How did Ramanujan prove this congruence?

Ramanujan observed the congruence $\tau(n) \equiv \sigma_{11}(n) \pmod{691}$, where $\tau$ is the Ramanujan $\tau$-function. Does anybody know how he proved it, or would anybody venture an educated guess?

I know there is a proof in http://www.math.uiuc.edu/~berndt/articles/pt.pdf, accessible to Ramanujan's techniques, and a more conceptual proof by Swinnerton-Dyer that was certainly not accessible to Ramanujan. But I haven't found any proofs claiming to be the original (if indeed he had one).

-

I think the Ramanujan's proof is given in the article you cited (Bruce C. Berndt, Ken Ono, Ramanujan's Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary). J. R. Wilton in his article "On Ramanujan's Arithmetical Function $\Sigma_{r,s}(n)$" http://www.google.com/url?q=http://journals.cambridge.org/production/action/cjoGetFulltext%3Ffulltextid%3D2024792&sa=U&ei=FFlmUYHxKufl4QT57IGQAg&ved=0CCAQFjAE&sig2=fQ7tQw0oBL2wATRgvogPpA&usg=AFQjCNHT5lRGk4GftrHZKNTm5seqMqm90Q writes: