Ron Guth: In 1803, engravers at the Philadelphia mint used two different punches for the 3 of the date on Silver Dollars of that year. One is known as the Small 3, the other as the Large 3. The difference is obvious, not so much because of an actual size difference, but because of the dramatic difference in the shapes of the 3's. On the Small 3, the left end of the top bar of the 3 has no upper serif, and the lower serif points down. On the Large 3, the left end of the top bar of the 3 ends with top and lower serifs aligned in a vertical arrangement, pointing up and down.
The two varieties appear to be fairly equal in terms of survivors, though the Small 3 is slightly more common and can be found in higher Mint State grades than the Large 3. Mint State examples of both varieties are very rare. According to the April 2012 PCGS Population Report, the finest 1803 Small 3 Dollars are a pair of MS64s.
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