Preheat oven to 400 degrees F (200 degrees C). In a large bowl, cream together butter, shortening, 1 1/2 sugar, and eggs. In another bowl, sift together flour, cream of tartar, baking soda and salt. Blend dry ingredients into butter mixture. In a small bowl, mix 2 tablespoons sugar and the cinnamon and set aside. Shape dough by rounded spoonfuls into balls and roll balls of dough in cinnamon mixture. Place balls 2 inches apart on ungreased baking sheets. Bake 8 to 10 minutes, or until set but not too hard. Remove from baking sheets and cool on rack.