SHORTLY after the fete of flowers, Laura started to pay a long visit to her uncle in Scythia. But before recounting the events which happened at Lone Mountain, a few words as to the character and life of Hugh Farmer will not be out of place. He was the only man in Unæa who believed in the third dimension. The occurrences by which Farmer was led to form his belief form an episode which is one of the most curious that can be conceived as happening in Flatland or any region of space. In Unæa, as with us, it was quite customary to represent a number by a line, and the square of a number by a square. If the number two was represented by a line, then 4, the square of that number, was represented by the square on that line. It was also quite obvious to the Unæans that the cube of two, or 8, could be represented by a figure with one more dimension than a square. They had the formal notion of a cube. But to conceive that such a figure actually existed, contradicted every principle of their science. For science involves a basis of observation—something given by the senses on which thought acts. On the other hand, to conceive a space of three dimensions meant giving thought a wrong part to play, a wrong function to perform. Thought would not give existence, it could only operate about existing things. The Unæan thinkers would as soon believe in chimeras or dragons as in three dimensional space. For those notions, just as three dimensional space, were deduced from thought, not founded on evidence of the senses. Farmer shared to the full this ardour of conviction of the supremacy of sense in giving materials for thought to work on. But in his day there was a sect who held the doctrine that the soul was separate and distinct from the body. They claimed that it was possible to hold communion with the spirits of the dead, and they asserted that these ghostly beings could make themselves seen and felt. Now anything that could be seen and felt Farmer held to be a legitimate object of scientific investigation, so he took up the study of these spiritualistic phenomena. He fell a victim to jugglery. Tricks were played on him, and curious and inexplicable phenomena were produced in his presence. And it so happened, by a curious coincidence, that the marvellous occurrences which were palmed off on him were of a kind which could physically be produced if there were a third dimension. The tricks were wonderful enough in his space. But in three dimensional space they would not be wonderful at all. For instance, in Flatland a box is a four-sided enclosure like a hollow square. Now Farmer saw objects outside such a four-sided enclosure, and afterwards inside it, without the sides being disturbed. Of course as a three dimensional feat there would be no difficulty in transferring an object from the outside of a square to the inside. It would simply consist in taking it up and putting it down in a different pace. Such occurrences and others Farmer witnessed. He believed they really happened. They made him believe in a three dimensional space. He had that impact of the senses which was the only way a scientific and thoughtful Unæan could be got to believe anything. And this impact of the senses, this seeing and touching in the curious and roundabout way I have described made him believe in the third dimension. When the first step was taken, of course, and when he mentally habituated himself and became familiar with three dimensional shapes, they afforded no more difficulty. They were evidently natural, and he saw it was absurd to limit existence to a plane. But his enthusiasm over his new conceptions led him into quarrels and disagreements with his contemporaries. He found it expedient to retire to a little property he owned in Scythia. There he shook off the load of other people's disapproval, and in solitary blessedness lived himself into the knowledge of three dimensions.

Nothing could have equalled Hugh Farmer's surprise and annoyance when his beautiful niece appeared and announced her intention of studying science with him. He told her he had absolutely no time and retreated into his inmost den. But she busied herself in his rooms, putting flowers on his shelves, and when hunger drove him out, he found it not so disagreeable to sit down opposite a fresh young face.

As is often the case with people who really know something, he was the last kind of a man for a young person to go to in search of information. He began to think aloud.

"Have you never thought it strange," he said, "that there should be two shapes, each of which is exactly alike in its disposition of parts, but such that we can't turn one into another."

"There are not any shapes like that," she said.

	* It is difficult to follow the old man's argument, but if one cuts out a couple of triangles like these (1 and 2), it is easy to see that keeping them against the surface of the paper they cannot be made to coincide.

Laura looked at them, and they reminded her of the little make-believe figures, the dolls she played with as a child, for those dolls were cut out in the form of triangles, and the triangle turned one way was always used for the boy doll, and the triangle turned the other way for the girl doll.

"They are like the little dolls I used to make," she said, "one is like the boy doll and the other is like the girl doll."

"Yes," he said, "and could you ever turn one into the other?"

"No," she said.

"Why not?"

"Why should you want to?"

He groaned. "I didn't say I did want to, but if two things are exactly alike they ought to be able to be put in the same space."

"Of course they ought," she said, trying to please him.

"Well," he said, " if you think of a third dimension you could turn one into the other."

"Oh, I have heard of the third dimension," she said.

"Yes, what do you know about it?"

"It is where our souls go, our spirits, I mean; of course there you could turn one into the other. That's what they mean by saying that there is no difference between men and women in the land above—it's just the same for dolls as for us."

"I didn't know your father had an idiot for a daughter," said the old man, and went off to his den.

Laura rather liked it. It was so different from the way she was generally spoken to. In fact, her uncle impressed her tremendously. And that he didn't like her, nerved her to do battle to win him. His books were all around. She took one to her bedroom, and failing to make any sense of the signs began to copy them out, and learn how to make curious marks of that kind. In the stillness of the night she frequently heard a tramp—up and down, up and down—and when she fell asleep it had not ceased—restless, nervous steps, as of some caged and suffering creature. She looked at her uncle nervously the next morning. He did not look any different, but she was sure he had hardly slept.

"Uncle," she said, "what is it makes you so unhappy?"

"Why do you think I am unhappy?"

"I know you are."

"I am an old man and must die soon."

"But all old men are not unhappy."

Ali, but they leave the world young and fresh. Even before I go a wave of cold will strike us all, and lakes and seas will freeze. No green thing will blossom, only a few in deep caves, or, with soon-to-be-extinguished fires, will struggle on in a miserable existence that will be the end of the greatness of our earth."

"No, Uncle," she said, "you exaggerate. Papa told me something of this. He said the winters would be very bad; but I am sure it will not be so bad as you think."

"Child, your father mercifully hid his knowledge from you."

"Oh, Uncle, is that why he looked so worn and sad?"

"Yes. To bear a hopeless secret like that is enough to make him worn and sad. Only its absolute certainty could force him to admit it. He sent me the work he had done and I found that his calculators had taken the favourable supposition in every doubtful case. I do not blame them. The alternative is too terrible. On the most favourable supposition after the next meeting with that great planet, Ardaea, our earth will swing into a new orbit—we shall go far out into cold space till the earth is frozen deep, then we shall rush back so close to the sun that every day the surface of the earth will be seething hot. Perhaps some of us may maintain bare existence in deep caverns and hollows."

"If you are sure of this, Uncle, you ought to tell it that we may all prepare."

"Prepare for what?"

"Why, dear Uncle, our bodies are not all. If you or I die we know that our souls survive, and are judgedby all the good and ill in our lives. You ought to tell everyone."

"And let them destroy all law and order in one short carousal? No, Laura, you do not know the world. There is more common sense in the common people than in all your bigoted idealists. We are here for a work and not for a theatrical play to manifest good qualities, and if men know that this work is to come to an end the fallacies of their preachers won't have any effect on them."

"They are not fallacies, Uncle."

"They are worse, Laura. They are interested deceptions. It grinds my heart out, child, to hear those glib preachers showing the way so confidently on evidence which no ordinary man of business would trust for the simplest speculation. If we have learned any one thing more certainly than any other, it is that we can only know about the proximate. We can take and take again, one little step forward. But all they do is to start from the ultimate. They know, forsooth, what is, and from that they deduce what must be."

"But you believe in God, Uncle?"

"I don't know what they mean by God. All theology is a vast fiction beginning from the wrong end, which prevents our finding out that proximate higher which we might have a chance of knowing. The fools," he muttered, "with the tools to their hands and with their eyes gazing to heaven—refusing to use them. Refusing till too late."

Thrilled to the heart with the fire of his gaze, Laura struggled with the enigma of his emotion. It was not helpless mournfulness that weighed him down—not despair; something else than the doom of the world filled his mind, something he did not want to tell her. All at once she said, guessing his secret thought,

Uncle, you could save the world!"

"What has your father told you?"

"Nothing. But I know you would not feel as you do if you could not."

"But no one will listen to me."

"Uncle, what is the good of hating anyone? They are all really in earnest. It is only because they don't understand you. Go and talk to the learned men who find out about the earth and the stars."

"You do not understand, Laura. The dogmatism of scientific men is stronger than the dogmatism of religion, because they can prove they are right. They can appeal to the evidence of their senses.

"I, too, was like them, and believed that I, my power of thinking, and every faculty I had, was produced by the things around me; that the processes I knew of would make me if only I sufficiently understood them. I laughed the idea of a spiritual existence apart from matter to scorn. And as to a third dimension, it seemed to me ridiculous to make an assumption for which we had no evidence. But I gained the acquaintance of a man of perfect loyalty and veracity, who was gifted with singular powers. He claimed to have communication with the spirit world, he showed me many things that people account miraculous. What I noticed was that these wonders were things which it would be easy for three dimensional beings to do. Scientific men called him an impostor and cheat. But I knew him too well to join in the chorus. He made me believe in the third dimension by the only evidence I would accept—the evidence of my senses. And, Laura, I am proud to say I stood by my benefactor. It was the only act I can account worthy of a man in my whole life. It's a little thing you would say, just to declare that certain things happened to little bits of matter. But it cost me every friend I had. I could not even retain my poor and insignificant position. It is as much as anyone's professional reputation is worth to have anything to do with me. If I had anexperiment as clear as day they would ascribe it to trickery. And, Laura, it is this truth that would save us all if men would only believe it."

"But," said Laura, "if you believe in spirits, the clergymen would listen to you."

"Much good that would do. I tell you, Laura, that those men are so versed in unrealities that, if anyone were to tell them of how what they talked about were possibly real, they would like to burn him alive, if they could still keep up their taste for that sort of thing. No, they have a closed system of their own; and their idea of thought is to try to make out exactly what is written in old books and find out whether this man or another really lived when he is reported to have lived. That's the kind of stuff they give to a perishing world."

"But if they make people better?"

"Yes, yes; it's their thought I'm thinking about; what they really understand. I've tried your father. I am always trying the scientific men, but they politely return my work. I know what they think of it."

"Uncle, I know someone who would help you."

"You are very beautiful," he said, as he drew her to him, "there is someone who loves you very much."

"Why do you say that?"

"My dear, I know it."

"Uncle, I will be frank with you; somehow I feel that I can tell you. I love someone very much. He has never said anything to me, but I hope, indeed I am sure, that he loves me. I feel this way about it. There is a great fountain of love from which we all drink. Now I love many people and think about them frequently, but there is one whose being gives colour to my every thought. Everything I think or do or say in some way relates to him; and when any beautiful thought comes to me, it turns to him. Now, Uncle, do not laugh at me. I am not investing him with supreme goodness, I simply feel as I have told you about him. And when I think of all these things and how much of his individuality has become the best part of me, I cannot help believing that he must in some way absorb something of me."

Farmer took her hand. "Thank you, my dear, for letting me see your heart. Yes, I think he must love you too. Do I know him?"

"He is Harold Wall," said Laura.

"I knew his father. After the great war he could hardly speak our language. He used a dialect which had sprung up in the long journey. To the end of his life, he was the same—rough, uncultivated, unable to adapt himself; men honoured him for the way he had hurled his men through the deserts, but did not love him. His life was used up in that effort, as mine has been in mine. Perhaps his son will understand that I, too, have ventured and succeeded, when to everyone else I am a drivelling dotard, speaking in a scarce intelligible language. I suppose," he added, "your father does not look favourably on him?"

"He has never spoken, he is too proud. If he did care for me, he would never speak."

"That is well. Laura, something tells me that the tie that binds you two is very deep and true. You must not think, as other lovers often do, only of one another; but out of the great tenderness and truth of your affection, you must turn and give yourselves—give one another—to help and save us all. Now write to him, giving him a message from me. Tell him that he can save his country."