Wow, does this bring back memories! I think sherbet is one of those terms that means different things depending on where you are from. I grew up in South Africa, and frozen sherbet was different to sorbet. We also had hard candies called sherbet, and, sherbet powder. I can only find a couple of recipes for the powder, but I know we used to make it with jelly (jello) powder.

Sherbet: A preparation of bicarbonate of soda, tartaric acid, sugar, etc., variously flavored, for making an effervescing drink; -- called also sherbet powder.

Lemon Sherbet
This is a poplar treat for children and a good seller at school fetes:
Place separate containers with 700g pure icing sugar, 225g bicarbonate of soda and 200g citric acid powder into a warm oven for a few minutes to dry. Then combine all together with 3-4 drops of oil of lemon. Put through a fine sieve 3 times and store in an airtight container. To serve, put a little into small bags with tops folded and insert a straw. Or put a little into tiny ice cream cones.