The British Museum owns about 8 million items. If you're a nefarious director, or even an employee with access, I'm sure it's easy to nick a few here and there. They're talking about 1500 items missing... a tiny fraction of the total. Most items are in boxes in storage... nobody would even know they are gone until they do an audit.
I have a few collections I'd like to donate to a museum or library at some point, but wouldn't consider an institution like the British Museum. Too big, too many items, and no chance of your collections ever being displayed. Plus there's a good chance they might just go "poof" Bruce
