"If he does that," whispered Phadrig to the Prince in Russian, "the story that Pent-Ah and Neb-Anat told will be true--which the High G.o.ds forbid!"

"As the trisection of the triangle is, perhaps, the simplest of the three problems," said the lecturer, with almost judicial calmness, "we will, if you please, begin with that. I hope that gentlemen who have brought note-books with them will be kind enough to follow my calculations and check any error that I may make."

But a good threescore note-books, pencils, and stylographic pens were out already, and hundreds of eyes were eagerly fastening their gaze on the black-board, their owners desperately anxious to detect the first slip in the demonstration. The demonstrator drew an isosceles triangle rapidly, and without speaking filled the remainder of the board with formulae. The almost breathless silence was broken only by the click of the chalk on the board and the scratching of pencils and pens on paper.

When he had finished he ran through the calculations aloud, and said in the most commonplace voice:

"Now, gentlemen, if, as I hope, you have found my working correct, I may draw the two lines which will trisect the triangle."

He drew them, and then, as calmly as though he had done nothing more than cross the much-trodden _pons asinorum_, he told two attendants to take the board down and put it in front of the platform; then, while they were lifting another on to the easel, he said:

"As those who have followed me would no doubt like a little time to revise the figures, I will go on with the next problem, which will be our old friend, or enemy, the squaring of the circle."

The second board was filled with diagrams and formulae as rapidly as the first.

"There is the demonstration, gentlemen," he said, as the attendants placed it beside the other in full view of everybody. "Now, as time is shortening, I will get on with the third problem."

The chalk began to click again, and the pens and pencils scratched on to the accompaniment of murmurs and whispers and occasional grunts and snorts of incredulity. By a master-stroke of strategy Franklin Marmion had, in placing the three demonstrations of the long-supposed impossible before them in quick succession, kept the learned, but now utterly bewildered mathematicians so busy that they literally had not time to begin "the trouble" which Brenda was now actually dreading. Her father's face, bent down over his note-book, was getting more terrible to look upon every moment. The mere fact that he had not uttered a sound since the demonstrations had begun was sufficiently ominous, for it meant that he was puzzled--perhaps even beaten--and if that was so, she dreaded to even imagine what might happen. On the other hand, Nitocris felt her spirits rising as she looked round and saw the many learned heads bending and shaking over the note-books, each owner of them working at high pressure to win the honour of first finding the error which all firmly believed must exist, and which none of them could detect.

When he had finished his third demonstration, Franklin Marmion, without interrupting the hard thinking that was going on, took a chair by the side of the President, poured out a gla.s.s of water, and waited for results.

"Marmion, what is this white magic that you have been springing upon us?" whispered the presiding genius of the learned a.s.sembly, looking up from several sheets of paper which he had been rapidly covering with formulae. "These things are impossible, you know--unless, of course, you have got a good deal farther than any of us. And yet the calculations are correct as far as I can follow them, and no one else seems to have hit on any error yet. I must confess, though, that these progressives of yours are too deep for me. I can follow them, and yet I can't. At a certain point they seem to elude me, and yet the calculations are rigidly right. It's almost enough to make one think you had done what Cayley once told us in this room some one might do some day."

"My Lord," replied Franklin Marmion, almost inaudibly, "I began my address by remarking, as you will remember, that perhaps, after all, the word 'impossible' might not be scientific."

Their eyes met, and the President, than whose there was no greater name in the higher realm of learning, saw something in Marmion's which sent a little chill through him, and that something told him that he was in the presence of a superior being.

"Dear me!" he murmured, looking down at his papers again, "the age of miracles is not past, after all--in fact, it is only just beginning."

"It is re-beginning, my Lord--for us," came the reply, in a voice which seemed to come from very far away.

The President did not reply. As a matter of fact, he had no reply ready, and he had something else to do. He rose, and said in a somewhat constrained voice:

"Ladies and gentlemen, Professor Marmion has shown us some very strange demonstrations which have certainly amply justified the t.i.tle which he selected. A good many gentlemen, and some ladies as well, I am glad to see, have followed his calculations very carefully. I have done the same myself, but I am bound to confess that I have not been able to find any error. I think I shall be right in saying that no one will be more pleased than the learned and--er--gifted lecturer to hear that some one else has been able to do so."

Franklin Marmion bowed his a.s.sent, and a faint smile flickered across his clean-shaven lips. The next instant Professor van Huysman was on his legs, note-book in one hand and stylo in the other. All the fresh colour had gone out of his face; his eyes were burning, and his lips were twitching with uncontrollable excitement.

"My Lord," he began, in a voice that even Brenda hardly recognised, "like yourself, I have been unable to find any actual error in the lecturer's demonstrations of which I will take permission to call the possibility of the impossible; in other words, that a contradiction in terms can be true and false at one and the same time. That, my Lord, and ladies, and gentlemen," he went on, raising his voice almost to a shout, "is still, and, I hope, in the interests of true science, and not adroit jugglery with figures and formulae, will ever remain, another impossibility. Professor Marmion has apparently trisected the triangle, squared the circle, and doubled the cube. It may be that he has persuaded some present that he really has done so; but, again, in the interests of science, I desire to protest against the way in which these demonstrations have been sprung upon us. Calculations which he has doubtless taken months to elaborate, he has asked us to test in a few minutes. For myself, I decline to accept them as true, and I hope that others will do the same until we have had time to satisfy ourselves that the hitherto impossible has been made possible."

He sat down, breathing hard and white with anger and excitement, and then the trouble began. The trisectors, the circle-squarers, and the cube-doublers, had seen their long-flouted theories proved to demonstration by one of the most learned and responsible men of science in the world, and one of their most sarcastic and hitherto successful flouters had been compelled to confess that he could find no flaw in the calculations of this mathematical Daniel so unexpectedly come to judgment. They did not understand his proofs, but that was no reason why they should reject them, and so they rose as one man in support of their champion to demand that Professor van Huysman should withdraw his imputations of jugglery. He sat still, and shook his head. He was too disgusted and bewildered to do or say anything more until he had made a searching a.n.a.lysis of these diabolical formulae.

But there were others who wanted to have their say in defence of scientific orthodoxy, and they had it--and the rest was a chaos of intellectual conflict until, at the end of nearly an hour, the President, who now saw with clearer eyes than any of the disputants, rose and put an end to the discussion by remarking that they had not the whole night before them, and that all that Professor Marmion had said and done would be published in the scientific papers; further, that such a controversy would perhaps be more profitably conducted in print than by word of mouth. Such a course would give every one ample leisure to work out the problems in the light of the new demonstrations, and also give a much better prospect of reaching a logical, and therefore just, conclusion than a discussion in which haste, and possibly pre-conceived opinions, from the influence of which no human being was really free, could possibly promise.

This, of course, put an end to the matter for the time being, and, after the usual votes of thanks and acknowledgments, the distinguished company dispersed--amused, mystified, gratified, bewildered, and exasperated: but, saving only four of its members, with no idea of the effect which that evening's proceedings were destined to have upon the fate of Europe, perhaps of the whole human race.

CHAPTER XV

THE ADVANCEMENT OF NITOCRIS--THE RESOLVE OF OSCAROVITCH

Franklin Marmion and Hoskins van Huysman parted that evening in what may be described as a state of armed neutrality, but with more cordiality than Brenda, at any rate, had hoped for. Still, they were both gentlemen, and, moreover, the American scientist was honestly looking forward to the discovery of some fatal flaw in the reasoning of his English rival which should leave the final triumph with him--and such a triumph would be not only final but crushing.

Brenda whirled her father and Lord Leighton--who, of course, sat beside her in front as she drove--off to supper; Merrill went to his club to ruminate happily for an hour; and the hero of the evening and his daughter drove home almost in silence, and it was a silence for which there was a very sufficient reason. Such people do not talk about trivialities when they are thinking about much more serious concerns.

After supper Nitocris followed her father into the study, as he quite expected her to do, and when she had shut the door, she faced him and said in a voice that was not quite her own:

"Dad, there seems to me to be only one explanation of what you did to-night. I know enough mathematics to see that it is the only one. If you tell me that I am wrong, of course I shall believe you--and then I shall ask you how else you did it."

As she spoke he felt that his soul was asking itself a momentous question. She had guessed--or did she already know?--the Great Secret.

And, if either, was she herself near enough to the dividing line between the two worlds for him to tell her the truth?

He sat down in the chair before his writing-table and stared hard at his plotting-pad for a few moments. Then he looked up at her and saw the answer.

"Niti," he said slowly, and with a little halt between the words, "you have asked me a question which I think some one else must answer, if it can be answered at all. Look behind you!"

She turned swiftly, and there, almost beside her, stood--not the Mummy, but the Queen, her living other-self, royal-robed and crowned as she had been in the dim past, which was now again the present.

Would she flinch or faint, or cry out with fear? If her unconscious feet had not advanced very near to the Border she would certainly do one or the other. Indeed, it was with an inward quaking of fear for her that her father had told her to turn. It might well have meant the difference between sanity and insanity, knowing what she already did of the Mummy and its mysterious disappearance. But no: there before his eyes was worked again the miracle which had already been worked in his own case, though now it was, if possible, even more marvellous than it had been before. As Nitocris turned she uttered a low cry of wonder and recognition, and held out both hands to her other twin-self. The Queen took them, and said in the Ancient Tongue, which now she understood again after many centuries:

"Welcome, thou who wast once myself, into this larger life to which the Perfect Knowledge hath led thee: where Time is not, and that which was, and is, and shall be are the same! Thou hast yet many days, as men call them, to live in that limited life known as mortal, and so the mortal lot, with its perils and sorrows and joys, shall yet be thine: yet, although, if the High G.o.ds will it so, that life shall end and begin and end again many times, thou hast already won through the shadows which bound that little life into the light of the Day which knows not dawn nor noon nor night. I who was, and thou who art, are one again!"

Then came silence. Franklin Marmion saw the two kindred shapes merge into each other. He closed his eyes for a moment, as he thought, and when he opened them again he was alone. He looked at the clock, and saw that it was after four.

"Dear me!" he said, getting up with a shake of his shoulders, "I must have fallen asleep. Where's Niti? Why, of course, she has been in bed for hours, and it's about time that I got there, too."

When they met before breakfast Nitocris said to him:

"I had a very strange experience last night, Dad. I either saw, or dreamt I saw, the Mummy alive again, robed and crowned like a queen of ancient Egypt; and then we seemed to become the same person, and I remembered that I had been Queen Nitocris of Egypt once. Then I found myself alone--so very much alone--in a new world which was still like this one, only there wasn't any time. I had another sense which made me able to see past, present, and future all at once, and here and there, and up and down, and something else were all the same, and yet it did not seem in the slightest strange to me, so I suppose it was a dream."

"It was no dream, Niti," said her father, looking at her with grave eyes. "Last night, as we have to say in the state of Three Dimensions, you had your first glimpse of the state of Four. I saw what you did."

"Ah!" she replied, without any sign of astonishment. "Then that is why I was able to understand your demonstrations last night when all the rest were puzzled. I didn't think I quite did then, however, but I see now that I did. And so I and Her Majesty are really one and the same! It ought to seem very wonderful, but somehow it doesn't in the slightest."

"I don't think that anything will seem wonderful to you now, Niti," was the quiet response. "But as we are at present on the lower plane of existence, it will be necessary for us to go to breakfast."

Oscarovitch and Phadrig went back after the lecture to the Prince's flat in Royal Court Mansions, which, as a bachelor and a bird of pa.s.sage, he found much more convenient in many ways than a house. He ordered his Russian servant to make coffee for his guest, and mixed a stiff brandy-and-soda for himself. He wanted it, for the experiences of the evening had shaken even his nerves not a little. He was essentially a man of power, both physically and mentally, of boundless ambitions and iron will, vast knowledge of the world, as he knew it, and of very high intellectual attainments; but the cast of his mind was absolutely material, and therefore he both hated and feared anything which appeared to transcend the material plane to which his mental vision was at present entirely confined.

When the servant had left the room after bringing the coffee, he gave Phadrig a cigar, lit one himself, and said through the first puffs of smoke:

"Phadrig, you know, or pretend to know, more about these things than I do, or want to do: but, still, just now I want you to tell me honestly if you believe that Professor Marmion did really solve those problems to-night. I ask you because I admit that the solutions went beyond the range of my mathematics."

"Highness," replied the Egyptian, speaking slowly and almost reverently, "he did. There is not, I think, another man on earth now who could have done so; but for those who had eyes to see there could be no doubt, and you will find that, though he has many rivals and will have countless critics, not one will be able either to explain his solutions or find a flaw in them."

"You did a few things that I should not have thought possible the other day, which you claimed to be really miracles. Now, if they were, I suppose you can explain Professor Marmion's?"