And Mr. Judson, with shining face, hurried off to the housekeeper’s room.

“I simply can’t understand it,” said Joan at length.  “My head is going round.”

“Can’t understand it?  Why, it’s perfectly clear.  This is the coincidence for which, in my capacity of Gridley Quayle, I was waiting.  I can now resume inductive reasoning.  Weighing the evidence, what do we find?  That young sweep, Freddie, is the man.  He has the scarab.”

“But it’s all such a muddle.  I’m not holding his letters.”

“For Jones’ purposes you are.  Let’s get this Jones element in the affair straightened out.  What do you know of him?”

“He was an enormously fat man who came to see me one night and said he had been sent to get back some letters.  I told him I had destroyed them ages ago and he went away.”

“Well, that part of it is clear, then.  He is working a simple but ingenious game on Freddie.  It wouldn’t succeed with everybody, I suppose; but from what I have seen and heard of him Freddie isn’t strong on intellect.  He seems to have accepted the story without a murmur.  What does he do?  He has to raise a thousand pounds immediately, and the raising of the first five hundred has exhausted his credit.  He gets the idea of stealing the scarab!”

“But why?  Why should he have thought of the scarab at all?  That is what I can’t understand.  He couldn’t have meant to give it to Mr. Peters and claim the reward.  He couldn’t have known that Mr. Peters was offering a reward.  He couldn’t have known that Lord Emsworth had not got the scarab quite properly.  He couldn’t have known—­he couldn’t have known anything!”

Ashe’s enthusiasm was a trifle damped.

“There’s something in that.  But—­I have it!  Jones must have known about the scarab and told him.”

“But how could he have known?”

“Yes; there’s something in that, too.  How could Jones have known?”

“He couldn’t.  He had gone by the time Aline came that night.”

“I don’t quite understand.  Which night?”

“It was the night of the day I first met you.  I was wondering for a moment whether he could by any chance have overheard Aline telling me about the scarab and the reward Mr. Peters was offering for it.”

“Overheard!  That word is like a bugle blast to me.  Nine out of ten of Gridley Quayle’s triumphs were due to his having overheard something.  I think we are now on the right track.”

“I don’t.  How could he have overheard us?  The door was closed and he was in the street by that time.”

“How do you know he was in the street?  Did you see him out?”

“No; but he went.”

“He might have waited on the stairs—­you remember how dark they are at Number Seven—­and listened.”

“Why?”

Ashe reflected.

“Why?  Why?  What a beast of a word that is—­the detective’s bugbear.  I thought I had it, until you said—­Great Scott!  I’ll tell you why.  I see it all.  I have him with the goods.  His object in coming to see you about the letters was because Freddie wanted them back owing to his approaching marriage with Miss Peters—­wasn’t it?”