This week the Royal Academy has become a saddened and embittered institution, and all because of a show of middling interest with few works of genuine merit. Sensation may make the RA some badly needed money. It has been mounted primarily for that purpose. But the RA has at the same time dealt itself a blow from which it will take long to recover. Academicians are divided as never before and their president, Sir Philip Dowson, has given little leadership. The RA's officers and its publicity machine are widely regarded as manipulators of controversy. The exhibition's education programme is a farce, especially as one gallery is closed to those under 18 and the most prominent painting on display is a portrait of the child murderer Myra Hindley.

That portrait has now caused the resignation of a senior Academician, who joins Michael Sandle in withdrawing from the RA. She has left, Gillian Ayres tells the IoS, because she feels for the mother of one of the victims of the Moors murders, Winnie Johnson. Mrs Johnson has appealed to the public not to visit the exhibition. She asked the RA not to show the painting (and is heartened now by the attacks on it). The Hindley portrait is by Marcus Harvey, who studied at Goldsmith's College in the mid-Eighties and has since exhibited paintings of pornographic images. They are copied from magazines, but the paint application is a mocking caricature of Willem de Kooning's touch in the Fifties. Harvey's Myra is not of this sort. It's derived from another American artist, Chuck Close, who does huge photo-realist portraits of his friends, always concentrating on their faces. Harvey doesn't have the technique needed for photo-realism; but he's taken the familiar police photograph of Hindley and has enlarged it to the sort of scale that Close uses.

As one approaches Myra it becomes apparent that the image is constructed from a child's handprint, repeated hundreds of times. Since a gruesome metaphor is involved it could be argued that Harvey's method is appropriate to his subject. That does not make Myra a better painting. It rings false. One senses that it has a design on its viewer. Harvey's aim is not aesthetic, let alone humanistic. He wishes to use the aesthetic arena to show that he has a cooler, more detached view of the modern world than the rest of us. And the same is true of the exhibition as a whole. A vital ingredient is missing: sincerity.

A lack of candid feeling was to be expected. "Sensation" is an exhibition assembled by an advertising mogul who likes artists who have been influenced by advertising. Everything in the show belongs to Charles Saatchi. He must have calculated the probable effect of his show on the public. That's his profession. The 110 works on display are a small proportion of the 875 items by younger British artists in his personal collection. He did not have to exhibit Myra, for it's no good and he owns so much else. The RA's Norman Rosenthal, who helped Saatchi select the exhibition, has talked a lot in recent days about artistic freedom. So has the RA Magazine, which is edited by Nick Tite, husband of the RA's press supremo Katharine Jones. Tite claims that the press and "public pressure" are forcing the Royal Academy "down the slippery slope of censorship". Other people may think "Sensation" is deliberately near the line; a clever poise governs the show, asking for controversy and hoping for financial return.

Around 40 of the exhibits are paintings. Their characteristic manner is ironic, post-modern and heartless. There's no formal invention at all, except perhaps in Chris Ofili's iridescent swirls of paint. Manchester- born Ofili found his way of painting during a stay in Zimbabwe. He has an honest attitude to multi-cultural influences. Alas, he is mainly known for putting elephant turds on his canvases. He doesn't need them; they are a distraction from the merits of his paintings. Ofili is best when most direct. Closer to the artificial style of the exhibition are paintings by Glenn Brown, who mimics more established artists (Auerbach, Dali) in a high-gloss technique that makes oil paint look like colour photography. Richard Patterson also likes advertising camerawork. Sometimes he hits the mark, as with his now familiar paintings - shots, one feels like calling them - of motocrossers, but his more elaborate Culture Station 2 - Dirty Picturefalls apart.

No painter in the show can manage a complicated canvas, though they often try. Perhaps Saatchi and Rosenthal had to look for big pictures in order to fill the Academy walls. Fiona Rae likes to throw everything into her pictures, so in theory a large size would suit her. It doesn't work out that way, though her Untitled (Sky Shout) is a brave try. Rae is one of only two artists purchased by Saatchi in the last decade who is getting better. The other is Gary Hume. But although he is now more interesting and competent, Hume cannot escape the cool stance with which he began his career: that of the painter who cares nothing about painting, so he'll pretend to be an amateur and let's see what comes out. That kind of coolness is a trap.

The room that's barred to children contains mannequins of children. They have been devised (though not made) by the brothers Jake and Dinos Chapman. Some of the noses of these little figures, which are all female, have been replaced by penises. In another piece, this one in the public rooms, similar toy girls act out routines derived from advertising and pornography. The Chapmans have borrowed their act from the American artist Jeff Koons. A lot of the art in "Sensation" comes from imitating Americans. Harvey gets his picture from Close, Patterson abjectly follows Rauschenberg, Gavin Turk is also a follower of Koons, Peter Davies gives us a swot's version of Basquiat and Damien Hirst's tanks are a late rerun of American minimalism. Startling a few years ago, they now look tired. Hirst's paintings are simply wretched.

The more satisfying pieces in a thin exhibition are Rachel Whiteread's Ghost, a sensitive painting by Simon Callery and photographs of a working-class household by Richard Billingham. Much other work is foolish or trivial. It's by artists who are wasting their time and our time. If the RA had wished to put on a decent exhibition of new British art in the last 15 years, they would have borrowed from other people besides Saatchi. Then we might have had a more responsible survey. "Sensation" is cheating its audience and it leaves some nasty experiences in the eye.

Royal Academy, W1 (0171 300 8000), to 28 Dec. A correction: in the `Sunday Review' of 31 Aug, we said that the artists Langlands & Bell were represented by the Victoria Miro Gallery. In fact, they are independent.