The original version of this drink was known as the "Harvard Cocktail" from 1895, which had a slightly different recipe. This "Fizz" version of it evolved from that one and is served as a traditional "Fizz" instead of in a cocktail glass.
The original Harvard Cocktail recipe was:
"One dash gum-syrup, three dashes Angostura bitters, half-jigger Italian vermouth, half-jigger brandy in half a mixing-glass of fine ice. Mix, strain into cocktail-glass, fill up with seltzer."