This was my first really good look at the middle-aged male with the mop of black hair. His quick-darting eyes were fully as black as his hair, and the appearance of his chin and jowls made it evident that his beard would have been likewise if he gave it half a chance. He sat down and was telling Cramer who and what he was.

Cramer nodded impatiently. “I know. You have something to say, Dr. Morley?”

“I have. Something vital.”

“Let’s hear it.”

Morley got better settled in his chair. “First, I assume that no arrest has been made. Is that correct?”

“Yes — if you mean an arrest with a charge of murder.”

“Have you a definite object of suspicion, with or without evidence in support?”

“If you mean am I ready to name the murderer, no. Are you?”

“I think I may be.”

Cramer’s chin went up. “Well? I’m in charge here.”

Dr. Morley smiled. “Not quite so fast. The suggestion I have to offer is sound only with certain assumptions.” He placed the tip of his right forefinger on the tip of his left little finger. “One: that you have no idea who committed this murder, and apparently you haven’t.” He moved over a finger. “Two: that this was not a commonplace crime with a commonplace discoverable motive.” To the middle finger. “Three: that nothing is known to discredit the hypothesis that this girl — I understand from Mrs. Orwin that her name was Cynthia Brown — that she was strangled by the man who strangled Doris Hatten on October seventh last year. May I make those assumptions?”

“You can try. Why do you want to?”

Morley shook his head. “Not that I want to. That if I am permitted to, I have a suggestion. I wish to make it clear that I have great respect for the competence of the police, within proper limits. If the man who murdered Doris Hatten had been vulnerable to police techniques and resources, he would almost certainly have been caught. But he wasn’t. You failed utterly. Why?”

“You’re telling me.”

“Because he was out of bounds for you. Because your exploration of motive is restricted by your preconceptions.” Morley’s black eyes gleamed. “You’re a layman, so I won’t use technical terms. The most powerful motives on earth are motives of the personality, which cannot be exposed by any purely objective investigation. If the personality is twisted, distorted, as it is with a psychotic, then the motives are twisted too. As a psychiatrist I was deeply interested in the published reports of the murder of Doris Hatten — especially the detail that she was strangled with her own scarf. When your efforts to find the culprit — thorough, no doubt, and even brilliant — ended in complete failure, I would have been glad to come forward with a suggestion, but I was as helpless as you.”

“Get down to it,” Cramer muttered.

“Yes.” Morley put his elbows on the table and paired all his fingertips. “Now today. On the basis of the assumptions I began with, it is a tenable theory, worthy to be tested, that this was the same man. If so he has made a mistake. Apparently no one got in here today without having his name checked; the man at the door was most efficient. So it is no longer a question of finding him among thousands or millions; it’s a mere hundred or so, and I am willing to contribute my services. I don’t think there are more than three or four men in New York qualified for such a job, and I am one of them. You can verify that.”

The black eyes flashed. “I admit that for a psychiatrist this is a rare opportunity. Nothing could be more dramatic than a psychosis exploding into murder. I don’t pretend that my suggestion is entirely unselfish. All you have to do is to have them brought to my office — one at a time, of course. With some of them ten minutes will be enough, but with others it may take hours. When I have—”

“Wait a minute,” Cramer put in. “Are you suggesting that we deliver everyone that was here today to your office for you to work on?”

“No, not everyone, only the men. When I have finished I may have nothing that can be used as evidence, but there’s an excellent chance that I can tell you who the strangler is, and when you once know that—”

“Excuse me,” Cramer said. He was on his feet. “Sorry to cut you off, Doctor, but I must get downtown.” He was on his way. “I’m afraid your suggestion wouldn’t work. I’ll let you know—”

He went, and Levy and Murphy with him.

Dr. Morley pivoted his head to watch them go, kept it that way a moment, and then came back to us. He looked disappointed but not beaten. The black eyes, after resting on me briefly, darted to Wolfe.

“You,” he said, “are intelligent and literate. I should have had you more in mind. May I count on you to explain to that policeman why my suggestion is the only hope for him?”

“No,” Wolfe said curtly.

“He’s had a hard day,” I told Morley. “So have I. Would you mind closing the door after you?”

He looked as if he had a notion to start on me as a last resort, so I got up and circled around to the door, which had been left open, and remarked to him, “This way, please.”

He arose and walked out without a word. I shut the door, had a good stretch and yawn, crossed to open a window and stick my head out for a breath of air, closed the window, and looked at my wrist watch.

“Twenty minutes to ten,” I announced.

Wolfe muttered, “Go look at the office door.”

“I just did, as I let Morley out. It’s sealed. Malefic spite.”

“See if they’re gone and bolt the door. Send Saul home and tell him to come at nine in the morning. Tell Fritz I want beer.”

I obeyed. The hall and front room were uninhabited. Saul, whom I found in the kitchen with Fritz, said he had made a complete tour upstairs and everything was in order. I stayed for a little chat with him while Fritz took a tray to the dining room. When I left him and went back Wolfe, removing the cap from a bottle of beer with the opener Fritz had brought on the tray, was making a face, which I understood. The opener he always used, a gold item that a satisfied client had given him years ago, was in the drawer of his desk in the office. I sat and watched him pour beer.

“This isn’t a bad room to sit in,” I said brightly.

“Pfui! I want to ask you something.”

“Shoot.”

“I want your opinion of this. Assume that we accept without reservation the story Miss Brown told you. By the way, do you?”

“In view of what happened, yes.”

“Then assume it. Assume also that the man she had recognized, knowing she had recognized him, followed her downstairs and saw her enter the office; that he surmised that she intended to consult me; that he postponed joining her in the office either because he knew you were in there with her or for some other reason; that he saw you come out and go upstairs; that he took an opportunity to enter the office unobserved, got her off guard, killed her, got out unobserved, and returned upstairs. All of those assumptions seem to be required, unless we discard all that and dig elsewhere.”

“I’ll take it that way.”

“Very well. Then we have significant indications of his character. Consider it. He has killed her and is back upstairs, knowing that she was in the office talking with you for some time. He would like to know what she said to you. Specifically, he would like to know whether she told you about him, and if so how much. Had she or had she not named or described him in his current guise? With that question unanswered, would a man of his character as indicated leave the house? Or would he prefer the challenge and risk of remaining until the body had been discovered, to see what you would do? And I too, of course, after you had talked with me, and the police?”

“Yeah.” I chewed my lip. There was a long silence. “So that’s how your mind’s working. I could offer a guess.”

“I prefer a calculation to a guess. For that a basis is needed, and we have it. We know the situation as we have assumed it, and we know something of his character.”

“Okay,” I conceded, “a calculation. I’ll be damned. The answer I get, he would stick around until the body was found, and if he did, then he is one of the bunch Cramer has been talking with. So that’s what occurred to you, huh?”

“No. By no means. That’s a different matter. This is merely a tentative calculation for a starting point. If it is sound, I know who the murderer is.”

I gave him a look. Sometimes I can tell how much he is putting on and sometimes I can’t. I decided to buy it. With the office sealed up by the crabbed and envious mind of Inspector Cramer, he was certainly in no condition to entertain himself by trying to string me.

“That’s interesting,” I said admiringly. “If you want me to get him on the phone I’ll have to use the one in the kitchen.”

“I want to test the calculation.”

“So do I.”

“But there’s a difficulty. The test I have in mind, the only one I can contrive to my satisfaction — only you can make it. And in doing so you would have to expose yourself to great personal risk.”

“For God’s sake.” I gawked at him. “This is a brand-new one. The errands you’ve sent me on! Since when have you flinched or faltered in the face of danger to me?”

“This danger is extreme.”

“So is the fix you’re in. The office is sealed, and in it are the book you’re reading and the television set. Let’s hear the test. Describe it. All I ask is ninety-nine chances in a hundred.”

“Very well.” He turned a hand over. “The decision will be yours. The typewriter in the office is inaccessible. Is that old one in your room in working order?”

“Fair.”

“Bring it down here, and some sheets of blank paper — any kind. I’ll need a blank envelope.”

“I have some.”

“Bring one. Also the telephone book, Manhattan, from my room.”

I went to the hall and up two flights of stairs. Having collected the first three items in my room, I descended a flight, found that the door of Wolfe’s room was still locked, and had to put the typewriter on the floor to get out my keys. With a full cargo I returned to the dining room, unloaded, and was placing the typewriter in position on the table when Wolfe spoke.

“No, bring it here. I’ll use it myself.”

I lifted my brows at him. “A page will take you an hour.”

“It won’t be a page. Put a sheet of paper in it.”

I did so, got the paper squared, lifted the machine, and put it in front of him. He sat and frowned at it for a long minute and then started pecking. I turned my back on him to make it easier to withhold remarks about his two-finger technique, and passed the time by trying to figure his rate. That was hopeless, because at one moment he would be going at about twelve words a minute and then would come a sudden burst of speed, stepping it up to twenty or more. All at once there was the sound of the ratchet turning as he pulled the paper out, and I supposed he had ruined it and was going to start over, but when I turned to look his hand was extended to me with the sheet in it.

“I think that will do,” he said.

I took it and read what he had typed:

She told me enough this afternoon so that I know who to send this to, and more. I have kept it to myself because I haven’t decided what is the right thing to do. I would like to have a talk with you first, and if you will phone me tomorrow, Tuesday, between nine o’clock and noon, we can make an appointment; please don’t put it off or I will have to decide myself.

I read it over three times. I looked at Wolfe. He had put an envelope in the typewriter and was consulting the phone book.

“It’s all right,” I said, “except that I don’t care for the semicolon after ‘appointment.’ I would have put a period and started a new sentence.”

He began pecking, addressing the envelope. I waited until he had finished and rolled the envelope out.

“Just like this?” I asked. “No name or initials signed?”

“No.”

“I admit it’s nifty,” I admitted. “Hell, we could forget the calculation and send this to every guy on that list and wait to see who phoned. He has just about got to phone — and also make a date.”

“I prefer to send it only to one person — the one indicated by your report of that conversation. That will test the calculation.”

“And save postage.” I glanced at the paper. “The extreme danger, I suppose, is that I’ll get strangled. Or of course in an emergency like this he might try something else. He might even arrange for help. If you want me to mail this I’ll need that envelope.”

“I don’t want to minimize the risk of this, Archie.”

“Neither do I. I’ll have to borrow a gun from Saul; ours are in the office. May I have that envelope? I’ll have to go to Times Square to mail it.”

“Yes. Before you do so, copy that note; we should have a copy. Keep Saul here in the morning. If and when the phone call comes you will have to use your wits to arrange the appointment as advantageously as possible. Discussion of plans will have to wait upon that.”

“Right. The envelope, please?”

He handed it to me.