Sift together flour, baking powder, and salt. Set aside.
In the large bowl of an electric mixer beat the butter until soft and smooth. Add the sugar and beat until light and smooth. Add egg yolks, one at a time, beating after each addition. Stop the mixer and scrape down the sides of the bowl and the beaters several times.
With the mixer on low speed, alternately add the flour mixture and milk, beginning and ending with flour. Stir in the vanilla.
In another bowl, with a clean beater, beat the egg whites until stiff but not dry. Stir about 1/2 cup of whites into the batter to lighten it, then fold in remaining whites in several additions.
Divide the batter evenly between 2 8 or 9 inch pans. Smooth the batter level, then spread it slightly from the center to the edges.
Bake in a 350 degree preheated oven for 30-35 minutes, or just until the tops are springy or a cake tester comes out clean.
Cool the cakes in their pans on a rack for 10 minutes. Invert the cakes onto racks.