Ron Guth: The Flowing Hair design appeared on the first United States Silver Dollars in 1794, but only lasted until sometime in 1795, when it was replaced with the Draped Bust design. The 1794 Silver Dollar is a rare coin, represented by approximately 150-200 survivors. The 1795 Silver Dollar is much more common, but the demand from type collectors keeps the prices high.
Sources and/or recommended reading:
"Walter Breen's Complete Encyclopedia of U.S. and Colonial Coins" by Walter Breen
Independent Coin Grading Company advertisement, Numismatic News, October 3, 2000, page 21
"The Flowing Hair Silver Dollars of 1794 - An Historical and Population Census Study" by Martin A. Logies