The Romantic JMW Turner was in deep sympathy with the scientists who forged the Industrial Revolution. Richard D North on two London shows that reveal a marriage of science and art
A new Turner is appearing. He is the man who saw more clearly and painted - even celebrated - the Industrial Revolution more certainly than anyone else. Can it be? The Turner of sea and sky, Romantic purveyor of the wild, in love with laboratories, furnaces and theorems? Well, yes it can.

We wander round the Turner and the Scientists exhibition at the Tate, curated by James Hamilton (more usually the part-time curator of all the University of Birmingham's collections) and it seems obvious. Rain, Steam and Speed - the Great Western Railway has it all: a fiery steam engine (its lollipop stick of a smokestack makes it comical only to us) charges across a bridge. Now, it looks quaint; then, its arch-work was a technical triumph.

Hamilton's catalogue makes the point that the depiction of big weather was far from coincidental. Brunel's critics had predicted that the bridge would not be able to support a train, but it did, in July 1839. "There were exceptional storms the following autumn and winter, and the bridge was again widely expected to collapse, but it did not," writes Hamilton. Turner captures the triumph.

There are plenty of such images to make Hamilton's main point. This is that the first third of the 19th century saw a passionate spirit of fraternity develop among the best of the country's scientists and the best of its painters. They met at London clubs such as the Athenaeum, of which Turner was a founder-member. Nearby, both sorts frequented the Royal Institution (devoted to the practical use of science) and the Royal Society (more committed to pure science). The Royal Academy for the arts and the Royal Society then shared a building, Somerset House. Hamilton sees this as powerfully symbolic of the way men such as Constable and Turner were constantly in touch with men of science such as Michael Faraday and Humphry Davy.

The vibrancy and vigour of it all are really inspiring. It had its practical side. The geologists, for instance, were delighted with painters and their new loves, accuracy and wild places: the best accounts of glaciers were in paintings (or there was

Turner's fine depiction of the convulsive rocks of Lulworth Cove). The painters hung around chemists to inquire how to make to better paints, around hydrologists to know how to codify weather better, and around technologists who could suggest optical devices the better to get truly accurate accounts of their subjects.

But something rather unexpected comes through. This is that both sets of people shared intense romantic feelings about the understandings that were emerging. Turner's friend, the populariser of science Mary Somerville, is typical in having a vision of the world that is giddy, almost unhinged, like an acid-head's or an adolescent's. In her "On the Connexion of the Physical Sciences", Chaos Theory is presaged and classical wisdom lurks: "In it [astronomy] we perceive the operation of a force which is mixed up with everything which exists on heaven or on earth; which pervades every atom, rules the motions of animate and inanimate beings, and is as sensible in the descent of a raindrop as in the falls of Niagara; in the weight of the air, as in the periods of the moon."

David Knight, of the University of Durham, the other day told a seminar at the Royal Institution, "Humphry Davy's vision was that forces, power and spirit matter more than matter itself". Justine Hopkins, of the University of Bristol, told the seminar how John "Mad" Martin (well and permanently represented at the Tate) painted an imagined world that was informed but also hugely revved-up by science.

But those early-19th-century visions were powerful because they were dark as well as fiery. Davy himself is a fine example. While still young he was ill, and perhaps prey to the heightened awareness of those who face death. He produced intense poetic writing: hallucinatory, Hamilton calls it. The rise and fall of civilisations was one of his great themes. Many of Turner's paintings were accompanied by bits of his "The Fallacies of Hope", which turned gloomily on the transience of human enterprises.

So beyond the intensity of feeling common to scientists and artists of the period (and so unlike the frosty formality we wrongly attribute to our forebears), there is the very reverse of triumphalism. This makes a second exhibition, Italy in the Age of Turner, at the Dulwich Art Gallery, doubly interesting. It shows wave after wave of painters trekking south in the relatively new comfort of mass tourism. But the images we have from their sorties - the classical ruins, the picturesque in Italy's modern life - are only superficially about order or gaiety. The new tourists acquired sombre baggage, too. The classical world had crumbled, its "project" (as moderns would say) vitiated. Its ruins were now inhabited by a superficially charming but in fact beggarly and squalid people. That was part of the excitement of the Tour, Grand or otherwise: Venice, for instance, was a disturbingly over-sexed repository of high civilisation's relics. Modern scholarship (the Yale University Press catalogue is a particularly rich seam) shows us how high culture and low life were twin draws to travel, and that the "sublime" included an almost deliberately fevered - almost neurotic - response.

Right from the start the importance of Turner is that his work contains so turbulent a range of responses which nonetheless never seem close to toppling over into the grotesque. In Rain, Steam and Speed a hare is seen, well, "haring" to escape the onrushing unnatural monster. Figures in a timeless pastoral scene are dimly seen mourning or admiring the new iron age. In The Fighting Temeraire (in which a steam tug tows a sailing ship to the scrapyard) we can admire either vessel, at will and alternately. The horrors and the glories of war conducted under wind power are replaced by the brilliant but functional new arts of peace.

The good thing about the new insights is that they allow a thoroughly nuanced view of this almost unbelievably vigorous and exciting period in our cultural history. Take Snow Storm - Steam-boat off a Harbour's Mouth Making Signals in Shallow Water and Going by the Lead, that most Turnerish of images, with the ship etched in a scene that is otherwise a mass of swirling sea and sky. Hamilton says that Turner's steam ships used to be taken as symbols of despair at modern man's hubris. "They aren't. The ships survive, they're getting through, they're coping. But it's not triumphalist, either". Other things in the show make the point: Turner liked life-saving devices - lighthouses, improved rescue kit - but didn't ever understate the force of the natural world in which they were useful.

It was Stephen Daniels, a brilliant cultural geographer at Nottingham University, who first really put this sort of feeling on the map, in his book Fields of Vision. He says, of both the artists and the scientists of the period, "There's always this millenarian undercurrent - that progress would overreach itself, maybe things aren't going to reach upwards and onwards for ever." Our own civilisation - gloriously technological and imperial - might collapse like all others before it. And the point is made, whether the artist is capturing the vitality of an industrial furnace (as Turner often did), or painting a Roman ruin.

Daniels says, "You're still dealing with an age which took religion and myth seriously. They're in awe of the new power but they're worried what the implications are and that this whole thing might blow up in their faces."

For James Hamilton, 1837 - when the Royal Academy left Somerset House - symbolises the beginning of the end of this special age. "That year marks the beginning of the tectonic shift which saw science and art move apart from each other," he declared at the seminar. The main impetus was that science had now developed specialisms and specialist languages. It grows alienatingly complex.

Arguably, the two camps have not grown apart en masse, so much as fractured. The lines of contact are there, but complicated. Modern young artists are still wrestling with the relations of man and nature, and probably know as much science as anyone else. Even the project of progress remains largely intact. What has gone is a clubbability, and a encyclopaedism: that sense that a person can know everyone, and everything, that matters. And the most striking difference between then and now? Surely it is that we are so much less emotional?

`Turner and the Scientists', Tate Gallery, until 21 June (0171-887 8000). `Italy in the Age of Turner: The garden of the world', Dulwich Picture Gallery, until 25 May (0181-693 5254)