Combine the 1 1/2 cups sugar, and the water and boil 5 min.
Combine the grapefruit juice, sieved apricots and lemon juice and add to the cooled sirup.
Pour into the freezer and freeze, using 8 parts ice to 1 part salt.
When the sherbet is of the consistency of a soft mush, open the freezer and fold into the sherbet the egg-white which has been beaten until very stiff with the 2 tbsp. of sugar.
Re-cover the freezer and continue freezing until the sherbet is stiff enough to serve.
Serve garnished with maraschino cherries cut in small pieces.