In a large bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add 1 1/2 cups sugar, cream of tartar, baking soda, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Cover and chill in refrigerator for 2 to 3 hours or until dough is easy to handle. Shape dough into 1-inch balls. Roll balls in 1/4 to 1/3 cup sugar. Place balls about 2 inches apart on an un greased cookie sheet. Bake in a 375°F oven 7 to 8 minutes or until edges are lightly browned. Transfer cookies to a wire rack, let cool.