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four[Pg 77] dimensions; and didn't Cayley, before this very Society, deliberately say that at the present rate of progress in the Higher Mathematics, the eye of Intellect might ere long see across the border of tri-dimensional space?

"Surely I cannot do any very great harm by carrying his arguments to their logical conclusions—if I can. Of course, physical demonstrations would never do: I should frighten my brilliant and learned audience out of its seven senses; but, as for mere mathematics—well, I may make them stare, and set a good many highly-respected brains—my gifted friend Huysman's, among them—working pretty hard. Of course, he will be especially furious, but there's no harm in that either. Yes, I shall certainly do it. If he can't understand my demonstrations, that's not my concern."

He went and sat down at his desk, still smiling, and went very carefully through the notes he had already made, and then through Professor Hartley's letter, and his speculations on the Forty-Seventh Proposition. This done, he plunged into a fresh vortex of figures, and symbols, and diagrams, in which he remained for the next two hours, his mind hovering, as it were, over the borderland which at once divides and unites the higher and the lower planes. When he returned to earth, the dreamy, abstracted look faded away from his face; his eyes lit up, and the pleasant smile came back.

He opened the middle drawer in his desk, and took out the first page of the fair copy of his notes, which Nitocris had made for him—thinking[Pg 78] the while how easy it would have been for him in the state of N^4 to take it out without opening the drawer at all—and looked at it. It was headed:

"RECENT PROGRESS IN THE HIGHER MATHEMATICS."

He crossed the title out carefully, and wrote above it:

"AN EXAMINATION OF SOME SUPPOSED MATHEMATICAL IMPOSSIBILITIES."

"There," he murmured, as he put the sheet back; "I think that such a theme, adequately treated, will considerably astonish my learned friends in general, and my esteemed critic, Van Huysman, in particular."

From which remark it will be gathered that Franklin Marmion had certainly recrossed the dividing line between the two Planes of Existence.[Pg 79]

CHAPTER VIII MISS BRENDA ARRIVES, AND PHADRIG THE EGYPTIAN PROPHESIES

"Now, this is just too sweet of you, Niti, to come so soon after we got here. In five minutes more I should have written you a note, asking you and the Professor to come and take lunch with us to-morrow, and here you've anticipated me, so we have the pleasure of seeing you all the sooner."

These were the words with which Miss Brenda van Huysman greeted Nitocris as she entered the drawing-room of the suite of apartments which formed her home for the time being in London. I say her home advisedly, because, although her father and mother also occupied it, she was virtually, if not nominally, mistress undisputed of the splendid camping-place.

She was an almost perfect type of the highly developed, highly educated American girl of to-day, a marvellous compound of intense energy and languorous grace. She had done as brilliantly at Vassar as Nitocris had done at Girton and London, and she had also rowed stroke in the Ladies' Eight, and was champion fencer of the College. Yet as far as her physical presence was[Pg 80] concerned, she was just a "Gibson Girl" of the daintiest type—fair-skinned, blue-eyed, golden-haired—her hair had a darker gleam of bronze in it in certain lights—exquisitely moulded features which seemed capable of every sort of expression within a few changing moments, and a poise of head and carriage of body which only perfect health and the most scientific physical training can produce. In a word, she was one of those miraculous developments of femininity which Nature seems to have made a speciality for the particular benefit of the younger branch of the Anglo-Saxon race. As for her dress—well, the shortest and best way to describe that is to say that it exactly suited her.

As she spoke, and their hands met, Mrs van Huysman got up and came towards them, saying:

"Good afternoon, Miss Marmion. We were real glad to get your 'phone, and it's good to see you again. How's the Professor? Too busy to come with you, I suppose, as usual. We see he's going to lecture before the Royal Society on the tenth, and I reckon we shall all be there to listen to him. I shouldn't wonder but there'll be trouble as usual between him and my husband. It seems a pity that two such clever men should waste so much time in scrapping over these scientific things, which don't seem to matter half a cent, anyhow."

"Oh, I don't know," laughed Nitocris, as they shook hands. "You see, Mrs van Huysman, they do think it matters a great deal, and, besides, I'm quite sure that they both enjoy it very thoroughly.[Pg 81] It's their way of taking recreation, you see, just as a couple of pitmen will try and pound one another to pieces, just for the fun of the thing. It's only a case of intellectual fisticuffs, after all."

"Why, certainly," said Brenda, as she rang for tea; "I'm just sure that Poppa never has such a good time as when he thinks he's tearing one of Professor Marmion's theories into little pieces and dancing on them, and I shouldn't wonder if Professor Marmion didn't feel about the same."

"I dare say he does," said Nitocris, remembering what had happened in the morning; "it's only one of the thousand unexplained puzzles of human nature. As you know, my father hates fighting in the physical sense with a hatred which is almost fanatical, and yet, when it comes to a battle of wits, he's like a schoolboy in a football match."

"It's just another development of the same thing," said Brenda. "Man was born a fighting animal, and I guess he'll remain one till the end of time; and with all our progress in civilisation and science, and all that, the man who doesn't enjoy a fight of some sort isn't of very much account. Now, here's tea, which is just now a more interesting subject. Sit down, and we'll talk about vanities. I'm just perishing to see what Regent Street and Bond Street are like. I don't think I've spent ten dollars in London yet. I'm twenty-two to-morrow, Niti, and my grandfather, who is just about the best grandfather a girl ever had, cabled across to the Napier people, and they've sent round the dandiest six-cylinder,[Pg 82] thirty-horse landaulette that you ever saw, even in Central Park, and a driver to match—only I shan't have much use for him, except to look after the automobile. I'll run you round in her after tea, and you can reintroduce me to the stores—I mean shops; I forgot we were in London."

Mrs van Huysman, as usual, took a back seat while her daughter dispensed tea, and did most of the talking. She was a lady of moderate proportions, and, unlike a good many American women, she had kept her good looks until very close on fifty. She was full of shrewd common sense, but she had been born in a different generation and in a different grade of life, and therefore her attire inclined rather to magnificence than to elegance, in spite of her daughter's restraining hand and frankly expressed counsel. She had a profound respect for her husband's attainments without in the least understanding them, and she very naturally held an unshakable belief that no quite ordinary woman, as she called herself, had ever been miraculously blessed with such a daughter as she had.

Nitocris was just beginning her second cup of tea when the door opened and her father's foeman in the arena of Science came in. He was the very antithesis of Professor Marmion; a trifle below middle height, square-shouldered and strongly built, with thick, iron-grey hair, and somewhat heavy features which would have been almost commonplace but for the broad, square forehead above them, and the brilliant steel-grey[Pg 83] eyes which glittered restlessly under the thick brows, and also a certain sensitiveness about the nostrils and lips which seemed curiously out of keeping with the strength of the lower jaw. His whole being suggested a combination of restless energy and inflexible determination. If he had not been one of America's greatest scientists, he would probably have been one of her most ruthless and despotic Dollar Lords.

"Ah, Miss Marmion, good afternoon! Pleased to see you," he said heartily, as Nitocris got up and held out her hand. "Very kind of you to look us up so soon. How's the Professor? Well, I hope. I see he's scheduled for a lecture before the Royal Society. He's got something startling to tell us about, I hope. It's some time since we had anything of a scientific scrap between us."

"And therefore," said Nitocris, as she took his hand, "I suppose you are just dying for another one."

"Well, not quite dying," laughed the Professor. "Don't look half dead, do I? Just curious, that's all. You can't give me any idea of the subject, I suppose?"

"I could, Professor," she replied, with a malicious twinkle in her eye, because she had already had a talk with her father on the altered title of the lecture, "but if I did, you know, I should only, as we say in England, be spoiling sport. However, I don't think I shall be playing traitor if I tell you to prepare for a little surprise."

Professor van Huysman's manner changed[Pg 84] instantly, and the warrior soul of the scientist was in arms.

"Oh yes! A surprise, eh?" he said, with something between a snort and a snarl in his voice. "Then I guess——"

"Poppa, sit down and have some tea," said his daughter, quietly but firmly.

He sat down without a word, took his cup of tea and a slice of bread and butter; listened in silence as long as he could bear the entirely feminine conversation on a subject in which he hadn't the remotest interest, and then he put his cup down with a little jerk, got up with a bigger one, and said, holding out his hand to Miss Nitocris:

"Well, Miss Marmion, I shall have to say good afternoon. You see we've only just reached this side, and I've got quite a lot of things to attend to. Bring your father along to dinner to-morrow night, if you can; I shall be glad to meet him again. You needn't be afraid: we shan't shoot."

When he had gone, Brenda rang and ordered the motor-car to be ready in half an hour. Then they finished their tea and talk, and Brenda and Nitocris went and put on their wraps—not the imitation of the mediæval armour which is used for serious motor-driving, but just dust-cloaks and mushrooms, both of which Brenda lent to her friend. As they came back through the drawing-room, she said to her mother:

"Well, Mamma, the car's ready, I believe. Won't you join us in a little run round town?"[Pg 85]

"When I want to take a run into the Other World in one of those infernal machines of yours, Brenda," said her mother, with a mild touch of sarcasm in her tone, "I'll ask you to let me come. This afternoon I feel just a little bit too comfortable for a journey like that."

"It's a curious thing," said Brenda, as they were going down in the lift, "Mamma's as healthy a woman as ever lived, and she's American too, and yet I believe she'd as soon get on top of a broncho as into an automobile."

The car was waiting for them in the courtyard under the glass awning. A smart-looking young chauffeur in orthodox costume touched his cap and set the engine going. The gold-laced porters handed them into the two front seats, and the chauffeur effaced himself in the tonneau. Miss Brenda put one hand on the steering-wheel and the other on the first speed lever, and the car slid away, as though it had been running on ice, towards the great arched entrance.

As they turned to the left on their way westward, a shabbily dressed man and woman stepped back from the roadway on to the pavement. For a moment they stared at the car in mute astonishment; then the man gripped the woman tightly by the arm and led her away out of the ever-passing throng, whispering to her in Coptic:

"Did'st thou see her, Neb-Anat—the Queen—the Queen in the living flesh sitting there in the self-mover, the devil-machine? To what unholy things has she come—she, the daughter of the[Pg 86] great Rameses! But it may be that she is held in bondage under the spell of the evil powers that created these devil-chariots which pant like

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