Pare and core apples. Cut into eighths and place in greased baking dish about 10x6 inches.
Sprinkle with combined spices, sugar, and a little of the salt. Mix water, lemon juice, and grated rind and pour over apples. Add baking soda and remaining salt to oats: work butter into this mixture until crumbly. Spread oatmeal mixture over apples and bake in preheated moderate oven (375 F) for 40 minutes.
Sift together the flour, sugar, baking powder, salt, and allspice: rub in the butter. Add caraway seeds. Add currants and mashed potatoes, mixing well. Add eggs. Place in a well-greased flat pan (8x8 inches), and bake in preheated hot oven (425 F.) for 30 minutes. Cut into squares and serve hot.