All you need to do is put the session_start(); command at the top of the second page. You need to call that command to initialize the session for that page. Here is what it says in the PHP manual:
Description
bool session_start ( void)
session_start() creates a session (or resumes the current one based on the session id being passed via a GET variable or a cookie).
If you want to use a named session, you must call session_name() before calling session_start().
This function always returns TRUE.
Note: If you are using cookie-based sessions, you must call session_start() before anything is output to the browser.
I tried it on your exampleand it works fine.