Professor William James Maynard was in a singularly happy and contented mood as he strolled down the High Street after a long and satisfactory interview with the solicitor to his late cousin, whose sole heir he was.

It was exactly a month by the calendar since he had murdered this cousin, and everything had gone most satisfactorily since. The fortune was proving quite as large as he had expected, and not even an inquest had been held upon the dead man. The coroner had decided that it was not necessary, and the Professor had agreed with him.

At the funeral the Professor had been the principal mourner, and the local paper had commented sympathetically on his evident emotion. This had been quite genuine, for the Professor had been fond of his relative, who had always been very good to him. But still, when an old man remains obstinately healthy, when his doctor can say with confidence that he is good for another twenty years at least, and when he stands between you and a large fortune which you need, and of which you can make much better use in the cause of science and the pursuit of knowledge, what alternative is there? It becomes necessary to take steps. Therefore, the Professor had taken steps.

Looking back to-day on that day a month ago, and the critical preceding week, the Professor felt that the steps he had taken had been as judicious as successful. He had set himself to solve a problem in higher mathematics. He had found it easier to solve than many he was obliged to grapple with in the course of his studies.

A policeman saluted as the Professor passed, and he acknowledged it with the charming old world courtesy that made him so popular a figure in the town. Across the way was the doctor who had certified the cause of death. The Professor, passing benevolently on, was glad he had now enough money to carry out his projects. He would be able to publish at once his great work on "The Secondary Variation of the Differential Calculus," that hitherto had languished in manuscript. It would make a sensation, he thought; there was more than one generally accepted theory he had challenged or contradicted in it. And he would put in hand at once his great, his long projected work, "A History of the Higher Mathematics." It would take twenty years to complete, it would cost twenty thousand pounds or more, and it would breathe into mathematics the new, vivid life that Bergson's works have breathed into metaphysics.

The Professor thought very kindly of the dead cousin, whose money would provide for this great work. He wished greatly the dead man could know to what high use his fortune was designed.

Coming towards him he saw the wife of the vicar of his parish. The Professor was a regular church-goer. The vicar's wife saw him, too, and beamed. She and her husband were more than a little proud of having so well known a man in their congregation. She held out her hand and the Professor was about to take it when she drew it back with a startled movement.

"Oh, I beg your pardon!" she exclaimed, distressed, as she saw him raise his eyebrows. "There is blood on it."

Her eyes were fixed on his right hand, which he was still holding out. In fact, on the palm a small drop of blood showed distinctly against the firm, pink flesh. Surprised, the Professor took out his handkerchief and wiped it away. He noticed that the vicar's wife was wearing white kid gloves.

"Oh, I beg your pardon!" she said again. "It—it startled me somehow. I thought you must have cut yourself. I hope it's not much?"

"Some scratch, I suppose," he said. "It's nothing."

The vicar's wife, still slightly discomposed, launched out into some parochial matter she had wished to mention to him. They chatted a few moments and then parted. The Professor took an opportunity to look at his hand. He could detect no sign of any cut or abrasion, the skin seemed whole everywhere. He looked at his handkerchief. There was still visible on it the stain where he had wiped his hand, and this stain seemed certainly blood.

"Odd!" he muttered as he put the handkerchief back in his pocket. "Very odd!"

His thoughts turned again to his projected "A History of the Higher Mathematics," and he forgot all about the incident till, as it happened that day month, the first of the month by the calendar, when he was sitting in his study with an eminent colleague to whom he was explaining his great scheme.

"If you are able to carry it out," the colleague said slowly, "your book will mark an epoch in human thought. But the cost will be tremendous."

"I estimate it at twenty thousand pounds," answered the Professor calmly. "I am fully prepared to spend twice as much. You know I have recently inherited forty thousand pounds from a relative?"

The eminent colleague nodded and looked very impressed.

"It is magnificent," he said warmly, "magnificent." He added: "You've cut yourself, do you know?"

"Cut myself?" the Professor echoed, surprised.

"Yes," answered the eminent colleague, "there is blood upon your hand—your right hand."

In fact a spot of blood, slightly larger than that which had appeared before, showed plainly upon the Professor's right hand. He wiped it away with his handkerchief, and went on talking eagerly, for he was deeply interested. He did not think of the matter again till just as he was getting into bed, when he noticed a red stain upon his handkerchief. He frowned and examined his hand carefully. There was no sign of any wound or cut from which the blood could have come, and he frowned again.

"Very odd!" he muttered.

A calendar hanging on the wall reminded him that it was the first of the month.

The days passed, the incident faded from his memory, and four weeks later he came down one morning to breakfast in an unusually good temper. There was a certain theory he had worked on the night before he meant to write to a friend about. It seemed to him his demonstration had been really brilliant, and then, also, he was already planning out with great success the details of the scheme for his great work.

He was making an excellent breakfast, for his appetite was always good, and, needing some more cream, he rang the bell. The maid appeared, he showed her the empty jug, and as she took it she dropped it with a sudden cry, smashing it to pieces on the floor. Very pale, she stammered out:

"Beg pardon, sir, your hand—there is blood upon your hand."

In fact, on the Professor's right hand there showed a drop of blood, perceptibly larger this time than before. The Professor stared at it stupidly. He was sure it had not been there a moment before, and he noticed by the heading of the newspaper at the side of his plate that this was the first of the month.

With a hasty movement of his napkin he wiped the drop of blood away. The maid, still apologising, began to pick up the pieces of the jug she had broken; but the Professor had no further appetite for his breakfast. He silenced her with a gesture, and, leaving a piece of toast half-eaten on his plate, he got up and went into his study.

All this was trivial, absurd even. Yet somehow it disturbed him. He got out a magnifying glass and examined his hand under it. There was nothing to account for the presence of the drop of blood he and the maid had seen. It occurred to him that he might have cut himself in shaving; but when he looked in the mirror he could find no trace of even the slightest wound.

He decided that, though he had not been aware of it, his nerves must be a little out of order. That was disconcerting. He had not taken his nerves into consideration for the simple reason that he had never known that he possessed any. He made up his mind to treat himself to a holiday in Switzerland. One or two difficult ascents might brace him up a bit.

Three days later he was in Switzerland, and a few days later again he was on the summit of a minor but still difficult peak. It had been an exhilarating climb, and he had enjoyed it. He said something laughingly to the head guide to the effect that climbing was good sport and a fine test for the nerves. The head guide agreed, and added politely that if the nerves of monsieur the Professor had shown signs of failing on the lower glacier, for example, they might all have been in difficulties. The Professor thrilled with pleasure at the head guide's implied praise. He was glad to know on such good authority that his nerves were all right, and the incidents that had driven him there began to fade in his memory.

Nevertheless, he found himself watching the calendar with a certain interest, and when he woke on the morning of the first day of the next month he glanced quickly at his right hand. There was nothing there.

He dressed and spent, as he had planned, a quiet day, busy with his correspondence. His spirits rose as the day passed. He was still watchful, but more confident; and, after dinner, though he had meant to go straight to his room, he agreed to join in a suggested game of bridge. They were cutting for partners when one of the ladies who was to take part in the game dropped with a little cry the card she had just lifted.

"Oh, there is blood upon your hand," she cried, "on your right hand, Professor!"

Upon the Professor's right hand there showed now a drop of blood, larger still then those other three had been. Yet the very moment before it had not been there. The Professor put down his cards without a word, and left the room, going straight upstairs.

The drop of blood was still standing on his hand. He soaked it up carefully with some cotton-wool he had, and was not surprised to find beneath no sign or trace of any cut or wound. The cotton-wool he made up carefully into a parcel and addressed it to an analytical chemist he knew, inclosing with it a short note.

He rang the bell, sent the parcel to the post, and then he got out pen and paper and set himself to solve this problem, as in his life he had solved so many others.

Only this time it seemed somehow as though the data were insufficient.

Idly his pen traced upon the paper in front of him a large X, the sign of the unknown quantity.

But how, in this case, to find out what was the unknown quantity? His hand, his firm and steady hand, shook so that he could no longer hold his pen. He rang the bell again and ordered a stiff whisky-and-soda. He was a man of almost ascetic habits, but to-night he felt that he needed some stimulant.

Neither did he sleep very well.

The next day he returned to England. Almost at once he went to see his friend, the analytical chemist, to whom he had sent the parcel from Switzerland.

"Mammalian blood," pronounced the chemist, "probably human—rather a curious thing about it, too."

"What's that?" asked the Professor.

"Why," his friend answered, "I was able to identify the distinctive bacillus——" He named the rare bacillus of an unusual and obscure disease. And this disease was that from which the Professor's cousin had died.

The professor was a man interested in all phenomena. In other circumstances he would have observed keenly that which now occurred, when the hair of his head underwent a curious involuntary stiffening and bristling process that in popular but sufficiently accurate terms, might be described as "standing on end." But at the moment he was in no state for scientific observations.

He got out of the house somehow. He said he did not feel well, and his friend, the chemist, agreed that his holiday in Switzerland did not seem to have done him much good.

The Professor went straight home and shut himself up in his study. It was a fine room, ranged all round with books. On the shelves nearest to his hand stood volumes on mathematics, the theory of mathematics, the study of mathematics, pure mathematics, applied mathematics. But there was not any one of these books that told him anything about such a thing as this. Though, it is true, there were many references in them, here and there, to X, the unknown quantity.

The Professor took his pen and wrote a large X upon the sheet of paper in front of him.

"An unknown quantity!" he muttered. "An unknown—quantity!"

The days passed peacefully. Nothing was out of the ordinary except that the Professor developed an odd trick of continually glancing at his right hand. He washed it a good deal, too. But the first of the month was not yet.

On the last day of the month he told his housekeeper that he was feeling a little unwell. She was not surprised, for she had thought him looking ill for some time past. He told her he would probably spend the next day in bed for a thorough rest, and she agreed that that would be a very good idea. When he was in his own room and had undressed, he bandaged his right hand with care, tying it up carefully and thoroughly with three or four of his large linen handkerchiefs.

"Whatever comes, shall now show," he said to himself.

He stayed in bed accordingly the next day. His housekeeper was a little uneasy about him. He ate nothing and his eyes were strangely bright and feverish. She overheard him once muttering something to himself about "the unknown quantity," and that made her think that he had been working too hard.

She decided he must see the doctor. The Professor refused peremptorily. He declared he would be quite well again in the morning. The housekeeper, an old servant, agreed, but sent for the doctor all the same; and when he had come the Professor felt he could not refuse to see him without appearing peculiar. And he did not wish to appear peculiar. So he saw the doctor, but declared there was nothing much the matter, he merely felt a little unwell and out of sorts and tired.

"You have hurt your hand?" the doctor asked, noticing how it was bandaged.

"I cut it slightly—a trifle," the Professor answered.

"Yes," the doctor answered, "I see there is blood on it."

"What?" the Professor stammered.

"There is blood upon your hand," the doctor repeated.

The Professor looked. In fact, a deep, wide stain showed crimson upon the bandages in which he had swathed his hand. Yet he knew that the moment before the linen had been fair and white and clean.

"It is nothing," he said quickly, hiding his hand beneath the bed clothes.

The doctor, a little puzzled, took his leave, but had not gone ten yards when the housekeeper flew screaming after him. It seemed she had heard a fall, and when she had gone into the Professor's bedroom she had found him lying there dead upon the hearthrug. There was a razor in his hand, and there was a ghastly gash across his throat.

The doctor went back at a run, but there was nothing he or any man could do. One thing he noticed, with curiosity, was that the bandage had been torn away from the dead man's hand and that oddly enough there seemed to be on the hand no sign of any cut or wound. There was a large solitary drop of blood on the palm, at the root of the thumb; but, of course, that was no great wonder, for the wound the dead man had dealt himself had bled freely.

Apparently death had not been quite instantaneous, for with a last effort the Professor seemed to have traced an X upon the floor in his own blood with his forefinger. The doctor mentioned this at the inquest—the coroner had decided at once that in this case an inquest was certainly necessary—and he suggested that it showed the Professor had worked too hard and was suffering from overwork which had disturbed his mental balance.

The coroner took the same view, and in his short address to the jury adduced the incident as proof of a passing mental disturbance.

"Very probably," said the coroner, "there was some problem that had worried him, and that he was still endeavouring to work out. As you are aware, gentlemen, the sign X is used to symbolise the unknown quantity."

An appropriate verdict was accordingly returned, and the Professor was duly interred in the same family vault as that in which so short a time previously his cousin had been laid to rest.