In Fairfax County, four people spend a couple of days a week in large apartment buildings promoting children's public library programs. The workers are paid by CETA.

In Arlington County, a group of unemployed women learns carpentry. Their training and their salaries are provided by CETA.

In Alexandria, a crew of men roams the town with an appointment book and a truckful of supplies. They weatherize the homes of the elderly. They, too, are paid by CETA.

Because it has the lowest unemployment rate (4 percent) in the Washington area, Northern Virginia's manpower programs are the smallest and the fewest in the Washington area. Nevertheless, Northern Virginia will have received nearly $12 million in federal funds in the current fiscal year to spend on the little-understood and often-controversial program called CETA.

CETA, which stands for Comprehensive Employment and Training Act, is the largest federal jobs and job training program ever undertaken in the U.S. Now finishing its fifth year, it will have pumped $11.2 billion into jobs and job training across the country during fiscal year 1978, which ends Sept. 30.

Nearly half that sum has been-added to CETA by Congress in the last 16 months. Although CETA has been a major source of federal dollars for Northern Virginia since its inception, CETA funds are now providing more local government employes than ever before - and are beginning to have a noticeable effect on Northern Virginia private industry as well.

Combined, Fairfax and Arlington counties and the city of Alexandria will have spent $11.9 million in CETA funds during this fiscal year. As a result, more than 4,000 Northern Virginians will have worked at jobs paid for by CETA or will have taken CETA training this year.

Of that $11.9 million, more than $6.7 million will have gone to fund employment in public service jobs, most of them with city or county government agencies. Just under $3 million will have gone to job training program. The remainder of the money will have gone to summer youth, veterans, Job Corps and English-language tutorial programs.

CETA, which is administered by the U.S. Department of Labor (DOL), used to be largely a training program. But last year, alarmed by 8 percent unemployment levels and prodded by President Carter, Congress rewrote CETA. As a result, in the current fiscal year, more than two-thirds of all CETA dollars are going to underwrite public service employment.

Most of those dollars are found in CETA's Title VI. Title VI funds are allocated to local governments on the basis of census data, are aimed at those only recently unemployed and do not take a whole community's unemployment levels into account. Northern Virginia will spend more than $6.5 million in Title VI funds this fiscal year.

Title II CETA funds cover public service employment, too, but are allocated according to a formula based solely on unemployment figures.

In Northern Virginia, only Arlington has a high enough jobless rate to qualify for Title II money, and Arlington's Title II stipend of $140,000 provides only six jobs. Moreover, the Arlington jobless rate has dropped so much in the last six months that county officials do not expect to receive Title II funds in fiscal 1979.

To qualify for a Title VI public service job, an applicant must demonstrate two things: unemployment for 15 of the previous 20 weeks and membership in a family whose previous year's income did not exceed 70 percent of the government's minimum standard of living. For a member of a family of four, that qualifying income "floor" works out to about $7,000 a year. For a single person, it is about $2,400.

CETA public service jobs generally do not require substantial skills. In Northern Virginia, they include such positions as office clerks, park maintenance workers, bus drivers, animal wardens and school crossing guards.

Many CETA critics claim, however, that the public service employment program, intended to pave a path into the economy for disadvantaged people, actually does the opposite. The reason is that, by law, CETA public service jobs cannot pay more than $10,000 a year in CETA funds (although CETA salaries can be supplemented with local government funds). Nor can a person remain in a CETA job for more than one year.

As a result, more than half the CETA employes who held public service jobs in fiscal 1977 were unemployed again a year later. In addition, while they hold CETA public service jobs, enrollees do not received fringe benefits.

In Northern Virginia, however, CETA programs are surmounting the "in-then-out" problem better than all other Washington-area jurisdictions.

More than 50 percent of all Northern Virginia Title VI "graduates" will have found unsubsidized jobs in the government or the private sector by the end of this fiscal year, officials say. In addition, more than 60 percent of Northern Virginia's 1,400 CETA job trainees will have found permanent work.

Perhaps more significant, Arlington, Alexandria and Fairfax have been largely free of the scandals and cases of questionable judgment and have dogged CETA programs elsewhere.

The Alexandria CETA program was the subject of a 1977 investigation by DOL's Philadelphia regional headquarters. Investigators found that Alexandria CETA administrators had paid part of an enrollee's back rent, bailed another enrollee out of jail and paid traffic fines for a third. All the money was CETA's, and all was earmarked for jobs and training.

Alexandria repaid all the funds (about $500) and City Manager Douglas Harman fired most of his CETA administrators. Under its new CETA regime, according to James Whitsett, DOL associate regional administrator for the Middle Atlantic Region, "Alexandria is doing very, very well."

Neither Fairfax nor Arlington has ever been investigated by DOL in other than routine fashion. "We've never been blessed with a Philadelphia raid" is how Gerald L. Gordon, Arlington's CETA director, put it.

Arlington was once found to have spent $11,000 to enroll two CETA people whose eligibility was questionable. The two people were dismissed, Gordon said, and no further action was taken, either by Arlington or Philadelphia officials.

Eligibility is a continuing sore spot for all CETA programs. Applicants can easily lie about their financial situations in order to join CETA programs. They must sign an agreement declaring that what they say is subject to penalties of perjury, but little if any checking of their statements is done prior to their enrollment.

Eligibility of enrollees is what led to the recent hassle over CETA employees of the D.C. City Council Eligibility was also the crux of the biggest episode of fraud in CETA history: a $2 million misuse of funds uncovered by DOL investigators last spring in Chicago.

Northern Virginia leaves CETA eligibility checking to the Virginia Employment Commission, a state agency. "The feeling is we can't be in the business of checking 900 people a year," said Arlington's Gordon.

The employment commission does no more than spot-check applicants, however. And how thoroughly the commission can check anything is open to question, since the commission lacks the power to subpoena bank or credit records.

"There's absolutely no check on it," acknowledged Michael Gilbert, the head of the Fairfax CETA program. "There's no system and no resources. If they (applicants) are lying, I've got problems. The best I can do is find them after they're in and get rid of them then.

"There is cheating.You'd be a fool to think otherwise. We just try to set up a system where you catch as much as you can."

Russell Owens, the head of the Alexandria CETA program, who was brought in after the DOL investigation, said "genuine misunderstanding of federal regulations" led to the misuse of funds in the Alexandria program.

"Do I think they were honest mistakes?I certainly do," said Owens. He stressed that no one was ever prosecuted after the Alexandria episodes, and he was bitterly critical of newspaper coverage of them, which he said he is "still laboring to overcome."

Summer youth programs in particular have suffered from newspaper coverage to CETA, Owens said. "I am having an extremely difficult time getting poor white youth in summer programs. Their parents have read these stories, and they don't want to have anything to do with CETA."

Another area in which all of Northern Virginia is having trouble is in sub-contracting on-the-job training projects to private industry.

Under its Title I, CETA would pay a private employer "all extraordinary training costs" involved in teaching a person a job. CETA would pay the participant a salary. The employer would not have to promise the participant a job at the end of training and would not have to pay either the government or the participant a cent.

But "the larger employers are generally not interested," said Owens. "They're afraid of the paperwork and the bureaucracy." Besides, he added, "OJT has a history of being a mess."

As a result, on-the-job training (OJT) in Northern Virginia is almost invisible. Fairfax devotes only $64,000 of its $1.6 million in Title I money to OJT. Arlington is spending $43,000 this fiscal year and Alexandria is spending about $16,000.

In all, that money is helping to train only about 140 people. The largest OJT project at any one place of business in Northern Virginia involves eight trainees.

However, Northern Virginia has two CETA job training centers that are run by the local governments themselves.

One, at Fort Belvoir, is cooperatively operated by Fairfax County CETA, the Army and the Fairfax County schools. In an old Army barracks, equal numbers of CETA trainees and Army recruits learn a wide assortment of skills. Gilbert calls Belvoir his "Cadillac program."

The other shining star in Northern Virginia is Arlington's skills center, where CETA trainees from all three Northern Virginia jurisdictions learn trades similar to those taught at Fort Belvoir. Jane Weizman, a Northern Virginia project officer at DOL headquarters in Philadelphia, calls the skills center "the best program of its kind in the country."

But despite high post-training placement rates and good training programs, Northern Virginia CETA directors complain that CETA goals, because they are national in scope, do not translate well to the special needs and quirks of Northern Virginia.

Gordon of Arlington, for example, runs a Title VI program which, by statute, is supposed to be targeted toward blacks as much as possible. But Arlington has a black population of only 3.8 percent.

Similarly, Gilbert of Fairfax is required by statute to aim part of his Title I program at high school dropouts. But the Fairfax dropout rate is only 2 percent.

Owens of Alexandria said that, because almost all the private industry in his city is small, he cannot reasonably hope to place half his Title VI "graduates" in subsidized jobs after a year, which is the goal written into CETA by Congress.

"It's absolutely impossible," Owens said. "The Department of Labor is asking us to do the impossible at the behest of Congress. They say get people into upwardly mobile jobs. If we can get them any kind of job, we consider it a miracle."

Gilbert cited another difficulty with CETA rules as they were written by Congress. Because Fairfax has many Southeast Asian applicants, it is often difficult to translate family income levels into terms that satisfy Philadelphia.

"I get guys in here, you ask them what was their last job, and they say they were captains in the Vietnamese Army," Gilbert said. "All they know is how many piasters they made. How do you translate that into dollars? What about inflation? It's hopeless."

In such cases, DOL officials have instructed Fairfax to "use common sense," Gilbert said. He acknowledged the possibility of deception, but he said DOL has never questioned the eligibility of a foreign-born Fairfax CETA participant.

In fact, Gilbert said, Vietnamese are much more appreciative of CETA than most Americans."They bake cakes for their teachers, you name it," he said.

For the future, Northern Virginia CETA officials expect to continue their program at approximately the same levels. Officials said they want to subcontract more on-the-job training to private industry, but they doubted they would meet with much success.

One area in which Northern Virginia CETA will be an area pioneer next year is in consortia. Fairfax will join with Loudoun County to run CETA programs under a combined administration. As a result, the consortium will get 5 percent "bonus" in federal funds.

Gilbert was optimistic about the consortium. "The Loudoun County people are very competent. It should be a very positive relationship," he said.

But none of Gilbert's counterparts was at all enthusiastic about consortia.

"Alexandrians have a different perspective on their needs. They feel many of their needs are unique," Owen said. "On the one hand, Washington is one market. On the other hand, Arlington and Alexandria are like two different worlds," said Gordon.

DOL officials in Philadelphia doubted that much enthusiasm could be mustered in the suburbs for a consortium that includes the District of Columbia. The D.C. CETA program is now under investigation by DOL.

As for Northern Virginia, "the programs are clean," said Owens. "We genuinely try to live up to the letter of the law. Besides, CETA does an awful lot of good."