1. Preheat the oven to 400F. Lightly grease baking sheets.
2. Combine 1 1/2 cups of the sugar, the butter and eggs in a large mixing bowl. Beat with an electric mixer set at medium speed until creamy. Sift the flour, cream of tartar, baking soda and salt together into another bowl. Add to the creamed mixture and stir to mix.
3. Combine the remaining 3 tablespoons sugar and the cinnamon in a shallow bowl and mix well. Shape the cookie dough into 1-inch balls and coat with the sugar mixture. Arrange the balls 2 inches apart on the prepared baking sheets. Bake until lightly browned but still soft, 8 to 10 minutes.
Variation
Snickerdoodles make terrific cookie sandwiches: Spread vanilla or cream cheese frosting on a cooled cookie and then top with another. For a delicate orange flavor, add 1/2 teaspoon orange extract to the frosting before spreading.