It was the kind of prize college presidents dream of: $10 million in federal money set aside for state-of-the-art supercomputers.

But for Cornell University President Frank H.T. Rhodes, the money was more dilemma than prize. Rhodes recognized that the extra computer power could push the university far ahead in a fiercely competitive research field. And federal dollars for research facilities have long been scarce.

But Congress had earmarked the money for Cornell without submitting the project to competitive "peer review," a system used for four decades to distribute federal research funds.

Rhodes considered the windfall and turned it down.

"It is not an easy thing to turn back $10 million," he said. "It was a loss to us . . . . But I still believe that was the right way to go."

Cornell's dilemma is becoming a serious one for higher education at large. Faced with drastic cutbacks in federal funding for university research facilities, administrators are scrambling for money. Many have found that they can turn to Congress -- often with the help of high-priced Washington lobbyists -- to set aside funds specifically for their institutions. These appropriations typically bypass peer review, a process in which a panel of scientists compares competing proposals and awards grants on the basis of merit.

No one in higher education wants to quibble over a gift horse. But this new "academic pork barrel," which has grown from $3 million in fiscal 1982 to more than $145 million this year, is escalating into a divisive controversy among university presidents.

Administrators at the smaller, less-established institutions claim that they have consistently lost out in peer review competition and that appealing directly to Congress is their only hope of receiving their share of funding.

Presidents at the larger, more prestigious research universities argue that any system that awards funds without competitive merit review will inevitably drive down the quality of American research.

"If we're going to have the best work, we have to put the funds in the hands of the best people," said Rhodes, whose university has been among the top recipients of federal research funds. The $10 million he turned down was not solicited by Cornell, but by a computer firm that works with researchers at the university.

"It seems self-evident . . . we will inevitably diminish the average quality of the research in this country if we don't try to make {funding awards} based on quality," said Robert M. Rosenzweig, president of the Association of American Universities (AAU), which represents more than 50 research institutions.

The debate recently shifted into high gear when administrators at 43 major research universities pledged not to accept earmarked funds from Congress if the grants had bypassed merit review. Ten institutions voted against such a moratorium.

Rosenzweig, whose organization took the vote among its members, said the results had pushed the issue to a "tipping point."

Despite tremendous pressure from trustees and faculty to seek earmarked funds from Congress, he said, many of the major universities have been "holding off." But he warned that if the current pilgrimage to Congress in pursuit of funds continues, the big universities will join the congregation.

"When that happens, it's going to be a different game," Rosenzweig said. "It would make us all look bad. It would be seen, quite properly, as an unseemly political scramble for spoils."

There is a different view at the University of Nevada-Las Vegas (UNLV), which won a $3.5 million grant late last year for computer science and robotics research. There, a dozen researchers are busy designing a robot for military and industrial use, with the funds arranged through former Republican senator Paul Laxalt (R-Nev.), who sat on the Appropriations Committee before he left his seat last year.

For the relative newcomer university, the grant has meant a chance to level the playing field and compete with the big research schools, according to William Wells, director of UNLV's School of Engineering. "This is the platform to launch a strong research base, the feeder that will allow us to compete." Peer review, he said, "is not going to be fair to these schools that are just getting started."

Wells admitted without hesitation that UNLV had benefited from a powerful home-state senator. "Unfortunately or fortunately, that's the way the political game will be played . . . . You simply revel in your good fortune," he said.

Both sides in the controversy agree that federal funding for university facilities -- where half of the nation's basic research is conducted -- is critically inadequate.

In the 1960s and 1970s, Congress shifted its university focus from funding research facilities to student financial aid. According to a Congressional Research Service study released this spring, federal funding for construction of university and college research facilities decreased 85 percent in constant dollars -- adjusted for inflation -- from $325 million in fiscal 1963 to $45.9 million in fiscal 1984.

The study warned of "increasingly disturbing signs that higher education's infrastructure for supporting research and development is deteriorating . . . . The ability of our institutions of higher learning to successfully carry out these responsibilities is a matter of great national concern."

As a result, Congress has become a much more attractive target as a source of funds and universities are equipping themselves to take advantage.

While some institutions employ their own lobbyists to seek earmarked funding, many have hired outside firms. The practice has spawned a lucrative business, dominated by the Washington firm of Cassidy and Associates, which represents 24 universities. According to Rosenzweig, the firm charges monthly fees around $20,000.

The company has helped secure numerous grants, including $11 million for the Rochester Institute of Technology for a microelectronics facility and $19 million for a science and engineering center at Boston University.

Roy Meyers, a spokesman for the firm, cites the Rochester grant as an example of how earmarking can break open what had become "pure and simple, an old-boy network" of peer review funding. He said the firm has concentrated on funding for research facilities, not research itself, arguing that improved facilities at the newer, smaller schools can help them compete for research funding.

"RIT has always been like a little sister to the University of Rochester," which would consistently win out in competition for funding, he said. But the RIT grant last year, he said, has spurred additional support for the school from several Rochester companies that traditionally had worked with the university.

Both sides point to statistics and studies to support their claims. Like other defenders of congressional appropriations, Meyers refers to National Science Foundation figures, which show peer review funding flowing predominantly to elite schools in the Northeast and California with established research records.

But opponents of direct appropriations cite a General Accounting Office study issued this spring on peer review funding that found no significant bias based on an institution's prestige or location or an applicant's age or gender.

While isolated institutions have received individual appropriations from Congress in the past, the flood of earmarked funding dates back only a few years. As in other pork barrel appropriations, powerful members of Congress -- many of them on the appropriations comittees -- tend to be most successful in securing funds for institutions in their districts or states.

The following projects, for example, were included in one supplemental appropriations bill passed a year ago, according to a list compiled by the AAU: $13.5 million for an engineering research center at Northeastern University, located in a state represented by Sen. Edward M. Kennedy (D-Mass.) and then-House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.); $2 million for neurotoxin research at the University of Kansas and $5 million for aviation research at Wichita State University, both represented by Robert J. Dole, who was then the Senate majority leader; and $1 million for semiconductor research at Oregon Graduate Center, represented by Sen. Mark O. Hatfield (R-Ore.), then chairman of the Senate Appropriations Committee.

Institutions in the Washington area also have benefited. Catholic University received nearly $14 million in the 1983-84 congressional session to build a laboratory for special physics research and, in 1983, Georgetown University received $820,000 for a fuel cell project.

The funds tend to go for high-technology research but include some nonscientific projects, including a Chinese-American student exchange program at Tufts University and a congressional studies center at the University of Oklahoma.

In an effort to stem the tide of direct appropriations, the AAU is supporting legislation introduced by Rep. Robert A. Roe (D-N.J.) to establish a $250 million annual authorization for the National Science Foundation to replace and repair obsolete research facilities on the basis of merit. The bill, which sets aside funds for less-established institutions, will be considered at hearings next month.

Rosenzweig also has vowed to fight any expansion of pork barrel appropriations to research itself, rather than research facilities.

While the vote by AAU presidents indicates the issue may be coming to a head, others predict it will not be resolved.

"It's going to remain difficult and divisive," said Arthur M. Sussman, vice president for administration at the University of Chicago and a strong opponent of earmarking. "Whatever short-run gains there are as a result of pork barrel legislation, in the long run higher education will suffer."

But for many, including administrators, members of Congress and education associations whose members are divided, the issue is baffling.

"There's a lot to be said on both sides," said John Brademas, president of New York University and a former member of Congress. "This is not an argument between good guys and bad guys."