For Eric Schmidt, Google's CEO, 2004 was a very good year. His firm led the search industry, the fastest-growing major sector in technology; it went public, raising $1.67 billion; its stock price soared; and its revenues more than doubled, to $3 billion. But as the search market ripens into something worthy of Microsoft's attention, those familiar with the software business have been wondering whether Google, apparently triumphant, is in fact headed off the cliff.

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