Daly's Bartenders' Encyclopedia by Tim Daly (1903, p.108)

1 ponyAbsinthe base
0.5 glassice — fine icebase
water — ice waterdilution
3 dashesanisette modifier
  1. Place the pony glass of absinthe in a mixing glass half filled with fine ice and add anisette.
  2. Drop ice water slowly into the absinthe from a small pitcher, remove the pony glass, and serve.

Ice: Fine ice

The slow-drop dilution ritual is the entire point of the drink.

See also: Absinthe Cocktail, Absinthe Frappe