1. Remove the stems and leaves from the kumquats. Wash well and drain. Place in a deep kettle, sprinkle with baking soda, cover with boiling water and let stand until cool.
2. Wash three times in fresh water, using a vegetable brush to remove the oil. Drain. Cut crosses one-quarter inch deep in the stem and blossom ends. Drop one at a time into rapidly boiling water to cover. Cook until tender, about ten minutes.
3. Prepare a syrup by boiling together the corn syrup, sugar and three and one-third cups water for ten minutes. Add the drained kumquats. Boil slowly, stirring occasionally, until the fruit is partly transparent and the syrup thickens (226° F. on a candy thermometer), about twenty to thirty minutes. Remove from the heat and cover. Let stand overnight.
4. Reheat to boiling and pack the kumquats into hot sterile jars. Bring the syrup again to a boil and pour it over the fruit to within one-half inch of the top. Seal immediately.