Tetromibi: Early coin dies were produced in such a fashion that each die was slightly different, thus many years later researchers were able to catalog the coins struck by those dies. For middle date (1816-1839) I can recommend two books that can help you with attributions.
"The Cent Book" by Jjohn D Wright
"United States Large Cents" by William C. Noyes
A word of caution, these books are somewhat expensive, so if you have an interest in early copper you should join Early American Coppers (EAC)(
http://www.eacs.org/ ), and as a member you can get good discounts on books.