Preheat the oven to 350F. Grease and flour two, 8-inch round layer cake pans or a 13-inch by 9-inch baking dish.
Combine dry ingredients in large mixing bowl. Add mayonnaise, water and vanilla; beat for 3 minutes on medium speed. Pour the batter into the pans and bake for 30-40 minutes, or until a cake tester inserted in the middle of the cake comes out clean. Cool for 10 minutes; remove from the pans and put on wire racks. Cool completely and frost.
Source: My mother, Phyllis Keene. She used this recipe to make our birthday cakes (5 kids) when we were growing up.