Butter and flour the bottom and sides of three 8 by 1 1/2-inch cake pans with the softened butter, tipping out the excess flour
Sift the flour, baking powder, and salt together
Beat the butter in a large bowl with an electric mixer on high speed until it is light, creamy, and fluffy, about 1 minute
Gradually add the sugar into the butter, and beat until the mixture is very light and fluffy, about 2 minutes more
As the sugar blends in it will change the color of the butter to a much lighter color, almost white
Whisk the egg yolks in a small bowl until they are well blended
Gradually beat into the butter mixture, mixing well after each addition
With the mixer on low speed, starting with the flour mixture, add the flour mixture in thirds, alternating with two equal additions of the milk, scraping down the sides of the bowl as needed
Beat in the vanilla
In a clean bowl using clean beaters beat the egg whites until they form firm, glossy peaks
Do not overbeat until they are stiff and dry
Fold the whites into the batter
Pour and scrape the batter into the prepared pans, dividing it equally among them
Give the filled pans a little knock on the countertop to level the batter
Bake in the center of a preheated 350°F oven for 25 minutes, or until each cake springs back when touched in the center
Remove the pans from the oven and put them on wire cake racks to cool for a few minutes, then loosen the layers by running the flat side of a knife blade around the sides of the pans, put a rack on top of each pan, and invert so the cake comes out onto the rack, top side down
Then reverse the layers so they are top side up
Mix the orange juice, lemon juice, sugar, and orange rind together and drizzle the mixture over the still warm cake layers, being careful not to let it all soak into one spot; then pile the layers on top of each other
