BRITAIN SET UP shop in what is now known as South Yemen in 1839 and let go in 1967, in the interim imparting the taste for modernization that has helped make it increasingly hospitable to Soviet overtures in recent years. By contrast, Yemen, or North Yemen, languished under the Ottomans and later fell into the orbit of Saudi Arabia, also a feudal reason of this colonial legacy there are two Yemens: hostile, divergent in ideology and outlook, both of them strategic enough and weak enough to attract virtually ceaseless manipulation by external powers.

So it is that late in February, Russian, Cuban and East German advisers on the scene evidently encouraged South Yemeni forces to cross the border. The Saudis, frightened at the specter of Soviet expansionism on their back doorstep, called on the United States to supply more help to the North Yemenis in this small but nasty war.

Wisely, we think, the Carter administration decided it was not enough to warn the Russians, it was necessary to see that their South Yemeni cliemts are taught a lesson. In the post-Iran circumstances, the administration feels it must demonstrate it can compete effectively with Moscow at points where a Soviet challenge of American security interests forces a test.

So a carrier task force has been dispatched for the general messages that such shows of the flag can convey to adversaries and friends alike. Additional Military supplies are being provided demonstratively to North Yemen. Otherwise, the United States is undertaking consultations on a larger military presence in the whole Persian Gulf region and pushing for an Egyptian-Israeli peace as a new foundation for an enhanced free-world strategic stand.

North Yemen is an unlikely and, some would say, unworthy vehicle to be loaded with so much geopolitical freight. It is small, backward and unstable and not widely known as a champion of human rights. It cannot possibly absorb the hundreds of millions of dollars of American military equipment that the Saudis want to buy for it. The answer, we suppose, is to limit the gear actually sent to a level closer to what the Yemenis need and can use: in brief, to get on with the job.

The Arab League has undertaken a mediation effort. South Yemen has formally accepted, but the fighting continues: South Yemen attributes this to North Yemeni rebels. The hope must be that the new display of American resolve will help convince South Yemen to abandon this subterfuge and to put the Arab League's peace plan into effect.