Preheat oven to moderate (375°F.). Grease two eight-inch layer-cake pans. Line the bottoms with wax paper and grease the paper.
Sift together the flour, baking powder and salt. Set aside. Blend the cranberries with one-third cup of the sugar. Set aside.
Add the baking soda and vanilla to the shortening. Cream well; gradually add remaining sugar and the grated rind. Beat in the whole eggs and egg yolks, one at a time. Add the flour mixture alternately with the milk. Stir in the cranberries.
Pour the batter into the prepared pans. Bake for thirty minutes, or until a food pick inserted into the center comes out clean. Cool in pans for ten minutes. Turn out on racks to finish cooling. Spread frosting between layers and over top and sides of cake.