"Beauty and the Beast" wouldn't be a bad title for the exhibition of portraits by Jean-Auguste-Dominique Ingres (1780-1867) which is about to open at the National Gallery. There he was, for over half a century the staunch defender of the classical ideal - "les bonnes doctrines!" - orchestrating elaborate allegories and mythologies, fine-tuning magisterial nudes, polishing and repolishing impeccable portraits of the pillars of French society. And yet the more this neurotic neo-classicist strove to refine his figures the more exotic and elemental they became. Ingres' career is like the myth of Apollo and Daphne revisited. Whereas the lovely nymph turned into a laurel tree when pursued by the Greek god, the ideal beauty pursued by this Apollonian painter became a monster of the deep.
Ingres took breathtaking anatomical liberties that could insidiously mutate even the most elevated human subjects. They are caught in a delicious evolutionary loop. To one critic, he was a painter "whose chilliness hatches polar bears". Bits of his sitters have been compared with sheep (Mademoiselle Riviere, 1805), with crows (Baronne de Rothschild, 1848) and with starfish (Madame Moitessier Seated, 1856). The hands of the journalist Monsieur Bertin (1833) elicited a frisson all of their own: "Look at this fantastic bundle of flesh under which, instead of bone and muscle, there can only be intestines." Octopuses, elephant tusks, bloodsuckers and crabs are other alien interlopers that have been detected in the unconscious of his work.
It's this incipient, subcutaneous wildness in the midst of bourgeois assurance that sends exquisite shivers down the spine of modern critics - and which leads some to claim Ingres as the greatest portraitist of the 19th century. I think they're right: portraits don't get more primal than Monsieur Bertin - or more intoxicating than Madame Moitessier Seated.
Ingres initially refused the request to paint this wealthy banker's wife, but when he met her he was so bowled over by her beauty that he agreed. This didn't make her any easier to paint. Far from it: he agonised over the portrait for the best part of a decade, beginning in 1847 and finishing in 1856 - by which time the sitter was 35 and the painter 76.
Madame M sits with Buddha-like poise on a tight-arsed upholstered settee. She is wearing an off-the-shoulder chintz dress decorated with a rich flower pattern. Every bloom is painted in hyper-real detail. The fabric spills lavishly over the furniture, a floral waterfall that fills the bottom half of the picture. The sitter's gently tumescent face, shoulders and arms float effortlessly and buoyantly over the deluge of her dress. You imagine that her head, with its Grecian-urn rotundity and porelessness, will always be inscrutable and steady. Its role in this picture is like that of a divine ballcock in heaven's own cistern.
The most famous feature of this portrait is Madame M's right hand. The fingers are splayed over the side of her face, teasingly tentacular. The pose derives from a Pompeian wall painting, where a head resting against a right forefinger signified female modesty. But here it holds out a promise of akimbo animal pleasures ahead - a swim in an ocean of squelchiness, suction and sheer pneumatic bliss. The left hand holds a fan, in readiness for the heat to come.
But this portrait is much more than a sophisticated come-on. Behind Madame M is a big mirror - a big, dark mirror - that carries a smoky reflection of her head and shoulders in austere profile. The soft-focus image is sexy, too, but it's undeniably a bit remote and claustrophobic. This sombre subtext would fit in with the mood of the painter, for the picture's gestation was interrupted by the death of his wife in 1849, an event which left him distraught and unable to paint for months. He only returned to this portrait in 1852.
Madame Moitessier Seated is surely a lament as much as a celebration of female beauty. But we don't need the crutch of biographical detail to say this. For the iconography of the painting points to this elegiac reading, too. In 1852 Millais painted his celebrated Ophelia, in which a pale beauty floats fully clothed in a stream filled with myriad flowers, each painted with pre-Raphaelite vividness and precision. I'm sure that the Ophelia story was in the back of Ingres' mind when he set Madame M adrift in a sea of floral chintz, her face tickled by tentacular fingers, her flesh uncannily bloated. What he finished up with was an epic double portrait that spoke of love and death by drowning in an airless Victorian sitting room.
"Portraits by Ingres" runs at the National Gallery (0171-747 2885) until 25 April