Combine orange peel and pulp with water to cover in a small sauce pan.
Cook until peel is tender; set aside.
Put opened container of rum in hot water.
Combine reserved orange mixture with remaining ingredients, except rum, in a large sauce pot.
Cook almost to jellying point.
Remove from heat.
Skim foam if necessary.
Stir in hot rum.
Pour hot into hot jars, leaving 1/4-inch head space.
Process 15 minutes in boiling water bath.