Scrub kumquats thoroughly.Prick each kumquat several times with a large needle.Put them in a large saucepan.Cover well with boiling water and simmer,uncovered,until fruit is tender(about 25-30 minutes.Drain.Combine the sugar,lemon slices,and 1 quart water in a large saucepan.Bring
to a boil and boil 5 minutes.Add the kumquats and boil gently until fruit is transparent(about 25 minutes).Remove from heat and allow to stand,covered loosely,overnight for the fruit to plump.Discard the lemon slices and seeds and bring the mixture,again,to a boil.Skim the kumquats from the syrup with a slotted spoon.Put them in hot sterilized half-pint jars.Continue to boil the syrup until it reaches 220 degrees on candy thermometer(about 8-10 minutes).Pour the boiling syrup over the kumquats,covering them well,to about 1/4 inch from the top of each jar.Seal and refrigerate.