Much of the back catalogue is already available open access direct from the Royal Society:
Most of our oldest content is now freely available, specifically, all papers older than 70 years. In addition, papers published between 10 years ago and either 12 months ago (biological sciences) or 24 months ago (physical sciences) are freely available. For Biographical Memoirs all issues are now freely available, apart from the most recent issue.
Let the downloaders become the sharing infrastructure.