Greenwich, time and 'the line'

Ask most visitors to the Royal Observatory, Greenwich, why they have come and they will tell you that they want to stand on 'the line'. Press them further and they might add something about standing astride longitude zero, one foot in the eastern hemisphere and one in the west. Few know how the Prime Meridian of the world comes to pass through Greenwich, or even realise that the line is there because of the observatory, rather than vice versa. But the line, of course, has a history, as does the public's response to it.