BISMARK PROPOSED a characteristically blunt solution for the vexing problem of the Irish: Let them trade places with the Dutch. The Dutch would then turn Ireland into a verdant garden; the Irish would forget to mend the dikes and drown.

One hundred years on, and the six countries of Northern Ireland - Ulster - seem no nearer to an answer for a problem that has plagued the place over four centuries - though a glimmer of a twinkle of a shadow of hope has emerged.

Ulster is still a community at war with itself, still divided between two tribes labeled Protestant and Catholic. The British gave up the 26 overwhelmingly Catholic countries to the South a half century ago. Now London has exhausted its limited stock of ideas for the North, still attached to the sometimes United Kingdom.

London's last, best plan, a local government sharing power between representatives of the half million Catholics and million Protestants, collapsed five years ago. Protestant workers brought it down with a strike, and they still impose a veto over any change in a status quo that preserves their near-monopoly of the best jobs in the dismal place. Protestant workers have the keenest vested interest in things as they are; they will not be moved, without cause.

Innocent Irish-Americans, who know little of the place, cling to the romantic belief that things will be solved if only the British pull out the 10,000 to 15,000 troops that police Ulster with a heavy hand. This, of course, is also the objective of the Irish Republican Army, the IRA, whose endless capacity to recruit gunmen and bombers from alienated Catholic youths surprises only the equally innocent British Army, press and politicians.

But withdrawal as an answer is regarded as mischievous nonsense by the vast majority of Catholics, more realistic than myth allows, in both the North and the South.

They know that a pullout would only strengthen the status quo, reinforcing the Protestant ascendancy in which Protestant workers enjoy so keen a stake. Ulster's Catholics would either yield or get out. The latter course would virtually ensure creation of a nasty, brutish, all-Protestant state, bristling behind the armed borders of perhaps 4 1/2 counties. It would likely spur the creation of an equally nasty, militarist state in an enlarged South, the "malign solution" of Conor Cruise O'Brien.

Ammost unnoticed, however, this bleak tableau has been broken. It is now possible for the first time to at least conceive of a way out of the dilemma, a route paved by economic circumstances and not by the blueprints of politicans, gunmen or romantics.

The way out lies in the astonishing burst of economic activity in the South, in the Dublin Republic. There, a wave of prosperity is bringing industrial plants and more to the soft, green countryside, a phenomenon noticed and exploited by the U.S. multinationals that are profiting handsomely from it.

The simple fact is that the Republic has been the growth star of the Common Market for the last two years and is virtually certain to repeat that performance again this year.

Over the three years (1979 is forecast), Irish production of goods and services will have increased at a yearly rate of 5.5 percent. This is about twice the level for the other eight, advanced Market members. It will be well above the 3.2 percent pace for West Germany, the number two state.

At the same time, Northern Ireland, like New England, tied to manufactures best made in the Third World - shipbuilding, textile machinery and more - is stagnating. Once the Protestant-controlled North could look down on its poorer country cousins in the South. Those days are over. Sometime this year or next, income per head in the South will probably pass that in the North.

Economics rarely figure in the songs, symbols and slogans that inflame Irish patriots on both sides of the sectarian divide and their co-tribalists across the waters. But jobs matter. Ulster's Protestant workers can't yield to the minimum demand of Ulster's Catholics, equal rights. That would threaten the Protestant workers' virtual monopoly of the better jobs in shipbuilding, machine tools, the police, civil service and more.

Jobs are more than a stream of income in Ulster. They are a legacy as well, at least in industry, where they are passed from father to son, from uncle to nephew. As unemployment, already above 10 percent in the North, increases, the pressure to hang on increases geometrically.

Loyalty to the half crown

To be sure, the Ulster problem is greater than economics. There are deeply rooted prejudices and hatreds, endlessly inflamed by the latest atrocity. The Protestants regard Catholics as lazy, incontinent, dirty, welfare loafers. Catholics see Protestants as cold, merciless, mercenary. But this is the penumbra. The core is jobs, Protestant jobs. That is why the border and the Protestant ascendancy must be maintained.

But if Irish prosperity continues - and there is reason to think it could - then the reason for border and ascendancy gradually disappear.

The sources of development in the Republic are easy to identify, at least after the fact. They lie in relatively cheap land and labor by European stanstandards, tariff-free entry to the Common Market's affluent consumers, massive subsidies to draw foreign industry to profit from this market, and the Rube Goldberg arrangements designed by Brussels to make rich farmers richer.

Traditionally impoverished Irish farmers are no longer so. They collect nearly $500 million a year from Brussels and are assured a floor under their prices and markets for their produce among the richer eight Market members. To be sure, Irish farming began to lift off six years before Market entry, as early as 1967 (reaching levels topped only by Bismarck's Dutch). Now this sector can look forward to more and increasing amounts of the same.

Industrial growth is even more impressive - except to ecologists, the unthinking left and lace curtain Irish-Americans who now must turn to Central America for maids. Industrial output in the South has risen 2.5 times as fast as in the North over the last 20 years. Manufacturing jobs in the Republic have risen by 30,000, while 47,000 disappeared in Ulster.

The pickings in the South are very good indeed, just as they were in Mississippi and South Carolina 20 years ago. Dublin uses the techniques of Jackson and Columbia to draw the plants. Export profits (and virtually all manufacture by foreigners is for export to the Market) go untaxed until 1981 and get a bargain rate thereafter. Plants, land and the training of farm woekers for assembly lines is financed to a large extent by Irish taxpayers. A mostly literate and numerate labor force (although a very fractious one) helsp enormously.

The last time I dropped in on the Merck plant at Tipperary, output per worker was 80 percent of that in Rahway (with pay about half), and general manager Joe Donahue of Philadelphia expected to draw even next year. Profits for U.S. plants in Ireland are nearly 30 percent of their subsidized investment, more than twice the rate at home and a third better than in Germany.

Well-off American tourists of Irish extraction may deplore the despoilation of the countryside. But that does not impress the former farm worker who made less than $50 a week and now earns $200 mixing chemicals.

If growth continues, the Republic is likely to reduce its high unemployment - close to the Ulster rate and just under 10 percent - and even run short of labor. As jobs grow scarcer in the North, there will be a move South. First Catholics, then Protestants will give up their grim rowhouse ghettoes for the better life. As hard-headed Protestants sometimes say, "Our loyalty is to the half crown, not the Crown."

A slender supposition

Inevitably, this would compel forms of cooperation between the governing authorities on both sides of the border, such as that which now exists between banks, agricultural agencies and even police. There would have to be joint approaches for immigrants, taxes, welfare, pensions and all the other minutia of everyday life.

There is no reason to believe that even hard-headed Protestants would yield what remains of their sentimental links to Britain, to the Union Jack that many workers in the shipyard place at their workbenches. Sensible Catholic politicians understand this. Already, Garret Fitzergald, the imaginative leader of the Republic's opposition party, has proposed a confederal arrangement to give all Irishmen citizenship rights in a triple sovereignty - Ireland, Ulster and Britain. The Dublin premier, shrewd Jack Lynch, has given this notion his typically Delphic blessing.

Industrial prosperity would undermine the myths. Industry and rationalization mean secularization all over the globe, and the easily available imported contraceptives in Dublin show the Irish are no exception. So the customs that Ulster Protestants find so repugnant - no divorce, no sale of contraceptives, education by church - are likely to dissolve.

(Ulster's fundamentalist Protestants are as hostile to abortion as the Republic's rural and older Catholics, so this is less of an issue. Anyway, everybody goes to England on the National Health to dispose of unwanted babies.)

Prosperity, in sum, could, over time, dissolve the border's reason for being and attenuate sterotypes that give it legitimacy. Alsace-Lorraine and Kashmir were once hopeless problems, too. Time and other concerns turn attention elsewhere.

To be sure, all this superstructure rests on a slender base of supposition - the continued Irish economic miracle. There is nothing foreordained about this. World stagflation, fueled by energy prices determined through twin cartels both bent on curbing supply, could choke the Republic's prospects.

The killings in Ulster could continue, the two communities could cherish their mutual hate. Irish-American contractors, journalists and others could enjoy unspoiled country inns, all the while easing their conscience with moral and more tangible support for the gunmen and bombers who have so enriched Irish drama and poetry. CAPTION: Picture, Continued growth is expected in Irish agriculture.