“‘I thought I heard you speaking to someone,’ I said.

“He looked a little embarrassed. ‘I sometimes speak aloud when I am thinking about something,’ said he.

“Later, I asked Mrs Wheeler if she had ever heard the professor speaking to himself.

“‘Bless you, my dear!’ was her response. ‘The professor is always talking to himself. It’d be a rare day if he wasn’t!’

“‘But he sounded so agitated,’ I persisted, ‘as if he were quarrelling with someone.’

“‘Ah,’ said she. ‘But you see, Miss Calloway, when he is discussing things with himself, sometimes he agrees with himself, and sometimes he doesn’t.’

“This sounded nonsensical to me, but I did not pursue the matter further. After that, I frequently heard the professor speaking to himself, and occasionally calling out loudly, as if in a heated discussion. The most common phrases I heard him repeat were ‘I’m sorry’ and ‘I don’t know’. The former varied in tone from a muttered, subdued utterance, as if he were accepting the blame for something, to a louder, more defiant statement, as if his apology were not quite genuine and he felt he was being accused of something that was not entirely his fault. The latter – ‘I don’t know’ – was generally spoken with great emphasis, as if to deny an accusation of knowledge upon which he perhaps should have acted but had not.”

“As the months passed, I became more accustomed to Professor Palfreyman’s eccentric ways, although I never really got used to his talking to himself. Sometimes at night, I would hear him talking to himself in his bedroom, and I was never quite sure whether he was asleep or awake. One night, however, I had confirmation that the professor’s troubled mind was not confined to the hours of wakefulness. It came at the end of what had been an odd day, which had begun with a most curious incident. It may be of no significance – I cannot judge – but it sometimes seems to me that a slight decline in Professor Palfreyman’s competence and health dates from about that time. He and I were seated together at breakfast, one morning in the spring, when the maid brought in the post, which had just been delivered. There were a couple of tradesmen’s accounts and one expensive-looking long envelope.

“‘I wonder what this can be?’ said the professor as he opened it and drew out the letter from within. Next moment, he let out a little cry of surprise. He held up the sheet and turned it over, and to my great surprise I saw that it was perfectly blank.

“I laughed. ‘Someone has made a rather silly mistake,’ I said.

“The professor did not reply, but looked again intently at the outside of the envelope.

“‘Do you recognize the handwriting?’ I asked, as I saw his face assume a thoughtful expression. He did not respond to my question, but after a moment asked me if I knew what the date was.

“I glanced at the calendar on the wall. ‘It is May the fourteenth,’ I said. At this an odd look came over his face, which contained something, I thought, of fear, and he sat without speaking for several minutes. ‘Perhaps there is a secret message on the sheet,’ I ventured at length in a jocular tone, as much to break the silence as because I thought it at all likely.

“‘What do you mean?’ he asked.

“‘I remember seeing in an Adventure Book for Girls which I read at school that spies and people of that sort send messages to each other in invisible ink.’ Afterwards, I regretted saying this, but what is done cannot be undone, and I wasn’t to know the effect it would have upon the professor. I had simply been trying to lighten the mood a little.

“‘How could we read it if it’s invisible?’ the professor asked.

“‘I understand that if you heat it the writing becomes visible,’ I said. I picked up the blank sheet, and, using the fire tongs from the coal scuttle, held it just in front of the blazing fire. At first nothing happened, then slowly something began to appear on the sheet. It wasn’t a message, however, but a drawing, a sketch of a human face. It was fairly crude, but I could see it was the face of a woman, with long hair and a broad smile. A strangled cry from behind me made me turn. The professor’s eyes were wide with fear.

“‘What do you know of this?’ he demanded sharply.

“‘Why, nothing,’ I cried in alarm. ‘What do you mean?’

“A moment later, the spark of anger in his eyes had vanished. He sunk his head in his hands and remained motionless for several minutes. I turned back to the fire, to see that the flames had caught the bottom edge of the paper, and it was beginning to burn. Quickly, I tossed it onto the fire, and watched as the flames consumed that strange smiling face. Then I turned once more as I heard the professor stand up from the table.

“‘Forgive me, Georgina, for speaking to you in that way,’ said he in a gentle tone. ‘I didn’t know what I was saying. Either someone has made a silly mistake, as you say, or someone is deliberately playing a trick upon me. In either case, let us say no more about it.’ He picked up the envelope from the table, tore it into several small pieces and threw them onto the fire, where they blazed up in an instant. He then began to speak to me about the architecture of ancient Sicily, which was something I had asked him about the previous day, and the incident of the letter was not mentioned again.

“That night was very dark and overcast. I had been fast asleep, when I was abruptly awakened by a terrible cry. Scarcely knowing what I was doing, I struck a match and lit the candle beside my bed. It was, as I saw from my bedside clock, about quarter to four. The next moment came that terrible cry again, a cry of utter terror, and I knew then for certain that it was Professor Palfreyman. His bedroom is next to mine and the walls are not particularly thick. It was evident that he was having some kind of awful nightmare, and I sat up in bed, unsure what to do. Then I heard him cry again, ‘No!’ Then, after a slight pause, ‘Don’t look at it! For God’s sake, don’t look at the face!’ This was followed by a series of bangs and crashes, and I wondered if the professor had fallen out of bed. I flung on my dressing gown, picked up my candle and went to see what had happened.

“My knock at his bedroom door brought no response, so I pushed the door open. Professor Palfreyman was sitting on the side of the bed in his night clothes, looking somewhat dazed, as if he were not fully awake. Before I could speak, he looked up and stared at my face with very great intensity, then emitted the most dreadful cry of fear that I have ever heard in my life, and put his hands up to cover his eyes.

“‘Professor!’ I cried, taking a step forward. ‘Professor! It is I, Georgina! There is nothing to fear!’ I lowered my candle, so that it was not casting my face in a strange light, which I thought might have frightened him in his half-awake state. As I did so, he looked up and lowered his hands.

“‘Georgina,’ he said. ‘Is it really you?’

“I assured him that it was, at which a look of indescribable relief came over him. ‘I heard you cry out,’ I said. ‘Did you fall out of bed?’

“‘I suppose I must have done,’ he replied. ‘I can’t really remember anything about it.’

“I could see that he was embarrassed and ashamed of the whole episode, so I did not ask him any more about it. ‘I think,’ I said, ‘that you must have had a nightmare.’

“He nodded his head, but insisted that, after a sip of water, he would be all right. I therefore returned to my own room, after lighting his candle from my own. Whether or not he managed to get back to sleep, I do not know, but I heard nothing further that night. I don’t know if Mrs Wheeler had heard much of this night-time commotion – she sleeps in the attic and is, besides, somewhat deaf – but her daughter, Beryl, certainly had. The next day I chanced to overhear her speaking to her mother about it and referring to the professor as ‘a madman’. I told her that she shouldn’t speak that way about Professor Palfreyman. ‘He has had rather a lot on his mind recently,’ I said, ‘and he simply had a bad nightmare, that is all. It could happen to anyone.’ She didn’t say much to this, but I think she resented being scolded by me, and it was not long after this that she ran off, as I mentioned earlier.