Jack's Manual by J. A. Grohusko (1910, p.85) — Rum

1 lemonlemon juice — Juice of 1 lemon.acid
2 limeslime juice — Juice of 2 limes.acid
1 portionrum base
1 teaspoonfulsugar base
1 bottleclub soda dilution
2 lumpsice other
  1. Build the sugar, lemon juice, lime juice, ice, and rum in the glass.
  2. Add the bottle of club soda, stir with a spoon, and serve.

Ice: 2 lumps ice

See also: Tom Collins Whiskey, Rum Daisy

Source says to mix the same as above, substituting rum for whiskey.