Stir together flour, baking soda, cream of tartar, and salt. Beat butter for 30 seconds. Add 2 c sugar and beat until fluffy. add eggs, milk, and vanilla, beating well. Add dry ingredients to beaten mixture, blending thoroughly. Form dough into 1-inch balls (it may help to refrigerate the dough for an hour first). Mix remaining sugar with cinnamon, and roll dough balls in this mixture. Place balls on cookie sheet and flatten slightly with the bottom of a drinking glass. Bake at 375 for 8 minutes or until lightly golden.