Maj. Louis Anatole LaGarde and Capt. John T. Thompson tried to settle the debate in 1904, when they took a variety of handguns onto the killing floor of a Chicago stockyard, shot 13 cows, and used their test results to recommend the .45 caliber pistol as the standard sidearm of American military officers. Among the six rejected guns was a 9 millimeter Luger.

Four wars and 79 years later, the debate over the relative merits of .45 caliber and 9 mm pistols is raging anew, this time on the floors of Congress. In military procurement terms, it's a flyspeck of an issue, a mere $200 million or so in a weapons budget of billions. But even in a nuclear age, when strategic debates focus on killing cities, not cows, handguns can generate a remarkable amount of congressional heat.

The combatants in this new duel are the partisans of the Colt .45 (formally known as the .45 M1911 A1)--the weapon of Mike Hammer, World War II tankers and 237,790 members of the United States armed forces--and those who favor the 9 mm pistol, the weapon of James Bond, the elite Navy SEALS and almost all the other NATO forces.

The duel began in 1978, when investigators for the House Appropriations Committee found there were more than 25 different makes and models of sidearms and 100 types of ammunition in military armories. "Standardize," the committee told the Defense Department.

Over the next two years, the Pentagon checked its inventory, appointed a panel to study the issue and recommended switching to a gun that would fire NATO's standard ammunition. The estimated cost for the guns alone was $125 million, and the most likely candidate was the Beretta 9 mm--an Italian gun whose purchase would help quiet complaints of NATO allies that the United States was hogging NATO's military procurement contracts.

Then the House Armed Services Committee got into the act, asking, among other things, why the military should spend all that money when no one had shown there was anything wrong with the old .45s. Why couldn't the .45s be refitted--by U.S. firms--to shoot 9 mm ammunition, at a fraction of the cost of buying 400,000 new guns? When holsters, belts and accessories were added to the conversion costs, one Armed Services staffer figured, total costs would run close to $230 million.

Over the months, pages and pages of testimony were transcribed covering the relative accuracy (the 9 mm came out ahead), reliability (again the 9 mm), weight (the 9 mm Beretta weighs a pound less than the .45) and "stopping power" of the weapons (tradition favors the .45).

And the positions hardened. The Appropriations subcommittee on defense, headed by Rep. Joseph P. Addabbo (D-N.Y.), wanted to have a 9 mm as the standardized weapon; the Pentagon wanted a new 9 mm pistol that would accommodate a silencer, would continue to work after being immersed in sand or mud and would hold more rounds than the seven in the clip of a .45; the Armed Services Committee questioned the cost and urgency of the whole business.

Pentagon officials testifying before the House Armed Services subcommittee on investigations have conceded several times that the sidearm switchover is a "low priority" and the cost of changing would be greater than maintaining the current inventory.

In June, 1981, the Pentagon spelled out the criteria the new gun would have to meet. Four gunmakers, including Beretta, prepared prototypes for a test in February, 1982. All four failed--though the Beretta did better than any of the others--and the Army canceled the 9 mm procurement order pushed by Appropriations.

Armed Services, some of whose members believed that the criteria were designed to favor the Beretta, weren't particularly upset. But over in Appropriations, Addabbo screamed foul, charging the Army with "footdragging," and hinting that behind their bland statements of support for the 9 mm, the Army munitions men were closet .45 fanciers.

He then led the subcommittee in eliminating $7 million earmarked for .45 ammunition in the fiscal 1983 budget and another $1 million for spare parts for the gun. If the Army got in gear on 9 mm procurement, the committee report said, they might get their money back.

Armed Services had no choice but to give in and authorize $3.9 million for 9 mm handgun procurement in the fiscal 1984 budget--asking, at the same time, that the Pentagon tell Congress what it plans to do with the old .45s. A new document delineating requirements for the handgun was developed last summer, and an Army spokesman said yesterday that a new acquisition plan "is currently being staffed . . . .

"Where we stand right now is in support of the 9 mm handgun," the Army spokesman said.