I finally found this music in the edition of Alexander's Hymns #3, published in 1915 -- but only the version of that book printed in London, not the USA edition! In the London edition, it is #42, and the title is "If We But Knew".

Thanks for your reply, songinmyheart, but sadly, none of the songs listed there match.

Here is a collection of George Coles Stebbins music
you will be able to click on the titles and the music will play
so hopefully you can identify the particular one you are searching for.

http://www.cyberhymnal.org/bio/s/t/e/stebbins_gc.htm

I trust this source will help.

Can any identify the original lyrics for this tune by George Coles Stebbins?

http://nevcal.com/temporary/unknown.mid

A source for it would be nice too.