"Fathom the Bowl" (Roud 880) is an English drinking song dating from the nineteenth century.
During the chorus, the singing slows down in order to relish a rising musical scale on "Fathom-the bowl".
On the other hand, it might be a song sung by wealthy middle-class young gentlemen or military officers, which gradually made its way down the social ladder.
According to the "folkinfo" website the "Clear crystal fountain" is supposed to refer to winter storms, but it is not obvious how this is either possible or relevant to the story.
It is a so-called "catalogue song", similar to "Good Luck to The Barley Mow" and "All For Me Grog".