AS THE U.S. government's public debt approaches $3.4 trillion, it seems logical to assume that every vestige of fluff and fun would have been chopped from the budget a long time ago.

But federal ax wielders are an unpredictable group, and collectively they seem to have a whimsical streak. How else to account for government programs that provide free help in fighting a speeding ticket, free birthday and anniversary cards from the White House, inexpensive aerial photos and all kinds of free or cheap classes and workshops?

Those are but a fraction of the little-known, unusual goods and services offered by the federal government. Matthew Lesko, who lives and works in Kensington, has made a livelihood of ferreting out such federal freebies. He's produced a fat paperback reference work called "Lesko's Info-Power," which is designed to make readers think of the government as approachable, competent and -- brace yourself -- generous.

Most Americans don't ever dream of asking the government for unusual kinds of help and information, according to Lesko.

"People have this attitude: 'I don't count,' " he says. "They're used to thinking nothing good ever comes from the government. They see it merely as a tax collector."

Virtually all of the free and cheap programs are informational -- pamphlets, reports, hotlines, clearinghouses, experts who give advice over the phone, bureaucrats and military officers who give speeches or slide shows. Most of the subject matter covered by these sources is dryly technical stuff -- photovoltaic energy, Congressional Budget Office reports, radioactive waste management. But if you search with an eye toward amusement, as I did, the federal government offers some juicy surprises.$10 GENEALOGY WORKSHOPS

This is probably a good place to mention that not all federal freebie and cheapie programs are totally underwritten by your tax dollars. Many government agencies have their own trust funds that solicit donations from private sources. By drawing on this money instead of regular operating funds, the agencies are able to tempt the public with goodies that budget-cutters might look askance on.

The National Archives and Records Administration offers a textbook example with its genealogy workshops. Partly funded by the National Archives Trust Fund, the workshops are designed to teach people how to use the Archives and other records repositories to find out about their forbears. Three-hour workshops, offered 32 times a year, cost $10 apiece. A six-day course, offered once a year, costs $85.

Archives workshops accommodate researchers of all kinds. For example, the one scheduled for Saturday is aimed at novices. The lecturer will discuss how to get started and where to look for resources in this area. Participants in a workshop to be held Tuesday will learn how to organize, file, document and cite genealogical research.

Wayne Cook, an Archives employee who has conducted many workshops as well as the six-day course, says, "I try to encourage the public to not just sit at home and mull over their scattered notes, but to fashion them into something that's going to be a valuable legacy to future generations."

The legacy could be as small as a compact family tree or as big as a book on a family's history. The workshops are much-needed because amateur researchers can obtain only rudimentary assistance from Archives employees in the public research rooms.

"I've found {those employees} to be helpful but overworked," says Ray Smoot, a genealogical hobbyist. "Often they're quite, quite busy. It really helps if you can take some of the Archives' educational programs because you're much more able to do things for yourself."

Smoot took his first course, a four-day session, three years ago. He recalls being staggered by the amount of information the students were offered.

"It really was mind-boggling," he says. "I got the feeling that most of {the fellow participants} were thrilled with the materials they got . . . . I'm glad to see it's been expanded to six days now, because there was so much material that sometimes it got to be a little overwhelming."

But not too overwhelming. Smoot has since enrolled in several three-hour workshops.

"I'm still doing a lot of research," he says. "I'm working on several different {ancestral} lines. At the moment I'm into the Colonial era."

Smoot says he recently was pleased to discover that one of his ancestors was James Madison's godfather.

To find out about future workshops and other Archives activities, get yourself put on the mailing list for the free monthly events calendar. Write to the Office of Public Affairs NSE-I, National Archives, Washington, DC 20408, or call Wayne Cook at 202/724-0457.NEWSREEL COPIES

Another great bargain from the National Archives: old newsreels.

Tucked away in a snug corner of the ground floor of the Archives is the motion picture, sound and video branch. The collection there, immense and well-catalogued, is worth perusing even if you don't intend to copy anything for your personal use. The rich cache includes everything from sound recordings of oral arguments presented before the U.S. Supreme Court to "USAF Project Blue Book," a 90-minute documentary about an Air Force investigation into flying saucers.

If you do want to make a video or audio duplicate, and you have a VHS or audio tape recorder, you're in luck. A large portion of the collection is in the public domain, so you needn't seek permission from a copyright holder. And do-it-yourself dubbing is free.

Polly Pettit, an independent motion picture researcher, says the most popular part of the collection is the Universal Newsreel Library. Thousands of 7- to 10-minute features, all replicated on videotape for easy access, were made between 1929 and 1967. Professional producers dip into them frequently to spice documentaries, feature films and TV commercials, and you can do so just for a cheap thrill.

"You could get the newsreel for the date of your birth or the date of your parents' anniversary," says Pettit. (Actually, it might not be the exact date, as Universal Pictures produced only two newsreels a week.) "You get a news event, a sports story, an offbeat human-interest story and some kind of fashion story."

Archives workers typically will help you find things in the collections, but they don't have time to guide you through the dubbing process. According to Pettit, they will give you basic instructions on how to hook your machine up -- the rest is up to you.

The branch's supply of playback equipment is small relative to demand, so you can't simply breeze in and expect to tape at your leisure.

Instead, spend a visit or two familiarizing yourself with the collection's contents. Make an appointment to screen or listen to material you might want to dub. Usually you can reserve a machine the day before you need it. Find out from a staffer what kind of cable you'll need to hook your recorder to the Archives' machines. Then make another appointment to do the copying.

To explore any part of the Archives you must obtain a researcher's card in Room 207; enter at the Pennsylvania Avenue entrance, between Seventh and Eighth streets NW. For information about the Archives' motion picture, sound and video branch, call 202/501-5449.TICKET-BEATING TIPS

By sending a request to the Law Enforcement Standards Laboratory (National Institute of Standards and Technology, Gaithersburg, MD 20899), you can get a free copy of "Police Traffic Radar," a 31-page report containing authoritative information on the weaknesses and flaws of radar devices that measure car speed. Quoting from the report in court is no guarantee you'll beat a ticket, of course, but Lesko says he has heard from plenty of people who claim to have done just that.

Arizona resident Elaine Hendricks had obtained her copy of the report not long before her husband got a $60 speeding ticket in Phoenix in 1988. As the cop handed over the summons, Hendricks asked which measurement system he was using. He said it was VASCAR Plus, a system not covered by "Police Traffic Radar."

Preparing for court, Hendricks called the lab in Gaithersburg (301/975-2757) for help. An engineer promptly came to the phone.

"He was very helpful and friendly," Hendricks recalls. "He explained to me how {VASCAR} worked and said there weren't really flaws in the system, and that the only loophole might be the training the officer had received."

In traffic court, Hendricks learned that the officer in question regularly trained other state cops in the use of VASCAR. Undaunted, she asked when he had last been recertified. A few years earlier, he said, and then acknowledged that yearly recertification was standard for Arizona police. Bingo.

"The judge felt that conceivably the officer could have made some sort of error in monitoring the speed," Hendricks says, "and he dismissed the case."SCIENCE DEMONSTRATIONS

Those huge-screen Imax movies at the Samuel P. Langley Theater in the National Air and Space Museum are loads of fun. And at $2.75 a ticket ($1.75 for kids and seniors), they qualify as a great government bargain. But they're so famous already that dwelling on them here is certainly superfluous.

However, directly across from the theater, in Gallery 110, grown-ups and kids can find a relatively unsung attraction. It's a free demonstration called "Forces of Flight" that's presented seven days a week at 11:30. Christopher Stetser, an education specialist in the museum's education division, conducts the 20-minute show in the manner of a charismatic grade school teacher.

Stetser starts with a warm-up exercise that has nothing to do with the main demonstration but efficiently draws families into the show area. He tosses an inflated plastic globe to a child, calling out the name of a country.

"The game is to try to point to that country," he says. "As soon as you find it you toss it to someone else and pick another country."

Producing a hand-held ornithopter -- a bird-like toy -- which he soon sends flapping across the room, he explains that only fairly recently have humans been able to fly.

Then he eases into the main part of the demonstration, in which he shows that air is stuff.

"It actually has mass," he says. "You can push it around, you can feel it, and it presses against things."

His prop here is a pair of Magdeburg hemispheres, matching metal globe halves with sturdy handles and a pump attachment that can drain air from the sphere when the halves are pressed together.

Once the pump has created a vacuum inside the globe, Stetser calls a youthful volunteer front and center and asks him to pull the globe apart. The kid yanks like crazy, but can't do it. Stetser turns a spigot, letting the air back in, and the globe separates easily in the youngster's hands.

"It's a graphic demonstration that air is considerable," Stetser says. "At sea level on a standard day, atmospheric pressure's greater than one ton per square foot, and that's a significant amount of push. People just don't have a good grasp of that."

By now, many of the parents in the audience are realizing this stuff is new to them, too.

"Adults seem to have many of the same misconceptions that youngsters have," Stetser says. "Many adults haven't got a clue why the astronauts are weightless, for example. {They} haven't got a clue how gravity and air relate to each other."

Gravity, lift, wing design, jet propulsion, drag, Bernoulli's principle, astronaut weightlessness -- Stetser tackles all these subjects, using props and humor and volunteers from the audience.

"Forces of Flight" is the first of a series of free or cheap science demonstrations developed by the museum's education division. Private contributions spurred their development and help keep them going. For information about other demonstrations, and about family workshops to be held on Saturday mornings this spring, call the museum's education department at 202/357-1400.GARDENING LECTURES

Anyone for edible landscaping?

That's creating a garden that is comely and comestible at the same time. And it happens to be one of many horticultural practices you can learn about on your lunch hour, if you work near Capitol Hill.

The place is the U.S. Botanic Garden Conservatory (Maryland Avenue and First Street SW), the price is free, and the 1991 course schedule is available from the Public Programs Office (202/226-4082).

Holly Shimizu, public programs and grounds chief, says the Botanic Garden is constructing a nursery in Anacostia at which hands-on, how-to gardening courses eventually will be offered. But the nursery won't be finished till 1992, so meantime the courses are only how-to.

Which is not to say these lunchtime lectures aren't a fabulous freebie.

"They have absolutely major authorities in the field," says John Grady, a horticultural history buff who works at the Department of Health and Human Services and attends all the lectures. Grady cites two speakers who have particularly impressed him: Mark Reeder, former director of the William Paca Gardens in Annapolis, and John Watkins, supervisor of glass houses (English greenhouses) at Wisley, the garden of Britain's Royal Horticultural Society.

The series draws a high-brow crowd, horticulturally speaking, Grady says.

"I bump into a number of people whom I know to be fellow serious students and practitioners. The lectures are at a level which is fully satisfying to the serious student, but they are generally accessible to someone with a less-deep interest in a given subject," he says.

The next lecture, "Looking at Small Scale Agriculture," will be held Feb. 1 at noon. Holly Shimizu's edible-landscaping lecture is June 14. Bon appetit.CAPITOL-FLOWN FLAGS

Last fall, Phil Burns of Olney came across two old flags he had stashed in a bureau. Their stars and stripes had once adorned the coffins of Burns's father and father-in-law, both World War I veterans.

Burns, a constituent of U.S. Rep. Constance Morella, said to his wife, "I think I should take these down to Connie and see if she can fly them over the Capitol."

He brought the flags to Morella's Capitol Hill office. Margaret Sollitto, Morella's staff assistant, sent them to the Capitol Flag Office, whose seven employees last year arranged for 141,565 American flags to fly from one of three poles on the Capitol roof.

Up went the Burns flags. Chris Benza, head of the flag office, says each flag flies between one second and half a minute. There is no charge for the service. Down they came.

A week after dropping them off, Burns fetched the flags at Morella's Wheaton office. Each was accompanied by a cream-colored certificate authenticating the details of the flying and bearing the signature of George M. White, Architect of the Capitol. "The certificates are very nice," Burns continued on next page from previous page says. "In fact, we framed one for my mother-in-law. We gave it to her at Christmas with the flag and she was just delighted with it. She hung it up."

People don't need to provide their own flags as Burns did. They can purchase Capitol-flown flags through any member of Congress. The flags -- available in different sizes in either cotton or nylon -- cost between $6.50 and $17.38.

"I think they'd make terrific wedding presents or gifts for people who are moving into a new house," says Burns, who'll give his father's flag, along with the framed certificate, to his son.CONVICTS' ADDRESSES

Former televangelist Jim Bakker is incarcerated at the Federal Medical Center in Rochester, Minn. At present, I cannot think of a reason to write to him. But who knows about tomorrow? Life is full of sudden contingencies.

Anyway, let's say I want to learn his inmate number and street address in a hurry. I pick up the phone and call the inmate locator service run by the Federal Bureau of Prisons (202/307-3126). Established in 1975, the center handles 110 to 120 calls a day, on average. The people who work the phones provide the name, federal prison register number, FBI number, location, race, sex, offense(s), projected release date and other data on any inmate housed within any of the 66 federal prison facilities.

The inmate locators don't ask why callers are seeking whatever information they ask for. So when I phone, I don't have to have a good excuse for inquiring about the former talk-show host and theme park operator. And I don't have to wait more than a minute for the reply.

Jim Bakker: inmate number 07407-058. Current address: Federal Medical Center, P.O. Box 4600, Rochester, MN 55903. Projected release date: Oct. 15, 2019.

A great government freebie, the inmate locator service is worthy of a punchier name than its present one. With all due respect, I'd like to suggest this: Penitentiary Tattle Line (PTL).WHITE HOUSE GREETINGS

Ay Bush.

Like many people who send a lot of cards, our president has a way of truncating his name when he signs it. So George looks like Ay on the White House birthday and anniversary cards mailed at the rate of half a million a year. (Barbara looks like Baibaea.)

The cards are sent free of charge to couples celebrating 50 years or more of marriage and individuals celebrating birthdays of 80 or more years. The signatures are engraved, not penned or autopenned. But each envelope is hand-addressed and bears the all-important return address: "THE WHITE HOUSE, Washington."

Dian Moore, director of presidential inquiries, says requests should be sent in writing four weeks before the birthday or anniversary date. Write to: The White House Comment Office, 1600 Pennsylvania Ave. NW, Washington, DC 20500.AERIAL PHOTOS

The U.S. Geological Survey runs something called the National High Altitude Photography Program. Since 1980, federal shooters have made more than 8 million aerial photographs of the country, including ones of your neighborhood. In fact, if you live in the Washington area, the most recent photos of your immediate environs are probably less than a year old.

For $16 to $65 you can buy a black-and-white print of one of these shots. If you were to commission such a photo -- for a den accouterment, say, or a housewarming gift -- you would pay $150 to $350 for the service, according to aerial photographer R. C. Kreider of Fairfax.

"I would think that the only drawback to the {USGS} photos is that they aren't taken on a monthly basis," Kreider says, "plus the fact that they use a mapping style of photography {shot straight down} and not an oblique style {shot on an angle}, which is often necessary to give a sensation of the potential of a site from a development standpoint."

But for a gift-type photo, he says, the mapping style is fine.

You can order a photo by mail by writing to Customer Service, EROS Data Center, Sioux Falls, SD 57198, or by calling 605/594-6151. Ask for aerial photo ordering information; you'll quickly get a packet of material telling what's available, how much it costs and how to order it.

Or visit the USGS Map Sales Office in Reston (12202 Sunrise Valley Dr.; 703/648-6045), where customer service clerks can help you order exactly what you want.IF YOU HAVE

a favorite, little-known bargain from Uncle Sam, please send details to Weekend, Attn: Federal Freebies, The Washington Post, 1150 15th St. NW, Washington, DC 20071.

For information on ordering "Lesko's Info-Power," write Information USA, P.O. Box E, Kensington, MD 20895 or call 301/369-1519.