Preheat oven to 400°F. Mix flour, cream of tartar, baking soda and salt in medium bowl. Set aside. Beat 1 1/2 cups of the sugar and shortening in large bowl with electric mixer on medium speed until light and fluffy. Add eggs, milk and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed.
Mix remaining 1/4 cup sugar and cinnamon. Shape dough into 1-inch balls. Roll in cinnamon sugar mixture to coat. Place 2 inches apart on ungreased baking sheets.
Bake 7 to 8 minutes or until lightly browned. Cool on baking sheets 2 minute. Remove to wire racks; cool completely.