Sotheby's Holdings Inc. said Wednesday its earnings for 1989 climbed 82 percent from a year earlier, while another fine arts auction house, Christies International PLC, reported a 61 percent earnings increase. Sotheby's, which announced its earnings in New York, said its net income came to $113 million, or $1.96 a share, in 1989 compared with $62 million, or $1.10 a share, in 1988. Sotheby's said its revenue rose 40 percent to $445 million from $317 million in 1988. For the fourth quarter, net income increased 94 percent to $62 million, or $1.07 a share, from $32 million, or 56 cents a share, a year earlier. Fourth-quarter revenue rose 48 percent to $200 million from $135 million. Michael Ainslie, Sotheby's president, said in a statement that the results showed ``we have further strengthened our leadership postion in the international art market.'' Sotheby's auction sales rose 62 percent to $2.95 billion for the year and 76 percent to $1.49 billion for the quarter. Christies said in London that its net profit for the year came to 40 million pounds, or $64 million, compared with 24.8 million pounds in 1988. Earnings per share came to 23.4 pence, or 38 cents, compared with 14.8 pence. Christies said its pre-tax profit rose 57 percent to 66.9 million pounds, or $108 million, from 42.5 million pounds. Sales soared 71 percent to 1.33 billion pounds, or $2.1 billion, from 777 million pounds in 1988. Christies Chairman Lord Carrington said sales in 1990 are ahead of a year ago. Growth in the breadth of interest in art, he said, allows the company to ``look forward to the 1990s with optimism.'' Christies didn't break out quarterly or six month results. It isn't required to under British law.