A 10-by-18 inch rendering of the painting "Icebergs" by Frederick Church, the 19th-century American artist, was purchased for $225,000 at an auction Saturday by a private collector.

Officals of the Stalker and Boos art gallery in Birmingham, Mich., a Detroit suburb, said the painting was a smaller version of a 5 1/2-foot by 9-foot painting of the same work that sold for $2.5 million on Oct. 25 at Sotheby Parke Bernet, the New York auction house. It was the largest sum ever paid for a painting by an American artist and the third highest for any painting.

The larger painting was recently discovered at a boys' school in Manchester, England. The work had been missing for more than a century and long had been sought by art connoisseurs. It is considered Church's most important work.

Gallery officials declined to identify the buyer of the smaller, recently discovered painting that belonged to Church's great-grandson who lives in Birmingham, said Frank Boos, an owner of the gallery.

Dave Stalker, a partner in Stalker and Boos who handled the auction and consulted with the heir on the sale, said "it seemed like a good time to sell it."

The unidentified Bloomfield Hills, Mich., businessman who is just starting an art collection bought the painting using a prearranged signal with the auctioneer. Two bidders at the art gallery competed with three others connected by telephone hookup from New York, Las Vegas and Los Angeles. About 500 people attended the auction.

Stalker said the buyer remained anonymous because of concern for the security of the painting.

The sale of the painting went about as expected, Stalker said. The work had been appraised for $50,000 two years ago, but Stalker said there were estimates it would bring from $200,000 to $400,000. Bidding on the painting opened at $100,000, and was over in about one minute, Boos said.