He was piecing together the puzzle which Thornton Lyne had made so much more simple.
The mystery was clearing up.

Thornton Lyne had gone to that flat not in response to the telegram, but with the object of compromising and possibly ruining the girl.

He had gone with the little slip of paper inscribed with Chinese characters, intending to leave the Hong in a conspicuous place, that somebody else might be blamed for his infamy.
Milburgh had been in the flat for another purpose.

The two men had met; there had been a quarrel; and Milburgh had fired the fatal shot.

That part of the story solved the mystery of Thornton Lyne's list slippers and his Chinese characters; his very presence there was cleared up.