“If you can show me her rope was cut that night, I’ll say you’re right,” the detective admitted.  “And if you are right, then the Swede must ‘a’ been right here when your uncle was killed.”

“May have been,” Kirby corrected.  “We haven’t any authentic evidence yet as to exactly when my uncle was killed.  We’re gettin’ the time narrowed down.  It was between 9.30 and 9.50.  We know that.”

“How do you know that?” the professional sleuth asked.  “Accordin’ to your story you didn’t get into the apartment until after ten o’clock.  It might ‘a’ been done any time up till then.”

The eyes of Kirby and Rose met.  They had private information about who was in the rooms from about 9.55 till 10.10.

The cattleman corrected his statement.  “All right, say between 9.30 and 10.05.  During that time Hull may have shot my uncle.  Or Olson may have opened the window while my uncle lay there helpless, killed him, stepped outa the window again, an’ slipped down by the fire escape.  All he’d have to do then would be to walk into the Wyndham, replace the rope on the roof, an’ next mornin’ leave for Dry Valley.”

The detective nodded. “If he cut the rope.  Lemme find out from the landlady whether it was cut that night.”

“Good.  We’ll wait for you at the corner.”

Ten minutes later the detective joined them in front of the drug-store where they were standing.  The hard eyes in his cold gambler’s face were lit up for once.

“I’ll say the man from Missouri has been shown,” he said.  “I let on to the dame at the Wyndham that I was after a gang of young sneak thieves in the neighborhood.  Pretty soon I drifted her to the night of the twenty-third—­said they ’d been especially active that night and had used a rope to get into a second story of a building.  She woke up.  Her clothesline on the roof had been cut that very night.  She remembered the night on account of its being the one when Mr. Cunningham was killed.  Could the boys have used it to get into the store an’ then brought it back?  I thought likely.”

“Bully!  We’re one step nearer than we were.  We know Olson was lookin’ in the window from the fire escape just outside.”

The detective slapped his thigh.  “It lies between Hull and the Swede.  That’s a cinch.”

“I believe it does,” agreed Rose.

Kirby made no comment.  He seemed to be absorbed in speculations of his own.  The detective was reasoning from a very partial knowledge of the facts.  He knew nothing about the relations of James Cunningham to his uncle, nor even that the younger Cunninghams—­or at least one of them—­had been in his uncle’s apartment the evening of his death.  He did not know that Rose had been there.  Wherefore his deductions, even though they had the benefit of being trained ones, were of slight value in this case.

“Will you take the key back to the Chief of Police?” Kirby asked him as they separated.  “Better not tell him who was with you or what we were doin’.”