Visual art - Degas repainted one ambitious scene time and again. Richard Cork on the work's eroticism and emptiness

Of all the French painters who revolutionised late 19th-century art, Degas was the most in thrall to the past. Manet became fascinated by Velazquez, and Cezanne looked hard at Poussin. But Degas wanted to vie with the far more remote achievements of Greece and Rome. Rather than shunning classical art as the epitome of academic dullness, he aimed to revitalise it through intense scrutiny of the modern world. Just how fervently he saw himself in the classical tradition is revealed in an enthralling exhibition at the National Gallery.

In the earliest image on view, which looks like a Hellenistic history painting, Degas transports the onlooker to a scene in ancient Sparta. As a young artist, Degas had studied drawing with a pupil of the arch-classicist Ingres. Subsequent visits to Italy confirmed this passion and, around 1860, he began work on an ambitious canvas known as Young Spartans Exercising.

It was not, however, an exercise intended to show how obediently Degas copied his revered sources. He was determined to inject his picture with a provocative, openly erotic tension based on his observation of contemporary French adolescents. He may also have taken his cue from Abbe Barthelemy's vivid account, published in 1788, of the liberated upbringing enjoyed by Spartan girls. Unlike their domesticated counterparts in Athens, they were "taught to dance, to sing, to wrestle with each other, to run swiftly in the sand, to throw the discus or the javelin, and to perform all their exercises without veils and half naked".

The artist's imagination was clearly aroused by the thought of these emancipated young women. The first large version of the picture, on loan from the Art Institute of Chicago, shows them flaunting their bare-breasted bodies in front of a group of naked teenage boys. According to Barthelemy, the Spartan girls enjoyed inciting the youths "to glory by their examples, or by flattering praise or stinging irony". But Degas pushes his painting in a more sensual direction. One of the girls places a hand over her companion's breast. She might, in theory, be teaching her friend a wrestling move, but the gesture looks amorous rather than sporting, and the girl in the foreground seems bent on parading herself for the male audience. As for the fourth girl, she darts eagerly forward and thrusts out her left arm in the direction of the youths. Is she challenging them to a fight, or daring them to indulge in a seductive dalliance?

At some point, Degas abandoned this version and turned instead to the still larger canvas owned by the National Gallery. He must have felt that the image needed simplifying because, in the second version, he dispensed not only with a temple in the background, but also the trees that had sheltered the youths. He clarified their poses and gave them a more brazen air. As a fascinating new X-ray shows, he started out painting the boy on the far right from the back, as though unaware of the girls' taunting, but then repainted him in the instant of turning to acknowledge their presence. The fair-haired youth is also given a more defined pose: now on all fours, he gazes across at the girls like a hungry young predator. Two of the other boys are bolder, too. The one with upstretched arms no longer hides his eyes from the girls. He gazes appraisingly in their direction, while the youth next to him raises his index finger with sly suggestiveness. Sex is in the air, and the girl lunging forward now looks more impulsive than she did before.

In the final analysis, though, all this burgeoning sensuality is held in check by an even stronger feeling of hesitancy. Take the girl on the far left, who stared straight across at the boys in the first version. At some point, Degas decided to lower her eyelids. She can no longer bring herself to look at their naked bodies, and we are more aware of the fierceness with which her left hand tugs at the forearm of her reckless companion. The same urge, to pull back from outright engagement with the youths, can also be detected in the artist's treatment of the other two girls. Their faces are merged with remarkable intimacy, so that they are almost transformed into the kind of two-in-one image often favoured by Picasso. One girl points towards the boys, but the other now appears to be restraining her. Rather than feeling her friend's breast with seductive intent, she seems more concerned about advising her to withdraw from closer contact with the opposite sex.

Even the youths are constrained by diffidence. The boy who leant against a tree in the first version, looking up with undisguised longing, now seems to fall backwards. He closes his eyes, as if determined to block off all thought of temptation. And none of the youths makes a decisive step in the girls' direction. They seem spellbound. We grow acutely conscious of the space between the two groups. It looks strangely inhibiting, and the slenderness of the girl's arm as it reaches out across the void only accentuates her fragility.

That is why Young Spartans Exercising is so haunting. Despite its preoccupation with distant history, this much-deliberated canvas may be one of Degas's most personal images. It is, after all, the work of a man who never married and led an increasingly reclusive existence with only a gruff housekeeper for company. He left no evidence of ever having experienced an amorous relationship, and placed the same emptiness at the centre of this melancholy, confessional painting.

"Art in the Making: Degas" is at the National Gallery, London WC2 (020 7747 2885) until 30 January

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