Once upon a time in America - say about the latter part of the 19th century, there were many glass makers who fashioned sets of glass dishes for the everyday Victorian Home. Some of the sets of dishes, we are told by Mrs. Ruth Webb Lee, included “water sets”, as they were known in the trade, and some of these water sets included a bowl.
    In her 1931 book, Early American Pressed Glass, she called all of these bowls “finger bowls”. Later on in her 1944 book, Victorian Glass, she illustrated some water sets. These sets, see below, all included a water pitcher, a tray and 2-4 drinking vessels and some included a piece she said the old glass factory term for was “waste bowl”. By this time, she did not believe that these bowls were usually intended to be “finger bowls” although she characterized at least one as a finger bowl!
Mrs. Lee does not name this bowl..... she calls this a finger bowl.... she calls this a waste bowl.. and she calls this a waste bowl!
  To add to the historical confusion, other authors are equally equivocal about
their characterization of these mystery pieces and none of them that we could find
ventured into a conjecture as to their intended purpose.

This is a water set in vaseline glass in a pattern unknown to us and.....

 ..a close up of its .......bowl.
So! What were these bowls originally made to do? Why have a 5" bowl
as a part of so many water sets? Well, years ago, PatternGlass.com
began to query pattern glass folks and here were some
of the answers we got......
Adam's Glass Company made this bowl to go with its Fleur d' Lis & Drape pattern ca 1888.....
 ...and the King Glass Company made this one in the Picket Fence aka London pattern in the 1880s.
....they provided a receptacle for the rinds of lemons. But did
                     all water sets just serve lemonade? We didn't think so.
This is a pattern called SHIELD BAND
with engraved fern & berry decor.		 This is the U S Glass
states' series pattern Carolina.
Well, said others, they were used to pour out the dregs from the pitcher
or drinking vessels before pouring another round. So were all liquid
refreshments so yucky that they had a big ol' sediment? Surely not.
This is a waste bowl in the
funky Egg in Sand pattern.
Polar Bear is a great pattern found
only in the water set pieces
as far as we know.
Others postulated that the bowls were to set under drinking vessels as they
were filled to catch the drips from unsteady hands of Victorians.  But.....
Another U S Glass States Series pattern; this is Indiana.
Even Monkeys were immortalized in a pattern of EAPG!

A dainty midwestern Pomona pattern called
Flower & Pleat by Crystal Glass Co. c1892
....none of these theories were convincing to us so we kept searching
until finally we asked a "grand dame" of pattern glass who
huffed with total aplomb -- as though she had been there--
"The bedroom water sets had slop bowls for cleaning teeth since
there were no indoor bathrooms and no running water."
Of course! The water set bowl was the perfect solution to
the need for a receptacle for ahhhh.... toothpaste waste.
So maybe now we know why the use was not memorialized
in any of the nice Victorian literature......