brought the unique delight - never, I imagine, to be repeated - of speaking about the West Indies as we saw St Vincent slip past on the starboard side, St Lucia on the port, with Barbados just over the horizon.

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The other two classrooms offer an altogether more horrible outlook: the walls are entirely mirrored and wherever I look, I see visions of my unappealing self, pontificating in what looks like narcissistic dramatics to a gallery of heads (or rather the backs and sides of heads).

Preparing for classes has its own problems. The cabin is too small to do anything but sleep in - barely that in rougher seas. The bathroom demands gymnastics of Romanian Olympic standards. The staff lounge offers free space but generally fills with colleagues and senior passengers more interested in relaxed conversation - although early mornings tend to be accepted as a time for private study.

The small library, at the bow of the ship, exaggerates all the movements of a heaving ship. It is very hard to concentrate on reading, especially at a computer screen. The strange movements of the ship and the eyes blend to create an oddly hallucinatory effect, and it is hard to maintain the task.

I have been trying to write, but if I can manage a page a day I am doing well. After that, my eyes and the screen seem to fuse into a seaborne electronic blur and I have to give up.

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The staff lounge, immediately above the bridge, affords a wonderful view across the bow of the ship, and sometimes provides its own pleasures. After a week at sea we saw our first birds - and one butterfly - east of the mouth of the Amazon. Best of all, my attention was suddenly caught, early morning on a dead-calm sea, one day out of Bahia, by a concentrated flurry of small waves. As I stood up to watch, two pods of dolphins (about ten in each) came skimming and looping towards the ship, attacking the bow, closing on us at enormous speed before disappearing, at breakneck pace, under the ship, leaving nothing behind but the vast expanse of the becalmed South Atlantic. It was a thrilling moment, lasting perhaps no longer than a minute.

But life on the ship is dominated by teaching. All the students have to do a "core course" at mid-morning - carefully geared to the places we visit and drawing on the various expertise of the particular staff on board. Classes begin at 8am and run through to late afternoon.

Evenings are normally filled with something instructive - another lecture, a film - with later times for fun and relaxation. The ship thus fairly hums with activity. It is, after all, filled with Americans who take their work seriously, and who work hard at everything that comes their way.

There are, of course, the usual slackers. But the teaching has provided a pleasant reminder of the great virtues and qualities of young Americans, of their enthusiasms and eagerness to learn, of the speed with which they absorb and make sense of the unknown, and of their zest in asking direct questions when they don't know. And all this in that relaxed, open style that is - to me anyway - one of America's most seductive charms.

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It is also great fun, again, to work with American colleagues in all their great variety, from the wonderful wise-cracking rabbi (it is like working with a superbly educated and highly intelligent New York cab driver) through to newly qualified colleagues, bringing to the task that earnest professionalism born of American graduate schools, and still in need of a leavening of worldliness.

It makes for a wonderful social and educational mix. Despite the physical queasiness, despite the close-quarter quality to daily life, despite the huge cost of finding out the football results, I have quite come to like teaching at sea. Perhaps the pleasure will evaporate by the time we hit the fogs and North Pacific swell of the last leg from Japan to Seattle.

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James Walvin is professor of history at the University of York.