HIS DEDUCTION The man in the corner cocked his funny thin head on one side and looked at Polly; then he took up his beloved bit of string and deliberately untied every knot he had made in it.

When it was quite smooth he laid it out upon the table.
"I will take you, if you like, point by point along the line of reasoning which I followed myself, and which will inevitably lead you, as it led me, to the only possible solution of the mystery.
"First take this point," he said with nervous restlessness, once more taking up his bit of string, and forming with each point raised a series of knots which would have shamed a navigating instructor, "obviously it was _impossible_ for Kershaw not to have been acquainted with Smethurst, since he was fully apprised of the latter's arrival in England by two letters.

Now it was clear to me from the first that _no one_ could have written those two letters except Smethurst.

You will argue that those letters were proved not to have been written by the man in the dock.
Exactly.

Remember, Kershaw was a careless man--he had lost both envelopes.