Long shot for gunboat diplomacy?

With nearly a dozen booming rounds from the largest conventional deck guns in the United States Navy's arsenal, President Reagan has driven home his vow to stand tough against Soviet-allied Syria in Lebanon.

The question in the minds of foreign diplomats and Arab analysts here is whether Wednesday's action may usher in an increasingly self-propelled escalation in the US-Syrian rivalry. US sources raised another possible problem: that the actual firing of the big guns might prove to be less effective than keeping them in reserve as an implied threat of escalation in the standoff with Syria.

The recently toughened US stance toward Syrian forces in Lebanon has failed visibly to win greater cooperation from Damascus in the Lebanese government's bid to reestablish control. Syria has also defied US demands to stop firing on US reconnaissance jets.

And it was thought likely here that, following Wednesday's shelling, US Marine ground positions near Beirut airport would at least come under heavy artillery fire from the Syrian-controlled areas near the capital.

So far the Syrians and their Soviet military patrons have seemed leery of pushing things too far. Syria has stopped short of greatly escalated, direct military action against the American forces - for instance, from trying to fire on the US Sixth Fleet off Lebanon.

The shelling - the first use of the mammoth 16-inch cannons of the USS New Jersey since US marines arrived in Lebanon more than a year ago - came exactly 10 days after a similar first in the US-Syrian rivalry. On Dec. 4, the Americans unleashed their air power for the first time, striking at Syrian targets in the hills northeast of Beirut.

Both the shelling and the earlier air strike followed alleged Syrian antiaircraft fire on US reconnaissance flights inland from Beirut. In the air strike, two US planes were lost. But administration officials promptly declared US determination to respond forcefully to any further fire on reconnaissance jets. The Syrians made it clear they would keep firing.

The New Jersey is said to have fired at least 11 of its one-ton shells on targets in Syrian-controlled territory in the hills east of Beirut. Each shell is capable of flattening an area larger than two football fields, leaving a crater some 50 feet around and 20 feet deep. The precise targets of the shelling were not immediately known.

The New Jersey and its giant guns have taken on an almost legendary image for the Lebanese - with front-page photos of the 16-inch guns in local newspapers helping things along. The ship has become something of a symbol of at least theoretical US ability to overwhelm opposition in Lebanon if and when initial rules of restraint fell by the wayside.

Now that the New Jersey's 16-inchers have actually blasted away, local political analysts seem uncertain to what extent their theoretical value will translate into practical advantage against the Syrians.

''The hope,'' a pro-government Lebanese analyst says, ''is that by (the US) hitting the Syrians, Damascus and Moscow will be jolted into realizing the potentially serious danger of a head-on clash with the US.''

But as a US source added, ''Now we've run out of everything we've got. We've hit them with just about everything.''

Meanwhile, Syria's official news agency seemed to shed light on an issue that could determine Damascus's stance toward Washington: the health of recently hospitalized Syrian President Hafez Assad. The agency said Mr. Assad, who has not met any foreign visitor since about a month ago, received Saudi King Fahd in Damascus Wednesday.

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