The hand-bag was of fine gold mesh with a catch set with small sapphires. It was unusually small, and obviously designed only for evening wear. The objects which it had held, and which Markham was now inspecting, consisted of a flat watered-silk cigarette-case, a small gold phial of Roger and Gallet’s Fleurs d’Amour[32] perfume, a cloisonné[33] vanity-compact, a short delicate cigarette-holder of inlaid amber, a gold-cased lip-stick, a small embroidered French-linen handkerchief with “M. St.C.” monogrammed in the corner, and a Yale latch-key.

“This ought to give us a good lead,” said Markham, indicating the handkerchief. “I suppose you went over the articles carefully, Sergeant.”

Heath nodded.

“Yes; and I imagine the bag belongs to the woman Benson was out with last night. The housekeeper told me he had an appointment and went out to dinner in his dress clothes. She didn’t hear Benson when he came back, though. Anyway, we ought to be able to run down Miss ‘M. St.C.’ without much trouble.”

Markham had taken up the cigarette-case again, and as he held it upside down a little shower of loose dried tobacco fell onto the table.

Heath stood up suddenly.

“Maybe those cigarettes came out of that case,” he suggested. He picked up the intact butt and looked at it. “It’s a lady’s cigarette, all right. It looks as though it might have been smoked in a holder, too.”

“I beg to differ with you, Sergeant,” drawled Vance. “You’ll forgive me, I’m sure. But there’s a bit of lip rouge on the end of the cigarette. It’s hard to see, on account of the gold tip.”

Heath looked at Vance sharply; he was too much surprised to be resentful. After a closer inspection of the cigarette, he turned again to Vance.

“Perhaps you could also tell us from these tobacco grains, if the cigarettes came from this case,” he suggested, with gruff irony.

“One never knows, does one?” Vance replied, indolently rising.

Picking up the case, he pressed it wide open, and tapped it on the table. Then he looked into it closely, and a humorous smile twitched the corners of his mouth. Putting his forefinger deep into the case, he drew out a small cigarette which had evidently been wedged flat along the bottom of the pocket.

“My olfact’ry gifts won’t be necess’ry now,” he said. “It is apparent even to the naked eye that the cigarettes are, to speak loosely, identical—eh what, Sergeant?”

Heath grinned good-naturedly.

“That’s one on us, Mr. Markham.” And he carefully put the cigarette and the stub in an envelope, which he marked and pocketed.

“You now see, Vance,” observed Markham, “the importance of those cigarette butts.”

“Can’t say that I do,” responded the other. “Of what possible value is a cigarette butt? You can’t smoke it, y’ know.”

“It’s evidence, my dear fellow,” explained Markham patiently. “One knows that the owner of this bag returned with Benson last night, and remained long enough to smoke two cigarettes.”

Vance lifted his eyebrows in mock amazement.

“One does, does one? Fancy that, now.”

“It only remains to locate her,” interjected Heath.

“She’s a rather decided brunette, at any rate—if that fact will facilitate your quest any,” said Vance easily; “though why you should desire to annoy the lady, I can’t for the life of me imagine—really I can’t, don’t y’ know.”

“Why do you say she’s a brunette?” asked Markham.

“Well, if she isn’t,” Vance told him, sinking listlessly back in his chair, “then she should consult a cosmetician as to the proper way to make up. I see she uses ‘Rachel’ powder and Guerlain’s dark lip-stick. And it simply isn’t done among blondes, old dear.”