David Akers (1975/88): The 1835 is not particularly rare and it is, in fact, the third most common date of this type after 1834 and 1836. There are two different style heads for 1835 but, as is the case of the 1834, the differences are minor. Despite its relatively "common date" nature, the 1835 is very hard to obtain in choice uncirculated condition.
Ron Guth: In the Pittman sale catalogue (Part One), David Akers recounted John McCloskey's assertion that there are eight different varieties of the 1835 Classic Head Half Eagle. Only three Proofs are known of this date, all from the same pair of dies. Breen illustrates an unattributed Proof 1835 Half Eagle (Breen 6506) which is most likely the Smithsonian's example.
Nearly straight truncation line, Small Date
Curved truncation line, Small Date
Curved truncation line, Large Date (illustrated above)
Sources and/or recommended reading:
"Walter Breen's Complete Encyclopedia of U.S. and Colonial Coins" by Walter Breen