THE INCREASINGLY serious armed conflict between South and North Yemen and both Saudi Arabia's and the United States concern that their "ally," North Yemen, might soon join Iran in the ranks of overwhelmed client states was reported in The Washington Post last week.

Much of the anxiety centers on the fate of Bab al-Mandab Strait, "the 15-mile-wide entrance to the Red Sea passage between the Suex Canal and the Indian Ocean," a strait over which the South Yemenites already exercise substantial control.

In the same edition of the newspaper there is a story in which readers are reassured that, recent remarks by Secrearies James Schlesinger and Harold Brown to the contrary notwithstanding, the United States has no intention at this time of sending troops to protect its oil sources or generally "stabilize" the maelstrom of Mideastern politics.

Perhaps President Carter, daily accused of irresolution and fecklessness by critics right and left, might take some consolation in learning that he would not even have to consider sending troops to the Straits of Bab alMandab had a previous administration shown sufficient foresight.

Letters buried in the papers of Hamilton Fish in the Library of Congress reveal what now looks like an extraordinary blunder committed 105 years ago. In the summer of 1874, George H. Boker, a minor literary light from Philadelphia and U.S. minister to Turkey, wrote Fish, U.S. Grant's sevretary of state, describing an American opportunity to gain control over these strategically located straits. Three Frenchmen, Boker wrote, proposed to him "the ceding to the United States of all the land lying around the Cape of Babelmandeb, which they have purchased and hold by the same title by which the English possess Aiden [sic].

"A look at the map," he continued urgently, "will show you the genographical importance of the position, as a coaling and a watering station for a fleet, besides enabling its owner to shut up the mouth of the Red Sea at pleasure." Further wondrous benefits would include control of "the entire trade of Mocha" and the possibility of opening up "a large commerce with Abyssinia."

Boker told the Frenchmen that he would send "the whole scheme" for Fish's consideration, along with relevant maps, charts and so forth.

He admonished Fish to jump at the chance:

"For an ambitious nation, here is a wonderful opportunity to make a mark, and to command a spot of little less importance to the world than Gibraltar." Nonetheless, he feared that the 30th secretary of state would refuse to deal and that the hated British would get the territory, "but it makes my blood boil to think that everything worth having, beyond national landmarks, is falling into the hands of that Power, while all the rest of the nations look tamely on."

BOKER'S PETITION went to a man little known for desires to make waves, let alone to expand American possessions so far away. What is also little known is that this Hudson River aristocrat owned a delicious streak of mirth. Wracked by pressing crises in Cuba, besieged by clamoring office seekers, doing what he sould to maintain some ambiance of recititude in a corrupt administration, Fish oviously relished the opportunity to reply to Boker. He responded on July 22, 1874:

"Yours of June 9th respecting the purchase of the Straits of Babelmandeb and the contiguous Continets, is engrossing serious attention.c He then urged caution: "before positively signing the contract, a careful examination of title will have to be made. By law, this examination can only be made by or under the direction of the Attorney General."

"I do not think that we can take any definite steps with regard to the Babelmandeb pubchase,c he continued, getting to the heart of the matter, "until after the completion of another purchase of great interest, and importance, of a site for an observatory on the reverse side of the Moon with the right of laying and maintaining a telegraph communication therewith from the Observatory in Washington. The proposition for a coaling station in the Coggia Comet," he added, "has met with little favor, perhaps by reason of the bashful retirement of the Comet while the Naval Engineers were sounding a passage to the proposed station. Babelmandeb, however -- no matter. Very faithfully yours, HAMILTON FISH."

So much for the amusing statesman's ability to see ahead a century! His loyal minister -- however unaware he might have been of the future need for Mideastern oil, of our current anxiety about Saudi security, of our fears of Soviet medding -- was instead disappointed at being unable to but the British "nose out of joint."

"I supposed," he wrote Fish on Aug. 18, "that you would poke fun at me for proposing to you the purchase of Babelmandeb," but he thought it had been his "duty to lay the matter before you in an unoffical way. How was I to know what use the Government might wish to make of the money that can be coined at a printing-press? Why not Bab-el-mandeb among other fancies? If the late Mr. Seward was permitted to furnish U. S. with a refrigerator, why should not you provide an oven?"

Boder, too, lived in an age of military retrenchment and concluded the matter with the remark that, "on the whole, I think it wise that we with our wretched little navy... should have nothing to do with distant possessions. Had I been in your position, I should have decided the question of Babelmandeb just as you have done. So exit Babelmandeb."

As Benjamin Franklin put it: For want of a nail the shoe is lost...