WASHINGTON GOES TO WAR; By David Brinkley; Knopf; 286 pages; $18.85.

Washington in the early 1940s was a city with too little air conditioning and not enough of almost everything else. Housing, typewriters, racial tolerance (especially racial tolerance): There was no shortage of shortages.Two things the capital did have in abundance, however: 15,000 outdoor privies and more than the usual quota of congressional buffoons. (Nebraska Sen. Kenneth Wherry, for example, "liked to boast that he was an embalmer licensed in not one but three Midwestern states.") Yet this was the city fated to lead the greatest military effort in history. As David Brinkley memorably puts it, Washington on Dec. 8, 1941, was "a rummage sale called to war."

It's one of the all-time castings against type, and Brinkley has a fine time with it: "a sort of `Our Town' at war, the story of a city astonished and often confused to find itself at the center of a worldwide conflict without ever hearing a shot fired."

He makes no great claims for "Washington Goes to War" it "is less a work of history than of personal reminiscence and reflection. Essentially, it is an account of my own observations and experiences in wartime Washington, supplemented by material drawn from interviews and other sources" but he has cobbled it together with affection and skill.

The sour-lovable manner Brinkley has perfected on television perfectly suits the sour-lovable story he has to tell. He practices a kind of gimlet-eyed nostalgia: Having been there himself, he remembers how nice it could be and knows how awful it usually was. There are inches of poignance to keep in line the yards of comedy, and vice versa.

Much of the comedy issued from a "a state of unreadiness that at times seemed hilarious but that actually was pathetic." Consider George Patton taking over a brigade of the 2nd Armored Division, and finding not only hundreds of tanks disabled for lack of nuts and bolts, but a supply service unable to provide them. So Patton called Sears, Roebuck. They had what he needed they delivered, too but he had to pay for it out of his own pocket.

The outbreak of war put the Secret Service in need of "an armored, bulletproof limousine for the president's protection." How to procure one, though, when federal regulations forbade the purchase of any automobile costing more than $750? Well, there was this car already in the Treasury Department's possession, and it fit the bill to perfection. "I hope Mr. Capone won't mind," FDR said when informed of the identity of its gangster-owner.

As such stories suggest, "Washington Goes to War" is largely a book of anecdotes. In addition to Embassy Row and official Washington, there are story-filled chapters devoted to the press, Congress, high society and (deadliest of all battles waged in wartime Washington) housing. The result is a lazy evening of good talk fueled by even better stories. Like most lazy evenings, it rambles and flags now and then, but divertingly so.