Famous New Orleans Drinks and How to Mix 'Em by Stanley Clisby Arthur (1938, p.36)

1 jiggerabsinthe substitute — Absinthe substitutebase
1 wholesugar — Sugarbase
water — Cold waterdilution
1 glasscracked ice — Cracked iceother
  1. Pour the absinthe substitute into a bar glass filled with cracked ice.
  2. Suspend the sugar over it in an absinthe glass or strainer and drip water slowly through the sugar until the desired color and strength are reached.
  3. Stir to frappé, strain into a serving glass, and serve.

Ice: Cracked ice

Arthur presents this as the original dripped absinthe of the Old Absinthe House, updated to use legal absinthe substitutes.