Itunes music file in the wrong place?

Hi all, I have an Imac and and a Macbook, and want all of my music on an external hard drive, so I can just plug the external hard drive into either computer and have iTunes on each computer bring up my whole library and playlists from the hard drive.

I have already moved my music onto the external hard drive. Itunes on my imac lets me drop music into it and saves it to the hard drive and knows where to look as I have adjusted the preferences for the location of the itunes media folder in advanced to the hard drive.

But when I plug the hard drive into my macbook and choose the location of the itunes media folder, there is no itunes library file on the external hard drive at all so the macbook cant find the library and itunes is empty.

The itunes library files are on the Imac and not the hard drive!

This has confused me as i would have thought they would be on the external hard drive with the music and i could get both computers to look there.

Can anyone help?

Thanks in advance, and sorry if I have missed something obvious!