In a large bowl, cream together the softened butter and 1.5 cups of sugar until smooth.
Beat in eggs one at a time, then stir in the vanilla extract.
Combine the flour, cream of tartar, baking soda, and salt; gradually add to the creamed mixture.
In a small bowl, mix together 0.25 cup sugar and 2 teaspoons cinnamon. Roll dough into 1.5-inch balls, and coat uniformly in the cinnamon-sugar mixture.
Place cookies 2 inches apart on ungreased baking sheets and bake for 8 to 10 minutes or until set. Cool on wire racks.
Notes
Store snickerdoodles in an airtight container to keep them fresh longer.