In a large bowl, cream butter and 1 1/2 cups sugar with an electric mixer. Add eggs one at a time and blend well.
In a large bowl combine the flour, cream of tartar, baking soda and salt. Blend the flour mixture into the butter mixture. Place the dough in the refrigerator for at least 30 minutes.
Preheat oven to 350 degrees. In a small bowl combine the 4 1/2 tsp. sugar and cinnamon. Roll the dough into walnut-sized balls and roll in the cinnamon-sugar, covering well.
Place dough balls on ungreased cookie sheets, about two inches apart, and bake for 9-11 minutes or until lightly browned.
Remove from pan immediately and cool on a wire rack. Repeat with the remaining dough.