On the morning of March 19, Sen. Robert C. Byrd (D-W.Va.) arrived late at a Senate Appropriations subcommittee hearing and began questioning the director of the National Cancer Institute.

The minority leader did not ask Dr. Vincent T. DeVita whether the institute was making any progress in the war on cancer. He did not ask what new avenues of research its scientists were pursuing or whether the billions of dollars it has spent have paid off.

Instead, Byrd wanted to know what happened to $4.5 million the subcommittee earmarked last year to build a Mary Babb Randolph Cancer Center at West Virginia University. Why hadn't the money been spent? Had DeVita misunderstood the intent of Congress?

DeVita said he could not award the grant until an advisory board approved it.

"We will be following this with interest, doctor," Byrd replied.

That moment in the Senate Appropriations subcommittee on Labor, Health and Human Services, Education and related agencies provides a classic illustration of how power has shifted in Congress in recent years.

There was a time when the House and Senate Appropriations committees were viewed as perhaps the most powerful on Capitol Hill. They controlled the budget; their senior members made grave pronouncements on national fiscal policy, and those pronouncements made headlines.

That no longer is true. Large chunks of the budget now pass outside the jurisdiction of the appropriations panels, in so-called entitlement programs where spending each year is automatic. Since 1974, both houses have had Budget Committees, which now set fiscal policy for Congress and dominate the public debate.

Perhaps most important is the altered national climate: an era of fashioning new federal programs has given way to an age of austerity. The appropriations panels are now called upon to curtail activities they once could freely fatten, a far less pleasant political exercise.

But the appropriations committees still wield enormous power, for their members function as a second set of government managers. They control the fine print that dictates the bureaucracy's marching orders. They use their power of the purse to tell agencies how many people to hire, how many offices to close, how many grants to award and sometimes which ones.

Sen. Lawton Chiles (D-Fla.) said that when he came to the Senate 14 years ago, "Each appropriations subcommittee sat like a feudal barony. Your role on the subcommittee was to get all the bucks you could for your constituents. You didn't monkey with anyone else's monkey. And the same people who added money in subcommittee felt free to go to the floor and add another amendment."

Chiles said the budget process has imposed greater restraints on the subcommittee. "But within the role of how the dollars are to be divided, we still have power," he said.

Over the next few months, The Washington Post will follow the Senate Appropriations subcommittee on Labor-HHS as it grapples with the government's second-largest money bill. Its 15 senators and eight staff members have line-by-line control over more than $100 billion in federal spending, a vast terrain that includes three Cabinet departments as well as the National Labor Relations Board, Railroad Retirement Board, Corporation for Public Broadcasting, Action, Soldiers' and Airmen's Home and the National Commission on Libraries and Informational Science, among others.

Subcommittee Chairman Lowell P. Weicker Jr. (R-Conn.) scoffs at the notion that the Budget Committee process has diluted his power. Appropriations, he said, "is the dominant committee in the Senate today. We're back in the driver's seat."

Indeed, many say the lawmakers have an excess of power to load up their chunk of the budget with pet projects, simply by inserting a few words here and there.

"It's too much of a pork-barrel committee," said Sen. William Proxmire (D-Wis.), the subcommittee's ranking Democrat. "Senators come in and say their state has a problem and they want to get language in the appropriations report. Then they'll often issue a press release back in the state, saying so-and-so got this project for the state. If a senator does it right, he might even get his name on the building."

Byrd, in fact, issued a press release on DeVita's assurance that the West Virginia cancer center would be funded. He also made sure no colleague would even presume to oppose it by billing the center as a "fitting tribute" to a cancer victim, the late wife of former senator Jennings Randolph (D-W.Va.).

For the staff, these line-item reviews can grow tedious. "It's green eyeshade stuff, a very narrow job," one staffer said. "The Budget Committee has stolen a lot of our thunder. You don't feel like you're making policy. You're just moving paper."

Under Weicker, the Labor-HHS subcommittee conducts its business in an informal style. It meets at 9:30 a.m. in a small, low-ceilinged room in the Dirksen Senate Office Building. Instead of peering down at witnesses from a lofty dais, the senators sit opposite them at a long conference table. When the testimony droned on at a recent hearing, Sen. Mark Andrews (R-N.D.) began leafing through a newspaper until it was his turn for questions.

The tone is conversational, with prepared statements kept short and objections voiced softly. There are no klieg lights or television cameras, only a few reporters from trade publications. The audience, mainly agency employes scribbling on yellow legal pads, sits nearby on upholstered couches and chairs.

Attendance is sparse as senators drift in and out. Weicker often is left on his own, even for key witnesses such as acting Labor Secretary Ford B. Ford. On occasion, Weicker leaves and another senator dutifully reads the questions that the chairman's staff prepared.

On a panel that used to provide billions to nourish new social programs, there is little enthusiasm for grappling with the Reagan administration's proposed cuts in domestic spending.

"People are never interested in coming in and arguing for cuts," said one staff member. "They may argue for reducing the deficit in the abstract, but the Appropriations Committee doesn't deal in the abstract."

At a hearing March 27, however, nearly a dozen senators filled their side of the conference table. They were there to talk about an issue that hit close to home: the Social Security Administration's plan to reduce its work force by 17,000 employes.

The witness, acting Social Security Commissioner Martha A. McSteen, insisted that her agency was still studying the impact of the reduction. But the senators were convinced that it would mean closing at least 200 Social Security field offices. One by one, they rose to the defense of their states.

"You don't know how many field offices would be closed or which ones?" Byrd asked McSteen. " . . . For the record, you're not prepared to state whether there will be any closings in West Virginia?"

"What would Florida's losses be?" Chiles asked.

"My Wisconsin constituents are concerned about rumors of field office closings," Proxmire said.

"Do you know North Dakota's weather?" Andrews asked. "Can you imagine a disabled elderly person driving 100 miles to review a Social Security case, with a wind-chill factor of 90 below zero, in an old car? This is what you're forcing people to do."

At other hearings, subcommittee members routinely question agency officials about relatively minor items. For example:

* Chiles told Labor Department officials he was "tremendously disturbed" that they were proposing to cut $114,000 from the Office of Labor Racketeering and had failed to fill 18 vacancies. "The department is retreating from investigating labor racketeering," Chiles declared.

* Sen. Tom Harkin (D-Iowa) demanded that the Health Care Financing Administration give him a revised report on estimated wage rates at rural hospitals, which affect their Medicare and Medicaid payments. Harkin would not let up until officials named the exact day they would produce the long-delayed report; when they suggested the following Tuesday, he insisted on Monday.

* Proxmire criticized the National Institutes of Health for awarding several grants he considers wasteful, including $95,000 to examine the effects of orthodontia on psychosocial functioning, $85,000 to analyze careers in a large bureaucracy, and $50,000 to study the use of personal computers to enhance the elderly's psychological well-being.

* Weicker criticized a plan to close the Labor Department's field office in Boston, saying this would leave the New York regional office with responsibility for eight more states, including Connecticut. He also berated HHS officials for filling only 45 of the 57 jobs the subcommittee had approved for inspecting homes for the mentally retarded. "I want to know why you're circumventing the clear intent of Congress," Weicker said.

One staff member offered an easy explanation for why senators deal with this kind of detail. "For some of these guys, it's easier to understand $100,000 than $100 million," he said.