“Far from it. It was cute in you, of course, to detect cigarette smoke so quickly. But I was the smoker. You’ll find the end of my cigarette in the cuspidor, if you care to look. Here is the box.” Kate took it from the pocket of her woolen robe. “Have one. They seem to steady one’s nerves for a time. It may sharpen you up a bit.”

“My wits don’t need the grindstone,” Nick replied dryly.

“No?” queried Kate, with his own tentative intonation.

“Far from it,” said Nick, imitating her. “You are the one who is not keen and clever. You were not the smoker, Miss Crandall. When a woman has just smoked a cigarette, the scent of it may be easily detected in her hair. I smelled of yours when I sat down.”

“Oh, indeed!”

“Now, having eliminated you, who was your visitor? Why did he hide when I knocked? I know, of course, that he did not depart, or I should have seen him.”

Kate Crandall’s mocking smile had given way to a frown, but it was not of long duration.

“You are very much mistaken, Mr. Carter,” she replied. “He left just before you arrived. If you think any person is concealed in my apartments, you are at liberty to search them.”

“No, indeed; it is not material.”

“I fail to see why you have any interest in me, or my visitor,” Kate quickly added. “Please explain. Why are you here? What have you to say?”