On the third floor of an office building at 1739 M Street, there winds and purrs and hums a cool, efficient IBM 370-138 computer which will tell you some very interesting things.

It will tell you, for instance, that last year the Environmental Protection Agency gave $84,000 to an outfit called Pickle Packers International for a study entitled "The Reduction of Waste in the Pickling Industry."

Push a few more buttons and you will learn of other, well, scientific research the federal government is pursuing. Such as the Department of Agriculture's unspecified grant to Rutgers University for a study of the effects of vitamin E on fatigue in horses. And here's another one to tickle the imagination, a project called "evaluation of New Orthopedic Appliances for Use in Fractures of Exotic Specimens." That bit of endeavor is being paid for by the Smithsonian and performed at the National Zoo.

Unless you stop to read the fine print on this next example, you probably would pass it off as a yawner: "Brain Protecting Mechanisms and the Prevention of Head Injury." It's really a study of woodpeckers, funded by the Veterans Administration.

These and other tax-supported research projects like them appear to be prime candidates for Sen. William Proxmire's (D-Wis.) "Golden Fleece Award," the monthly prize the senator bestows upon a government agency which he feels has swerved from the public interest for a brief detour into the sublime and ridiculous.

Anyone is entitled to ask - and many have - what business the government has sponsoring studies on pickles and woodpeckers. There is bound to be someone somewhere who knows.

But the people on M Street who run the IBM 370-138 can't be concerned with such whys and wherefores. Their job is simply to keep track of most of the research the federal government pays for.

This is no small task, of course, and the Smithsonian Science Informantion Exchange (SSIE) - a private, nonprofit business affiliated with the Smithsonian Institution - has a staff of 100 to do it. About half are scientists responsible for indexing roughly 10,000 restarch projects each month under headings ranging from "acoustics" to "zoogeography."

Other persons at SSIE run the computer, keep the books and answer search requests from all over the country, supplying lists of government research grants and contracts. SSIE also maintains files on projects supported by a number of nonprofit associations and foundations, universities and, to a more limited extent private industry.

By the way, officials at SSIE defend most of the research that the government funds as serious-minded and worthy. They say the silly examples have been magnified out of proportion, or frequently taken out of context. Also some projects may sound strange to someone not familiar with the particular field of research involved, they assert.

Searching SSIE's files can be easier than fingering through a library card catalogue, providing you have a computer terminal, a telephone and a credit account in good standing.

Since 1972, SSIE's data base has been feeding into a mammoth computer file in Santa Monica, operated by the System Development Corp.Using a telephone and a computer terminal that looks like a typewriter with a phone coupling device, exployees can dial into this data base from anywhere in the country.

Type a few code words and commands and, within seconds, they can obtain a single-page description of any government research project, known to SSIE.

"The Santa Monica computer has our complete information file," said William Payne, director of engineering for SSIE. "Now you can just phone it up. Of course, if California falls into the Pacific, we'll have to go back to the old search methods."

In an age in which bureaucracy has run away with government, it is uncommon to find any agency with much of an idea of what eveyone else is up to. The exchange was established in 1949 so that the government's right hand would at least have an inkling of what the left hand was doing.

"For so many years, the government found it had been supporting the same research twice," said Payne."We were set up to control that."

But in the beginning. SSIE had a much narrower focus. It was simply to be an appendage to the National Academy of Sciences to collect medical sciences information. The susequent blooming of scientific research across a wide spectrum, and the expansion of government, propelled the exchange into other areas.

Along the way, the exchange had to scramble for funds from a handful of agencies engaged in scientific research. Then in 1972, it joined the Smithsonian and asked and received from Congress an appropriation.

Last year, the appropriation totaled $1.97 million. The rest of the firm's $3.5 million in operating revenues came from researching contracts with federal agencies and the sale of information products. For the individual customer who requests a search, the exchange charges $60 and promises an answer within one week.

This year, Congress trimmed SSIE's appropriation to $1.7 million. One reason was a study by the General Accounting Office recommending that the exchange be dissolved and its functions incorporated fully into the Smithsonian. The government's auditors were nervous about continuing to make federal appropration to a private company which is free of federal statutes and Civil Service rules.

"We're having some trouble struggling to maintain institutional stability," said David Lakamp, SSIE's treasurer.