Preheat the oven to 350°F (175°C).
In a large bowl, cream together the softened butter and sugar until smooth.
Beat in the eggs one at a time.
Combine the flour, cream of tartar, baking soda, and salt; gradually add to the creamed mixture.
In a small bowl, mix 3 tablespoons of sugar with 1 tablespoon of cinnamon.
Roll dough into balls, then roll in the cinnamon-sugar mixture.
Place on ungreased baking sheets.
Bake for 8 to 10 minutes until lightly browned.
Allow to cool on the baking sheets for a few minutes before transferring to a wire rack.