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"This is Trabol," explained Danus, placing a finger upon that portion of the map I have briefly described. "It entirely surrounds Strabol which lies in the center of Amtor. Strabol is extremely hot, its land is covered with enormous forests and dense undergrowth, and is peopled by huge land animals, reptiles, and birds, its warm seas swarm with monsters of the deep. No man has ventured far into Strabol and lived to return.

"Beyond Trabol," he continued, placing his finger on the outer band designated as Karbol (Cold Country), "lies Karbol. Here it is as cold as Strabol is hot. There are strange animals there too, and adventurers have returned with tales of fierce human beings clothed in fur. But it is an inhospitable land into which there is no occasion to venture and which few dare penetrate far for fear of being precipitated over the rim into the molten sea."

"Over what rim?" I asked.

He looked at me in astonishment. "I can well believe that you come from another world when you ask me such questions as you do," he remarked. "Do you mean to tell me that you know nothing of the physical structure of Amtor?"

"I know nothing of your theory concerning it," I replied.

"It is not a theory; it is a fact," he corrected me gently. "In no other way may the various phenomena of nature be explained. Amtor is a huge disc with an upturned rim, like a great saucer; it floats upon a sea of molten metal and rock, a fact that is incontrovertably proved by the gushing forth of this liquid mass occasionally from the summits of mountains, when a hole has been burned in the bottom of Amtor. Karbol, the cold country, is a wise provision of nature that tempers the terrific heat that must constantly surge about the outer rim of Amtor.

"Above Amtor, and entirely surrounding her above the molten sea, is a chaos of fire and flame. From this our clouds protect us. Occasionally there have occurred rifts in the clouds, and at such times the heat from the fires above, when the rifts occurred in the daytime, has been so intense as to wither vegetation and destroy life, while the light that shone through was of blinding intensity. When these rifts occurred at night there was no heat, but we saw the sparks from the fire shining above us."

I tried to explain the spherical shape of the planets and that Karbol was only the colder country surrounding one of Amtor's poles, while Strabol, the hot country, lay in the equatorial region; that Trabol was merely one of two temperate zones, the other one being beyond the equatorial region, which was a band around the middle of a globe and not, as he supposed, a circular area in the center of a disc. He listened to me politely, but only smiled and shook his head when I had finished.

At first I could not comprehend that a man of such evident intelligence, education, and culture should cling to such a belief as his, but when I stopped to consider the fact that neither he nor any of his progenitors had ever seen the heavens, I began to realize that there could not be much foundation for any other theory, and even theories must have foundations. I also realized, even more than I had before, something of what astronomy has meant to the human race of earth in the advancement of science and civilization. Could there have been such advancement had the heavens been perpetually hidden from our view? I wonder.

But I did not give up. I drew his attention to the fact that if his theory were correct, the boundary between Trabol and Strabol (the temperate and the equatorial zones) should be much shorter than that separating Trabol from Karbol, the polar region, as was shown on the map, but could not have been proved by actual survey; while my theory would require that the exact opposite be true, which was easily demonstrable and must have been demonstrated if surveys had ever been made, which I judged from the markings on the map to be the case.

He admitted that surveys had been made and that they had shown the apparent discrepancy that I had pointed out, but he explained this ingeniously by a purely Amtorian theory of the relativity of distance, which he proceeded to elucidate.

"A degree is one thousandth part of the circumference of a circle," he commenced. (This is the Amtorian degree, her savants not having had the advantage of a visible sun to suggest another division of the circumference of a circle as did the Babylonians, who hit upon three hundred sixty as being close enough.) "And no matter what the length of the circumference, it measures just one thousand degrees. The circle which separates Strabol from Trabol is necessarily one thousand degrees in length. You will admit that?"

"Certainly," I replied.

"Very good! Then, will you admit that the circle which separates Trabol from Karbol measures exactly one thousand degrees?"

I nodded my assent.

"Things which equal the same thing equal each other, do they not? Therefore, the inner and outer boundaries of Trabol are of equal length, and this is true because of the truth of the theory of relativity of distance. The degree is our unit of linear measure. It would be ridiculous to say that the farther one was removed from the center of Amtor the longer the unit of distance became; it only appears to become longer; in relation to the circumference of the circle and in relation to the distance from the center of Amtor it is precisely the same.

"I know," he admitted, "that on the map it does not appear to be the same, nor do actual surveys indicate that it is the same; but it must be the same, for if it were not, it is obvious that Amtor would be larger around the closer one approached the center and smallest of all at the perimeter, which is so obviously ridiculous as to require no refutation.

"This seeming discrepancy caused the ancients considerable perturbation until about three thousand years ago, when Klufar, the great scientist, expounded the theory of relativity of distance and demonstrated that the real and apparent measurements of distance could be reconciled by multiplying each by the square root of minus one."

I saw that argument was useless and said no more; there is no use arguing with a man who can multiply anything by the square root of minus one.

Chapter 5—The Girl In The Garden

FOR some time I had been aware that I was in the house of Mintep, the king, and that the country was called Vepaja. Jong, which I had originally thought to be his name, was his title; it is Amtorian for king. I learned that Duran was of the house of Zar and that Olthar and Kamlot were his sons; Zuro, one of the women I had met there, was attached to Duran; the other, Alzo, was attached to Olthar; Kamlot had no woman. I use the word attached partially because it is a reasonably close translation of the Amtorian word for the connection and partially because no other word seems exactly to explain the relationship between these men and women.

They were not married, because the institution of marriage is unknown here. One could not say that they belonged to the men, because they were in no sense slaves or servants, nor had they been acquired by purchase or feat of arms. They had come willingly, following a courtship, and they were free to depart whenever they chose, just as the men were free to depart and seek other connections; but, as I was to learn later, these connections are seldom broken, while infidelity is as rare here as it is prevalent on earth.

Each day I took exercise on the broad veranda that encircled the tree at the level upon which my apartment was located; at least, I assumed that it encircled the tree, but I did not know, as that portion assigned to me was but a hundred feet long, a fifteenth part of the circumference of the great tree. At each end of my little segment was a fence. The section adjoining mine on the right appeared to be a garden, as it was a mass of flowers and shrubbery growing in soil that must have been brought up from that distant surface of the planet that I had as yet neither set foot upon nor seen. The section on my left extended in front of the quarters of several young officers attached to the household of the king. I call them young because Danus told me they were young, but they appear to be about the same age as all the other Amtorians I have seen. They were pleasant fellows, and after I learned to speak their language we occasionally had friendly chats together.