"Tin rickies"

This is the closest reference I found on line in a quick search for the song about the river of rum (the song called "Happy Land" on a page about the Berkshire Boys Camp). Here are the words as we learned them:

Have you ever been
In the land of gin
Where the river of rum flows by,
Where the little gin rickeys
Grow in the trees
And the highballs grow on the ground?

The singers begin, say, at G (or "sol") and sing the tune as follows:

Sol sol mi sol sol
Sol sol fa sol sol
Sol sol mi mi sol mi re do
Sol sol mi mi sol sol sol
Mi sol sol sol
Sol sol mi sol mi re re do

The next verse repeats the words but begins at C an octave above middle C, in the key of F, as follows:

C1 C1 B-flat C1 C1, etc.

And so it goes on until no one can sing any higher. Here's a virtual keyboard with sounds so that you may try it out for yourself. This is a song from childhood; I have a feeling that it may be an old fraternity or sorority song. I'd be interested in learning whether anyone else remembers anything about it. This is a personal inquiry along the lines of my entry on "Mister Mustard, Mister Mustard, please let me down."