WHEN YOU SAY "Smithsonian," millions of Americans think of Washington's wonderful collection of museums. But the Smithsonian Institution, established by Congress in 1846 in accordance with the terms of a will left by James Smithson of England in 1826, has grown into a giant, worldwide research and museum conglomerate. The organization spends about $100 million in public funds every year, in addition to about $11 million in private donations and grants. In the District telephone directory alone, the Smithsonian listings take up a column; activities elsewhere - such as research operations in the Canal Zone, India, Pakistan, Egypt or the Cooper-Hewitt museum of design and decorative arts in New York.

There is also a subsidiary organization, the Smithsonian Research Foundation, which has received federal money transferred from the Smithsonian's account at the Treasury. Until Congress found out about it two years ago, there was a $1-million contingency fund maintained by S. Dillion Ripley, secretary of the Smithsonian.

It is this complex of activities - together with some financial arrangements involving Mr. Ripley's connection with the American Security and Trust Co. here - that are now attracting investigatory attention. Last fall, Sens. Robert C. Byrd (D-W.Va.) and Ted Stevens (R-Alaska), chairman and ranking minority member respectively of the Senate Appropriations subcommittee with responsibility for federal payments to the Smithsonian, requested a General Accounting Office audit of the organization's books. While noting that the request "in no way should be construed to imply any suspicion of wrongdoing or deliberate impropriety," the request pointed out that the Smithsonian had not "undergone the usual federal reviews and examinations accorded most government agencies."

This week, staff writer Charles A. Krause of this newspaper reported that the GAO also has been asked to determine whether it was proper for Mr. Ripley to sit as a director of American Security at the same time the Smithsonian was depositing hundreds of thousands of dollars a year in non-interest-bearing accounts at the bank. As a result of this arrangement, the Smithsonian appears to have lost thousands of dollars in interest by leaving its money in checking accounts instead of investing the funds in short-term securities.

Smithsonian officials defend the system as an efficient cash management arrangement. Mr. ripley, who resigned from the American Security board in December after 10 years, sees no conflict of interest. The Smithsonian secretary, who reportedly received at least $2,400 a year in directors fees from the bank and who owns 150 shares of its stock, said he knew nothing about where the Smithsonian was keeping its money during the period he served on the American Security board.

This kind of link between private and public funds and bank directorships is nothing new. As some readers may recall, four years ago staff writer Ronald Kessler detailed a similar dual role involving the treasurer of the Washington Hospital Center who also happened to be a vice president of American Security. A year later, there were reports by staff writer Douglas Watson on the then-Maryland state treasurer who had placed millions of public dollars in non-interest accounts in various private banks - including one he headed.

In each case, the arrangements may have been merely convenient, friendly - and entirely legal. But when they involve taxpayers' money, questions having to do with conflicts of interest and public confidence cannot be lightly dismissed. For the sake of everybody involved, the GAO should pursue an exhaustive review of the Smithsonian's financialpractices.