AT THE MOMENT, the publishing business in Edinburgh is alive and kicking vigorously, despite some ominous medical signs. The city no longer needs to console itself with memories of the Scottish Enlightenment of the late 18th century, when it was the most exciting intellectual center of the English-speaking, or at least English-writing, world; or of the great days of the Edinburgh Review in the early 19th century when Sydney Smith, Carlyle and Macaulay wielded stiletto, hammer and thunderbolt in endless profusion.

Although publishing, like the theatre, had owed much to hopes of a much more independent Scotland (dashed first by the Callaghan administration and then by Mrs. Thatcher, in spite of the 1979 referendum favoring a Scottish legislature), it seems stronger today than two years ago. The Scottish General Publishers Association, Edinburgh-based and Edinburgh-dominated, represents 41 publishing companies now. Eight of those firms will travel to the American Booksellers' Association convention in Atlanta at the end of May, and the SGPA will also be present. Even the recession which hurls more and more workers on the British dole, and the accompanying belt-tightening of the savagely monetarist Thatcher administration, are having surprisingly little effect.

In some ways, indeed, the strength of Edinburgh publishing lies in its smallness. The firms are tiny by most American and London standards, and both they and their clientele can have little use for the paraphernalia of expensive public relations, ostentatious displays of premises and merchandise, or the manic pursuit of trendiness such as mark so many London houses and leave them so vulnerable to British economic downswings. The city is small -- well below a million in population -- and is dominated by the University. It is hardly surprising that many of the youthful publishers started out as students, and that indeed the most unusual firm of the lot is run by the Edinburgh University Student Publications Board, marketing as Polygon Books, many of whose former members have gone on to play a considerable part in Scottish communications in general.

Two of the most enterprising publishing houses, Canongate and Mainstream, owe much of their rise to success to the work of one-time EUSPB leaders while the chairman of a third, Paul Harris of Paul Harris Publishing started his career while a student in Aberdeen. Finding he had a book based on his researches into pirate radio, the independent stations which illegally competed with the BBC in the late 1960s, he answered the indifference of London houses by becoming his own publisher and succeeding.

His next venture, still in his Aberdeen days, was made possible by a gruesome murder trial where the victim proved to be a voyeuristic husband who had incited his wife to countless variations on adultery for which she ultimately dispatched him with the assistance of a helpful policeman. Harris may find Edinburgh material less exotic, but one of his most recent successes have been to persuade Allan Massie, Scottish novelist and critic, to write a book of essays on five famous Edinburgh murders. The results are said to be superior to the work of such popular criminologists as William Bolitho, Alexander Woolcott and even the doyen of Scottish crime connoisseurs, William Roughead.

The Edinburgh trade, like the Edinburgh public, likes to think of itself as cosmopolitan and self-aware, and the city's culture has been exciting enough to justify local emphasis. The great poet Hugh MacDiarmid, who died in 1978, still draws markets for spin-off products, varying from Gordon Wright Publishing's majestic pictorial biography to Mainstream's recent collection of critical essays whose contributors ranged from front-rank political reporters to such academic critics as David Daiches. Mainstream has also won attention by a recent history of literary Edinburgh.

Dr. Johnson's nasty remark about the finest prospect a Scotchman saw being the road to London still haunts the city. It's far from being completely true: Edinburgh books find local publishers and audiences, and Edinburgh plays find directors, not because they are not up to London standards, so much as that the metropolis suffers from its own parochialism and slavishness to passing fads. Certainly Edinburgh audiences have in the past glorified the parish pump, but today they can at least claim to be looking at the parish reservoir.

But London still beckons to Edinburgh's detriment. The big names continue to seek big publishing names, and success may mean departure. Canongate won international acclaim for Colin Douglas, an Edinburgh doctor, whose mordantly satirical novels of medical life were paperbacked by agreement with Fontana: but for his latest offering he has gone to the mammoth London house of Hutchinson. On the other hand, Mainstream are now republishing the novels of James Kennaway, a remarkable Scottish novelist of the '60s, whose first work, Tunes of Glory, was filmed with enormous success starring Alec Guinness, John Mills and Dennis Price, but whose reputation declined after his accidental death in 1968. Major names in the British literary scene have contributed enthusiastic introductions, and Mainstream hopes that what may have been Kennaway's initial disadvantage -- his extraordinary variation in style and method -- will prove his title to ultimate endurance. Nor is the publishing accent simply on human success. The students at Polygon have recently brought out Odyssey, based on a set of radio programs incorporating oral recollections of Scotland's past from ordinary people: it challenges comparison with Walker Evans and James Agee's Let Us Now Praise Famous Men.

The cosmopolitanism is no mere aspiration. Harris is bringing out a study of Bob Dylan by John Herdman, a young Scottish writer of remarkable economy and insight. Editors at Canongate are currently revelling in an extraordinary triumph, Alasdair Gray's Lanark, which London critics have grudgingly placed alongside Tolkien both for the originality of its intricate, explosive and mind-shattering fantasy, and for the cult it is likely to produce. Polygon's quarterly, the New Edinburgh Review, stretches its net so wide that it is probably the last journal to which Henry Miller contributed in his lifetime; indeed death and publication raced each other. Edinburgh University Press has won particular laurels in the field of Africa, drawing heavily on the University's expertise and links therein. The press, however, has to look to those laurels: academic writing in a popular vein can find a Scottish readership if sufficient work goes into editing and marketing, as a variety of houses have shown, such as John Donald with its impressive list in Scottish history, often stressing events of universal relevance, notably the Highland clearances and the labor struggles that culminated in Red Clydeside.

Edinburgh is a place where books are bought on reflection rather than on impulse, where bookshops, new and secondhand, cater more for the book-hunter than the hurried consumer, where old loyalties play a greater part in the business of book purchasing than the lure of current TV idols. Still the paperback market is supreme, and it is almost entirely non-Scottish, however Scottish the origin of its authors and even publications. The students at Polygon did manage to combine the best of both worlds when they ventured into paperback to reissue John Buchan's Huntingtower, helped by a television serial, and sold some 7,000 copies. On the same lines they have more recently combined the old, the Scottish, the popular and the unexpected by producing a work whose content had been lost to sight -- The Edinburgh Stories of Conan Doyle, headed by a forgotten Sherlock Holmes squib which he wrote for the Edinburgh Student. But this time, they settled for the security of a hardback.

Edinburgh's real case as a publishing capital is that it is producing culturally important material which finds its initial success at home. But for all of their Edinburgh loyalties, the publishers still sigh for hitting the international jackpot -- and that means getting the world to listen to Edinburgh with some of the attention it gave it in the l8th century.