The Hoffman House Bartender's Guide by Charles S. Mahoney (1905, p.212)

0.5 glassRhine wine base
0.5 glassseltzer — Balance with seltzer.dilution
  1. Fill the glass half full with Rhine wine and the balance with seltzer.
  2. Keep both the Rhine wine and seltzer on ice.

Jack's Manual by J. A. Grohusko (1910, p.75)

2 glassesSoda water — seltzerbase
Rhine wine — Fill with Rhine wine.other
  1. Build the seltzer in a glass.
  2. Fill with Rhine wine and serve.

Ice: None

The Buffet Blue Book by John H. Considine (1912, p.48)

0.5 star champagne glassRhine wine base
seltzer or other carbonated water — Fill the balance of the glass.dilution
  1. Fill a star champagne glass halfway with Rhine wine.
  2. Fill the balance with seltzer or any other carbonated water and serve.

Ice: None

Bartenders' Manual by Bartenders Association of America (1913, p.39)

0.5 glassRhine wine base
0.5 glassseltzer — Seltzerdilution
  1. Fill half the glass with Rhine wine and the balance with chilled seltzer.

The Up-to-Date Bartender's Guide by Harry Montague (1913, p.35)

0.75 glassRhine wine — Off the ice.base
0.25 glassseltzer — Off the ice.dilution
  1. Fill a large bar glass three-quarters with Rhine wine and one-quarter with seltzer, both off the ice.
  2. Serve cold.

See also: Claret and Ice, Rhine Wine and Seltzer-Water

Source explicitly says both components are off the ice.