It is possible they all saw themselves as standing on a magnificent canvas, one that might run the length of an old hall. It would be filled with smoke. There would be hills with men toiling up the slopes, other men firing down from above. A gorge. A swamp. Far embrasures and redoubts – strategic details compressed into a tea-coloured distance before the Paraguayans run out of wall. In the centre, the river, shallow and lazy, flows or dallies past the story of the war fought along its bank: the battles of Riachuelo, Tuiuti, Curupaiti, the trenches at Curuzú and, looming above it all, the besieged fort of Humaitá; its builder, the gallant Captain Thompson, unrolling his plans high up there on the mud wall.

Below him, Brazilian ironclads squat on the river while, from ship and shore, the mouths of cannon spit primitive flame. The river is spattered with shot that falls just shy of the ships: the walls of the fort, though vaguely pocked and dented, are never breached. It seems a pleasant enough stalemate – an expensive way to fish. Along the wicker battlements, men point into the middle distance or click out a telescope to glint in the sun. Their names might be written on ribbon unfurling below them. In the centre, Lopez; with an unlikely white stallion rearing under him on the high wall. Pedro Inácio Meza, the ruined hero of Riachuelo dying of his wound, stiffly, on the church steps. Colonel José Diaz charging, and taking, a battery of La Hitte cannons from the Uruguayans at Estero Bellaco. Huzzah! General Francisco Isidoro Resquin running up the left flank at Tuiuti, General Vicente Barrios on the right, the fierce Guarani soldiers wading through swamp and thicket under close enemy fire to face the sixty thousand Brazilians, Uruguayans and Argentines, housed in that vast city of cloth. How could one man paint them all? And though we see men throw up their arms and roll their eyes, although we see the bullet even as it enters; the stricken faces of comrades who reach but can not save ('oh, no!' the picture might be called. 'Oh, No!'): although we see plenty of dying, we do not see one corpse – so quickly are bodies emptied and then discarded, even by their own stories – nor do we see the vast heaps of the dead. We might miss the vast heaps of the dead: we have come to relish them; the unexpected anatomy lesson of a man's neck open to the spine; the way a group of bodies tangle and subside; the way we must follow the line of a leg to see whose foot that is, so strong is our impulse to unite the body and give each man his proper parts. Also the horror, of course, when the leg stops short. Ten thousand men died at Tuiuti, and as their skin leathers in the open air, the hill of the dead settles and grows horribly flat (who would have thought there could be so many elbows in the world?). A lone photographer stands on the field of death, and there is no one to paint them: the painters are all fled. What happened at Tuiuti? A battle, that is all. Nothing but swamp was lost and nothing but swamp was gained. But the man who lost the swamp was Lopez.

Still, you must never underestimate the Guarani soldier. He is there in the picture too, in dull-eyed ranks and rows, ever-advancing. Again and again, facing superior forces and overwhelming odds, the Paraguayan Indian outfoxes, outfights, outdies the combined enemy. His pants are blue and his coat is red. And he takes both off to fight in the swamp, which he knows and calls home.

He is sickened by the meat, though, as Milton tells it many years later. Not because the meat is rotten, though it is often rotten, but because these men are not used to eating such stuff – they only make it, or become it. In which case, there is plenty meat made in the five and a half years of the war. As the battles slowly creak into place, and one strategy slowly crunches into another, the Guarani Indian fights on; bilious, gripe-ridden, suffering from meaty breath and meaty wind; and there is no surrender. Ever.

Despite which, the story of the war is a story of retreat. Curupaiti held and lost. The cunningly double line of trenches at Curuzu, then back to the fort of Humaitá: three hundred and eighty guns, a mess of defences out front, the ground seething with twenty thousand boys and old men, because only boys and old men are left, now.

The stranglehold tightens around them and the names keep unscrolling in the painterly wind: on the river, the fearless Diaz floats in his fatal canoe; General Barrios makes a sortie, Paulino Álén shoots himself, in the face of defeat; Bernardino Caballero holds Acosta Nu – these are names that must be said out loud. As too must the names of the staunch ships who sailed in this war, the Tacuari, the Paraguart, the captured Brazilian steamship Marques de Olinda, the Ygurei, the Salto Oriental and the Pirabebé. Ships where men fought, and in which they burned; ships from which they drowned.

There is some comfort in listing the brave men of other wars: history is a litany, and all we are doing, here on this earth, is making lists of the dead.

So busy intoning, indeed, that we miss the three Brazilian boats as they cut the chains that have been slung across the river, then run the battery at Humaitá. They are the Barrosso, the Tamandaré and the Brasil: all monitors; blind-looking things of unnatural iron – even the deck is closed over, so that the men inside it are either safe or dead: there is no middle way and no romance to them either. Monstrous modernity, which chugs past the open mouths of two hundred and four guns – from the Curupaiti battery to the final array at Humaitá – as though they were going on a picnic. Then moves upriver to pound Asuncion.

And so there it is. The city is burning. Somewhere in the background, the ghost of Whytehead lays his hand on the bulge of a cold smelter, looking sad yet proud. So much for the remnants of the maiden Tacuari – they pale in comparison to the great names of this war, Spanish Creole and Guarani. At the very end of the canvas it is the gallant Captain Thompson who surrenders, finally, the fort at Angostura, because no Paraguayan knows how.

And where is Stewart? Was he brave? Low down, on a nameless piece of ground, he lifts some dying man by the shoulders, as though to help him face out of the picture. The man rolls his eyes. His last, trembling gesture is back towards Humaitá and the unlikely stallion on the high wall – my captain, Lopez. (Or is that Lopez himself, impossibly dying in Stewart's arms? With more beard, perhaps, and a different look in his eye?)

And where is Eliza in his hour of need? She is out of the picture. Her portrait would be hung on the opposite wall, endlessly looking. Trying to discover where it all went wrong.

She will not find it here. This is a heroic painting -one of the last such – and tenderly naïve. It is full of errors, of course, but that is a different thing. Stewart might have pointed out that the chains slung across the river were, for the duration of the siege, most beautifully clogged with water hyacinth. Every morning he wondered at the line becoming sharper – the water downstream becoming smooth as glass, as the river behind grew solid with vegetation. One morning the whole thing flowered and he had the greatest urge to walk the floating path from the near bank to the freedom of the other side.

He might, either, have complained about the lack of red – that most distracting colour. He might say the painter had failed to capture the various and romantic colours of blood, for example, from the dry rust first pointed out to him by Whytehead, to the liquid red of the river, soaked with light as the sun went down. It might be bougainvillaea shooting, from one day to the next, out of the rich mud beside his hut at Humaitá, or a man's shirt in full bloom just before he died, but Stewart's eye was punctured by red during the war, as his heart was sometimes pierced by the peculiar blue of the sky.