Cream together butter and sugars until light and fluffy. Add eggs, one at a time, beating well after each addition. Blend in oil and vanilla. Sift together flour, baking soda, cream of tartar and salt. Gradually add dry ingredients to creamed mixture; mix well. Chill dough in refrigerator 8 hours or overnight. Shape dough in balls the size of a walnut. Place balls about 2 inches apart on ungreased baking sheets. Bake in 350 degree oven 10 to 12 minutes or until done. Remove from baking sheets; cool on racks.