Preheat oven to 400 degrees.
Melt the butter, but keep the sticks separated. That is, melt 1 whole stick in one bowl, and the other half of a stick in another bowl.
Brush a little bit of the butter on the inside of a 9 inch cake pan.
Mix half of a stick of butter (4 tablespoons), melted, with the brown sugar and add in 1/4 cup of the pineapple juice.
Pour the brown sugar mixture in the bottom of the cake pan.
Arrange the pineapple rings on top of the brown sugar mixture. Set pan aside.
Stir together the flour, salt, white sugar, and baking powder.
Separate the eggs.
Beat the whites until stiff.
Beat the yolks until lemony yellow.
Stir in the remaining pineapple juice, vanilla, and remaining melted butter.
Add this mixture to the flour mixture.
Gently fold in the egg whites.
Pour batter over the top of the brown sugar and pineapple rings.
Bake for 30 minutes.
Let cake cool in pan for 10 minutes.
Remove it by covering up the pan tightly with a serving dish and invert so that the pineapple side is up.