Can anyone identify this tune?

Hi. This is a music box my grandmother has owned for some time. I've listened to it since I was a very young child, and I'm curious if anyone here can identify the tune it plays. I've been thinking about writing something using this melody as a theme, since it has some personal sentiment to me, but I'd like to attribute the melody to its original composer if at all possible. 

It is "The Way We Were" from a movie by the same name sung by Barbara Streisand. The movie is from the 1970s.

Thanks. I've always been curious about that little object.