ART / The theory behind the execution: Manet and Sisley in the same week: it ought to be a clash of the titans, but it's a mismatch

ANY Manet exhibition is welcome, and the National Gallery's especially so, because it brings out one of his lesser-known interests: political violence. There are 20 Manets assembled around this theme, from large paintings to tiny prints. Some are of specifically political subjects, such as the sea-escape of the radical journalist Rochefort from a penal colony. (Manet was a keen republican living unwillingly under the French Second Empire.) Others are more directly concerned with violence, such as The Dead Toreador. But these strands converge on the main event, the execution of Emperor Maximilian of Mexico, and the three big canvases in which Manet treated it.

One of these is in the National's collection anyway. But for those who only know this version, or rather the four surviving fragments of it, the historical event is obscured by the fact that the figure of Maximilian himself is one of the missing parts. And his story is important. In 1862, France launched an imperial venture against Mexico. The invasion was initially successful, and an unemployed Habsburg, the Archduke Maximilian, was installed as Emperor. His reign was brief. An army of national resistance gradually made gains against the occupying French, finally forcing a withdrawal. Maximilian was abandoned and, in 1867, was captured, tried and shot by firing squad: for France, a national embarrassment, tragic or scandalous depending on your point of view. Shortly after news reached France, Manet set to work. And after completing the final version, came up against an official ban on exhibiting it.

There is still (unfortunately) a thrill to be got from linking any art with political activity, and this exhibition - subtitled 'Painting, Politics and Censorship' - is rather too tickled by the idea. It is not surprising for an artist to be engaged with contemporary politics, and, though censorship may excite outsiders, for a working artist who wants his pictures shown, it is more an annoyance than part of a political struggle. Besides, Manet is not obviously a struggler. These paintings can be placed in a series of notable artistic responses to political violence, from Goya to Picasso. But the curious thing about them is how unresponsive they are. In their treatment of both victims and executioners, they are remarkably deadpan.

Goya's Fourth of May, for instance, is probably a source for Manet. But there the protagonist is one of the victims, raising his arms in a crucified gesture. The firing squad is a line of anonymous, malevolent figures, lurching forward. Manet's squad is also anonymous. But, as becomes clear in the final version, they remain the central figures. And their violence is breezily casual. There is no feeling of attack, or of recoil among the riflemen. They fire coolly and steadily.

The spacing of the action is most odd. The Emperor and his two supporters seem to be at almost point-blank range - or would be, if they were in the firing line at all, which isn't clear. The effect is of men being fired through, rather than at, simply 'blown away' in the fusillade. They are painted in very low definition, and with no gestures of tragedy or martyrdom. Maximilian is allowed perhaps a calm dignity, barely distinguishable from helpless passivity. He hardly rises to the occasion: it is how Mr Pooter would face death, neither hero nor villain, but merely the fall- guy. The gesture that takes Manet's interest is the splayed grip of the soldier on the right, cocking his rifle for the coup de grace. It is an outrage, but a job being done with admirable efficiency.

And what a fine body of men this firing squad is. The political event provided the initial impulse for Manet, but the squad came to win all his attention. In his first version he imagined the executioners as a band of Mexican irregulars in sombreros. But later information arrived that the Mexican soldiers, with a pleasant irony, were in fact wearing French-style uniforms. Manet revised his scheme accordingly, and it was the making of the painting. Manet liked smart uniforms (the cute boy Piper, also in the show, being another case in point). And he paints a disciplined but dashing group, with baggy pantaloons, spats and dangling sabres, their feet at dandyish angles. It is, in a foppish way, a very pro-army picture - really rather in love with firing squads.

The beauty of the painting is at one with its insouciance. Manet's detachment is the most painful political gesture he could make, implicating the government and its disengagement from the adventure it started - packing up and moving out before the catastrophe. Manet gives the event the full works. At the same time he treats it as what it had become: a sideshow.

Alfred Sisley never suffered from the censor. In the last year of his life, the local police compiled a report on him, noting that 'his views do not seem to pose a threat to national security'. He was applying, not for the first time, for French nationality. Though his family was English, he stands chiefly as a French painter, and is known as the purest of the Impressionists. He was very much in with the set, but since his death in 1899, he has suffered a certain neglect. The 60 paintings - almost all landscapes - at the Royal Academy constitute his first retrospective. A surprising omission perhaps, but then being the purest of the Impressionists reveals in fact how limited the Impressionist project is. And as a landscape painter, Sisley's 'views' do not offer much of a threat to, or a purchase on, anything.

The pre-Impressionist paintings from the 1860s are the best, and show the point. In one of these, the (very distant) View of Montmartre of 1869, a row of saplings, trussed with supports, occupies the foreground almost like human protagonists. The picture treats trees as things which have a history - vulnerable in their beginnings, though 40 years later this view will be unrecognisable - and which involve human help and planning. It is just this kind of point that Impressionism loses.

In its pursuit of the light and air of the moment, Impressionism is a leveller, blurring any interest in the substance of things, their uses or pasts or futures, or in places as places of work or habitation or even play. A few years later you find a river-bank scene such as Fishermen Spreading Their Nets (1872). Though you can attend, say, to what the fishermen are up to, it feels perverse to do so: the whole tendency of the painting discourages this, dissolving all into that atmospheric unity which Sisley achieves so well. He produces an infinitely continuable sequence of rivers, fields, country and suburban roads. They repay a long look, full of small beauties and surprises, a sure sense of colour and composition. And? And? One always senses a point that is never reached - though a writer in the catalogue argues that Sisley's retiring approach to the world is a model of ecological care, which is certainly ingenious.

Manet: National Gallery (071-839 3526), to 27 Sept. Sisley: Royal Academy (439 7438), to 18 Oct.