Years ago I went to a house concert where a husband and wife who were retired Navy and still lived on a boat said that in the olden days (prob 1700's) a pub sold a mix of liquors from a punch bowl with fruit in it. To fathom the bowl is to dip the ladle to the bottom and retrieve some fruit for the drinker. The couple may have been named Nash.

I guess a flowing bowl is providing lots of ladlefuls, because normally you wouldn't want any liquor flowing out of the bowl to be wasted.* I remember this scrap of a song from that night:

There's a whole world of pleasure in England's control.
Give me the punch ladle; we'll fathom the bowl.
We'll fathom the bowl [2x]
Give me the punch ladle; we'll fathom the bowl.

It had a good tune to it.

*Spellcheck doesn't like "ladlefuls". Get over yourself, Spellcheck. Humans are the only animals that invent new words.