Resource paths when using a forward proxy?

I have a Rails 3 app running under Passenger on one machine, and on
another, which is our public-facing Apache web server, I’ve setup a
forward proxy to point to the server where the Rails app is running. It
works, but the path to the javascripts and stylesheets directories are
not properly completed.

I’ve spent most of the day researching the right thing to do here, but
haven’t found any tips that worked.

Does anyone know the right way to get the paths to be complete? I’m not
sure if the public-facing forward proxy needs more info or if there’s
something to configure in the rails app.

To be perhaps more informative, this works in all respects: ← takes you to the default
list of recording tasks, all css, javascripts, etc., work fine

This works, but no css, etc.

The browser console reports 404 errors for

Failed to load resource:
the server responded with a status of 404 (Not Found)

And so on.