Holmes chuckled and rubbed his hands.  “Great!” he said.  “Great!  Tell me, Friend MacDonald, this pleasing and touching interview was, I suppose, in the professor’s study?”

“That’s so.”

“A fine room, is it not?”

“Very fine —­ very handsome indeed, Mr. Holmes.”

“You sat in front of his writing desk?”

“Just so.”

“Sun in your eyes and his face in the shadow?”

“Well, it was evening; but I mind that the lamp was turned on my face.”

“It would be.  Did you happen to observe a picture over the professor’s head?”

“I don’t miss much, Mr. Holmes.  Maybe I learned that from you.  Yes, I saw the picture—­a young woman with her head on her hands, peeping at you sideways.”

“That painting was by Jean Baptiste Greuze.”

The inspector endeavoured to look interested.

“Jean Baptiste Greuze,” Holmes continued, joining his finger tips and leaning well back in his chair, “was a French artist who flourished between the years 1750 and 1800.  I allude, of course to his working career.  Modern criticism has more than indorsed the high opinion formed of him by his contemporaries.”

The inspector’s eyes grew abstracted.  “Hadn’t we better—­” he said.

“We are doing so,” Holmes interrupted.  “All that I am saying has a very direct and vital bearing upon what you have called the Birlstone Mystery.  In fact, it may in a sense be called the very centre of it.”

MacDonald smiled feebly, and looked appealingly to me.  “Your thoughts move a bit too quick for me, Mr. Holmes.  You leave out a link or two, and I can’t get over the gap.  What in the whole wide world can be the connection between this dead painting man and the affair at Birlstone?”

“All knowledge comes useful to the detective,” remarked Holmes.  “Even the trivial fact that in the year 1865 a picture by Greuze entitled La Jeune Fille a l’Agneau fetched one million two hundred thousand francs—­more than forty thousand pounds—­at the Portalis sale may start a train of reflection in your mind.”

It was clear that it did.  The inspector looked honestly interested.

“I may remind you,” Holmes continued, “that the professor’s salary can be ascertained in several trustworthy books of reference.  It is seven hundred a year.”

“Then how could he buy—­”

“Quite so!  How could he?”

“Ay, that’s remarkable,” said the inspector thoughtfully.  “Talk away, Mr. Holmes.  I’m just loving it.  It’s fine!”

Holmes smiled.  He was always warmed by genuine admiration—­the characteristic of the real artist.  “What about Birlstone?” he asked.

“We’ve time yet,” said the inspector, glancing at his watch.  “I’ve a cab at the door, and it won’t take us twenty minutes to Victoria.  But about this picture:  I thought you told me once, Mr. Holmes, that you had never met Professor Moriarty.”