“Let us sit down on this bench,” said Thorndyke, “and thrash the matter out. I will put my case to you and you can give me your criticisms on it. I will begin by stating that some months ago I came to the conclusion that Purcell was dead.”

Both the brothers started and gazed at Thorndyke in utter astonishment. Then Rodney said: “You say ‘some months ago.’ You must mean within the last three months.”

“No,” replied Thorndyke. “I decided that he died on the 23rd of last June, before the yacht reached Penzance.”

An exclamation burst simultaneously from both of his hearers and Rodney protested impatiently: “But this is sheer nonsense, if you will pardon me for saying so. Have you forgotten that two persons have received letters from him less than four months ago?”

“I suggest that we waive those letters and consider the other evidence.”

“But you can’t waive them,” exclaimed Rodney. “They are material evidence of the most conclusive kind.”

“I may say that I have ascertained that both those letters were forgeries. The evidence can be produced, if necessary, as both the letters are in existence, but I don’t propose to produce it now. I ask you to accept my statement for the time being and to leave the letters out of the discussion.”

“It is leaving out a good deal,” said Rodney. “I find it very difficult to believe that they were forgeries or to imagine who on earth could have forged them. However, we won’t contest the matter now. When did you come to this extraordinary conclusion?”

“A little over four months ago,” replied Thorndyke.

“And you never said anything to any of us on the subject,” said Rodney, “and what is more astonishing, you actually put in an advertisement, addressed to a man whom you believed to be dead.”