A sightseeing tour of Washington conducted by Vinnard Parria, owner and founder of American Sightseeing Tours, is a stern test ot the mind's capacity to absorb and retain date.

The narrowest house in Washington, 1239 30th St. NW, is 11 feet wide. The Washington Monument is 558 feet 5-5/8 inches tall (an elevator ride to the top takes 90 seconds). The buttons on Abe Lincoln's coat - as rendered for the Lincoln Memorial by Daniel Chester French - are four inches in diameter.

But the number weighing most heavily on Vinnard Parris mind as he parks as empty tourbus outside the Museum of History and Technology, is $110,000. That's the asking price for a new bus he has just inspected. Not counting the smoked-glass skylights - are $8,000 option.

Parris decides it is an offer he can refuse, with or without skylights.

Vinnard Parris, who looks somehow like a minor vaudeville act with his red-white-and-blue bowtie, elongated smile and slicked-back hair, came to Washington from Colorado in 1929, just in time to complete his senior year of high school at Western High. With his mother and sister, he lived in a cottage erected on stilts adjoining Fletcher's Boat House in Georgetown. They paid about $500 for the cottage, he says, plus $20 a year to rent the site from the government.

Later the family went into the rooming house business downtown, buying a string of piperties across 6th Street from what is now Hecht's parking garage.

Parris worked his way through George Washington University and GW law school as, of all things, a butler in the Japanese Embassy - a job that lasted until the ambassador's remains and the ambassador's widow to California, where an American battleship was waiting to forward them to Japan.

"I asked his wife, 'Aren't you going to ride the battleship? Parris recalls." 'Oh no," she said. "I wouldn't want to detract from his glory."

Armed with a law degree - a shaky asset in the 1930s - he became a tour guide for the Gray Line, which hired him in tha fall of 1939, and put him through a four-week training program. But after a few months he quit to go into business for himself, buying a "32 Packard V-12 8-passenger limousine - "the same car," says Parris, "that Charles Evans Hughes had used when he was chief justice.

World War Two soon put Parris in uniform and his fleet of three limousines in mothballs, but when he returned, he reopened the sightseeing business at the same address.

The bus is about two-thirds full as Parris slips into the westbound flow of early afternoon traffic on Constitution Avenue. "This wasn't always called Constitution Avenue," says Parris over the bus's thunderous PA system. "It used to be called B Street."

When you are driving a 40-foot-long-by-8-foot-wide vehicle through downtown Washington, and the landmarks are packed together like MacDonald's french fries, brevity is unequivocally the soul of wit. There is no point in telling some juicy story about Blair House, for instance, if it means letting the statues in Lafayette Park slip past unackowledged.

Those statues in Lafayette Park are statues of the European luminaries who assisted the American colonies in their fight for independence, and Parris says Baron von Steuben is "the man who was probably more valuable to us than the rest for his help in training the Continental Army.

And oh yes, not to forget the White House. Orginally constructed of Virginia sandstone, which was, ironically, brown. Burned in the War of 1812, when Dolley Madison courageously rescued Gilbert Stuart's portrait of George Washington.

As we pass St. John's Episcopal Church and turn north onto 16th Street, Parris calls our attention to the ramp built to accommodate FDR's wheelchair. He points out the Soviet Embassy ("constructed by Mrs. Pullman of sleeping car frame") the National Rifle. Association ("probably one of the strongest lobbies in Washington"), the horse-borne statue of General Winfield Scott (whose preportions, compared to those of his horse, are said to have inspired the exclamation, "Great Scott" says Parris, the Brookings Institution (whose "Brilliant men have aided the government with atomic energy and so forth") and the statue of Gen. Philip Sheridan ("that's the work of Philip Sheridan - it's the ork of Gutzon Borglum").

After a brief turn through George town - including a glimpse of the house briefly owned and still more briefly occupied by Jacqueline Kennedy in 1964 - the horison is suddenly overwhelmed by the Watergate complex, and Parris aims an index finger at the stretch of toothy balustrade behind which once dwelled the legendary John and Martha Mitchell.

At the Lincoin Memorial, we disern bark for a 15-minute on-site inspection, informed up front that the memorial's columns, which appear vertical, actually incline slightly inward, because if they were vertical (architeet Francis Bacon is said to have feared) they would seem to bulge at the top.

Parris, about to catch a plane to a tour guides' convention in Florida, stands outside the bus and bids fare well to his charges, the red-white and blue bowtie sparkling in the late afternoon sun.

To the tourists, however, he is only "Charley", a veteran emplye of the firm. He introduces himself this way because the figures it will make them more comfortable than knowing that their escort is the company president.

As a result, according to his son John, after a group of demonstrating farmers took the tour last spring, one of them called up and said, "You've got to give Charley a raise."