The coin designer’s aesthetic universe is measured in micrometers. Stacking requirements rule out the beautiful high relief typical of ancient coins, and U.S. law requires a clutter of mottoes and legends on every coin. “Liberty” and “E Pluribus Unum” were borrowed from regional coins and congressional medals predating 1792.

“In God We Trust” came from religious pressure early in the Civil War; Roosevelt fought the inscription, but in 1908 Congress made it mandatory. “The United States of America,” year of issue, and the designation of value bring the total to six. One of the most elegant solutions to the creative challenge these requirements impose never made it into your pocket. In 1932, when the Treasury wanted a new quarter-dollar to commemorate George Washington’s two hundredth birthday, it held an open competition, with the winner to be chosen by the National Fine Arts Commission. The commission’s choice was unanimous: Laura Gardin Fräser, wife of the coin designer James Fraser. Andrew W. Mellon, then Secretary of the Treasury, opposed the selection of a woman for so prestigious a commission and revoked their decision. The three finalists were invited to modify their designs and resubmit them. Fraser’s entry won again, but once more Mellon overruled; the eventual winner was John Flanagan, a friend and student of Saint-Gaudens. His Washington quarter, somewhat altered over the years, circulates today.

Acknowledging past wrongs, the mint has issued a new coin featuring Laura Fraser’s winning entry. Her Washington likeness, dynamic and confident, would have been the perfect choice for the new state-motif quarter, a coin people will actually see and use. Instead, it became a limited-edition $5 gold piece commemorating the two centuries since Washington’s death. Two versions of the coin were minted, selling for more than $200 apiece. Neither coin is available now.

—E.D.