Preheat oven to 300°F (150°C).

Sift together flour, baking powder, and salt.

Set the dry ingredients aside.

Cream together butter, sugar, lime rind, nutmeg, cinnamon, and allspice until light and fluffy.

Beat in eggs one at a time.

Gradually add the sifted dry ingredients alternately with the milk, beginning and ending with the dry ingredients.

Mix until just combined.

Grease and flour a 9 x 5 x 3-inch loaf pan.

Pour batter into the prepared pan, spreading evenly.

Bake for 1 to 1.5 hours, or until a toothpick inserted into the center comes out clean.

Let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely.

Slice and serve.