Cut the peaches in half and discard the pits. Cut the fruit in wedges and place in a medium bowl with the sugar and stir well. Cover with plastic wrap and refrigerate overnight.
Sprinkle the gelatine over ½ cup of cold water and stir to combine, setting it aside for 5 minutes. Stir in ½ cup boiling water and stir to combine. With a wooden spoon and a sieve set over a bowl, press the pulp through the sieve, scraping the fruit to remove the skins and pulp and pressing to extract as much liquid as possible. Discard the pulp. Stir in the gelatine mixture and 2 cups of ice water.
Transfer to an ice cream maker and freeze according to the manufacturer’s instructions. Transfer to a container, cover, and freeze for about 4 hours, or until the sherbet is firm. Scoop and serve frozen.
Adapted from a recipe by Mrs. D.P. Washburn, Copyright 1886, The Woman Suffrage Cookbook, Published by Mrs. Hattie A. Burr.