To look at this picture, with hindsight, is to see the soul of American painting squeezed into the narrow dimensions of a canvas 2ft high by 11 2 ft across. It is a study in determination, one of the first images in American art of the all-American, dogged drive to get on. But it is also a study in loneliness, a picture that sees rapt absorption in a task at hand as a form of alienation from the world. Eakins paints the river and its environs as a bright and sunlit place, but one to which his oarsman seems entirely indifferent. The picture predicts the heavy melancholy of Edward Hopper's barflies or office-workers, lost in their concerns, painted some half century later. It is prescient in other ways besides.
John Biglin in a Single Scull (what an unassuming title) contains, suspended within it, the two contrary impulses of the American artistic imagination: the impulse to observe, in its clear-eyed and close-focused concentration on things (an oar, a knotted red kerchief, the white rim of a sock); and the impulse to idealise, to abstract, to see the world as a pretext for visionariness. To scan the picture as its tall format suggests you do is to register the tripartite division of Eakins' landscape and to see, too, how it has been painted as a kind of ascension from the real to the ideal: the eye moves up from foreground detail (busy shards of reflection in its watery foreground) to vague middle distance (the foliage on the far bank of the river has been painted with a deliberate sketchiness, a realist relaxing his hold on things) and up to empty sky, a blue void of feathered paint. Ignore the oarsman and the painting becomes a Rothko in embryo, a New York School painting painted before the New York School was dreamed of.
'Thomas Eakins', at the National Portrait Gallery, has been installed with abominable insensitivity but the pictures refuse to be stifled by the purple mausoleum created for them: they confirm Eakins as an artist who, though barely known in Europe, stands comparison with the more famous French painters of his time, Degas, Bonnard and Vuillard. Eakins lived and worked in his native Philadelphia but he trained in France in the 1860s and acquired a lifelong distrust of the played-out conventions of Salon academicism. In 1868 he wrote to his father complaining that 'the professors talk classics & give out classic subjects & make a fellow draw antique . . . I love sunlight & children & beautiful women & men their heads & hands & most everything I see & some day I expect to paint them as I see them.' Those breathless ampersands signal Eakins's enthusiasm and, too, his integrity. Paintings, for him, seem always to have sprung from deep internal necessity - would have to be made because people and the emotions they roused in him had to be exorcised in paint.
Eakins saw with a sharp and nervous clarity shot through with deep and intense feeling. His acuteness is often embarrassing and sometimes painful. Painting The Artist's Wife and his Setter Dog, Mr Eakins sees Mrs Eakins with both tenderness and ruthlessness: a pale, skinny waif slumped in a chair, she has the look of a child who has just stopped crying (her eyes are red- rimmed and tearful) but has yet to be properly consoled. She occupies one of those 19th-century interiors which, all heavy dark brown furniture and Persian rugs, speak of the weighty and consequential world of adulthood. But, childlike, her blue silk dress draped over her tiny frame like a piece of fancy dress, she seems out of place, not yet grown-up enough for her responsibilities: human in a raw way that always seems to have touched Eakins.
The Concert Singer is a stange painting about the strangeness of performing. The singer is splendid in salmon-pink silk but her pose and expression are gawky and moronic, her half-open mouth and far- away gaze suggestive of idiocy. The conductor's hand and the fronds of a palm tree intruding on the right, as daringly cropped as details in any Degas of the time, announce Eakins's determination to see things obdurately askew and, by implication, afresh.
Eakins was a great painter of the way in which people fail to fit the worlds they occupy, and of the way in which feelings have a way of spilling out of those who most strive to contain them. Edith Mahon, a bust-length picture of a lady in an elegant black dress, could easily have been a society portrait. It is not hard to imagine what Sargent, say, would have made of the same subject - glittering sequins, creamy flesh emerging from decollete dress, the sexy flash of an eye - but Eakins has painted a picture of someone whose social poise has suddenly deserted her. Her elegant costume is almost cursorily handled so that all your attention is focused on a face that seems charged with an extraordinary sense of loss. Eakins's Edith Mahon gazes, moist-eyed, into space, an image of profound human sadness caught unawares. She hated the painting.
Eakins's greatest gift may have been his ability to see and paint the unexpected. He was always finding, or at least projecting, sadness or vulnerability in odd places. One of the most extraordinary pictures in this show is a portrait of a physicist, Professor Henry A Rowland. Eakins paints him a little bit like Saint Jerome in his study but there is something disconcerting about the glassiness of his stare: he seems present yet absent, abstracted by thought. What is most daring is the picture's frame, which Eakins has - with fantastic skill - carved with opaque diagrams and equations in precise mimicry of the subject's handwriting. The frame imprisons the sitter, makes him seem hemmed in (almost paralysed) by his concerns.
Eakins' work resists pat generalisations because each picture demands to be looked at on its own terms, as a feeling or an insight preserved in paint rather than merely an example of the oeuvre, just another Eakins. The painter constantly surprises. A portrait of a young man (Douglass Morgan Hall) is charged with unexpected sensuality, the sense of a living body suddenly and simply conjured in the painter's observation of a shirt just slightly too tight. A portrait of an infant(Baby at Play) yields an unexpected image of gravity, of the sober intentness of a two-year-old concentrating on her game. At their best, Eakins's pictures are naked, entirely unaffected, almost involuntarily honest. Perhaps that letter he wrote to his father in 1866 could provide his epitaph. Eakins painted things as he saw them.
National Portrait Gallery, London WC2H 0HE to 24 Jan 1994 (071-306 0055)