How to use the Tag description as the title attribute?

Question

I'm trying to use tags to create a list of cross references for each post and want the tag description to show next to the tag and/or as the title attribute for the hyperlink so the description shows when a visitor holds the cursor over the link.

Using the TwentyTen theme I have located the code in functions.php and amended it as below:

function twentyten_posted_in() {
    // Retrieves tag list of current post, separated by commas.
    $tag_list = get_the_tag_list( $before = '<br /> <br />' , $sep = ' here'.'<br /><br />' , $after = '<br />' );
    if ( $tag_list ) {
        $posted_in = __( 'Cross Reference %2$s. ', 'twentyten' );
    } 


    // Prints the string, replacing the placeholders.
    printf(
        $posted_in,
        get_the_category_list( ',  ' ),
        $tag_list,
                get_permalink(),
        the_title_attribute( 'echo=0' )
    );
}
endif;

As you can see I've changed the heading to say Cross Reference and by adding breaks I have a list of tags rather than a paragraph. I've identified where I want the Tag Description to go with the word "here".

I thought it would be as simple as adding tag_description() but that didn't work. If I put a number in the brackets, e.g. tag_description(5) it displays the tag description in the correct place, but of course all the tags have the wrong description.

Help!

Thanks Ian.