September 19th, 2014, 10:03 AM
Have you installed the Seagate Media App for iOS?
Looks like it only works with a subset of content (music, photos, videos) and does not allow direct downloads of files from a web browser on the iPad to the hard drive.
If the wireless external hard drive supports an FTP/sFTP connection, you might have some luck with the newly-released Transmit iOS app. It's an FTP/sFTP client for iOS, and might allow some type of workaround for what you're trying to do.