Cheerio! A Book of Punches and Cocktails by Charles (1928, p.24)

1 fresh limelime juice — Squirted in.base
4 portionsold Jamaica rum base
1 ponywater dilution
ice — shaved iceother
1 dashred pepper — Optional.other
2 portionssugar sweetener
  1. Use a long glass with the fresh lime juice, sugar, water, old Jamaica rum, and shaved ice.
  2. Shake well, add a dash of red pepper if desired, and serve very cold with long straws.

Garnish: Long straws.

Ice: Shaved ice

The Artistry of Mixing Drinks by Frank Meier (1936, p.83)

0.5 limelime juice — Lime juiceacid
3 piecesice — Icebase
1 glassrum — Rumbase
1 dashAngostura bitters — Angostura Bittersbitter
Soda water — Soda waterdilution
1 teaspoonGrenadine — Grenadinesweetener
  1. Build over ice in a tumbler, add a squirt of soda water, stir, and serve.

Ice: Ice

Café Royal Cocktail Book by W. J. Tarling (1937, p.168)

0.33 partlime juice — lemon or lime juiceacid
0.5 partrum — Jamaica rumbase
0.17 partsyrup base
  1. Shake and strain into a cocktail glass.

Famous New Orleans Drinks and How to Mix 'Em by Stanley Clisby Arthur (1938, p.63)

1 limelime juice — Lime juiceacid
2 jiggerrum — Rumbase
2 wholesugar — Sugarbase
1 dashPeychaud's bitters bitter
1 jiggerwater — Waterdilution
crushed ice — Shaved or crushed iceother
nutmeg or red pepper — Nutmeg or red pepperother
  1. Squeeze the lime onto the sugar in a tall glass.
  2. Add the bitters, water, and rum, fill with shaved or crushed ice, frappé well with a long spoon, and finish with a little nutmeg or a dash of red pepper if desired.

Ice: Crushed ice

Lineage reconciliation

See also: Jamaica Rum Cocktail, Tom Collins

Source gives the sweetening as two portions of sugar and allows a dash of red pepper if desired.