If at first you don't succeed...

There's something irresistible about catching genius in two minds, and it's a pleasure you can get quite a lot of at the National Gallery right now. Generally speaking, of course, dithering and genius are not related concepts. We cherish a notion of unerring instinct - the supreme instance of which is the untrembling hand of the fresco painter, laying pigment on to fresh plaster in one bold, irreversible stroke. And if we're inclined to forget that hours of compositional agonising preceded that gesture (and quite a few minutes of secco adjustment might also have followed it), that's because a painting is often at pains to erase its own uncertainties.

This isn't always true by any means, particularly in the past two centuries, but it's certainly what you feel when you look at a painting by Raphael. The assurance of the image seems to rule out any speculation about whether things might have been ordered differently. And if, like me, you find this swan-like composure a tiny bit aggravating, it's particularly pleasing to find evidence of the webbed feet beneath the surface, paddling furiously through the nearly infinite possibilities of shape and form that confront an artist.

One of the most gripping things in the National Gallery's current Raphael show, From Urbino to Rome, is one of his preparatory drawings for his great Vatican fresco, the Disputa. Done in pen and brown ink, it shows the figure that ends up at the bottom right of his theological crowd scene - a man leaning forward over the balustrade apparently in order to get a good view of the action. One side of the sheet shows Raphael grappling with the torsion of the man's neck, trying to work out how the tendons and the Adam's apple will appear when twisted into profile. The first go is decidedly wonky - the figure looks as if he has a serious thyroid deficiency - so he has another try underneath. At the same time he's testing positions for the man's hands.

On the other side of the paper the figure has three arms, the result of Raphael sketching in an alternative position for the right arm, one which (if you look at the completed fresco) would have him impatiently tugging back the shoulder of the man next to him. And perhaps because of the loose, sketchy nature of the draughtsmanship this little drawing has an extraordinary vitality. Raphael is so intent on the details, on the way that leaning your weight on your hand will push a little bulge of flesh out sideways, that the image is entirely unselfconscious. It's not going to be looked at, after all. It's the act of looking traced on to paper and it's so vivid that it's disappointing to find that Raphael didn't use the pose in the final fresco, opting instead for a rather blander arrangement of hands and body.

The gallery's new Degas show, the latest of its fascinating Art in the Making series, is even more explicitly devoted to the disjunction between the finished work and the progress towards it. "Nothing in art should be accidental," Degas famously said, and this show, which itemises his changes of mind through X-ray images and infrared photographs, confirms how vigilantly he policed his work.

The most interesting study here is of his striking painting of a music hall strong woman, Miss La La at the Cirque Fernando, in which the subject suspends herself by her teeth, as if dangling above the viewer. Degas had such difficulty with the background for this picture that he apparently confessed to Sickert that he'd hired an architectural draughtsman to work out the perspectives for him. But even when he'd got his backdrop he still struggled to locate his subject on it.

X-rays and preparatory drawings suggest he'd considered a quite different angle - placing her against the highest rafters - and there's also an oil-and-pastel study that adds at least another third to the depth of the picture. What Degas seems to be groping for here is vertigo, and it's only because you can compare these three images that you can see that the obvious solutions wouldn't work. The high placing removes the sense of architectural depth and the deep format pushes the figure away from you, so you lose the sense that you're craning backwards to see.

What's more, only the final composition allows the beautiful bouncing syncopation of architecture and body, the horizontal arches of the building intersecting with the curves and arched limbs of Miss La La. Even her odd placing in the upper-left corner accentuates the sense of suspension; our eyes naturally fall on the centre of the canvas, but she defies that aesthetic gravity.

Somehow, it doesn't detract from the effect of the painting to learn that it was so hard won. Both Degas's and Raphael's false starts aren't failures of talent, they're proof of it.