"And who might have been the other part of the subject, Dad?" she asked, with excellently simulated composure.
"That, Niti," he replied slowly, "I expect you know quite as well as I do. I am inclined to consider myself the victim of something very like a conspiracy."
"I think you are quite right, Dad," she replied, with perfect calmness.
"But the chief conspirators were the Fates themselves. We others only did as we had to do. When you have solved that problem of N to the fourth, I think you will see that we could really have done nothing else, because, if you once crossed the border-line--the horizon which Professor Cayley spoke of, I mean--you ought to be on speaking terms with them."
Before he replied to this somewhat searching remark, the man who _had_ crossed the horizon emptied his coffee cup, and set it down in the saucer with a perceptible rattle. Then he said more slowly than before:
"My dear Niti, there are other mysteries than N to the fourth. I only wish now to confess frankly to you that I have tried to solve one of them, perhaps the greatest of all, and ignominiously failed. I learnt a great deal last night from a young man to whom I thought I could have taught anything, and I got up this morning in a distinctly chastened frame of mind; and so, to make a long story short, if you like to drive into town and bring Commander Merrill back to lunch, I shall be very pleased to have a chat with him afterwards."
The next moment Nitocris was on the other side of the table, with her arm round her father"s shoulders. She kissed him, and whispered:
"You dearest of dears! If I could have loved you any more, I would now, but I can"t. I won"t drive into town, because Brenda"s coming out with Lord Leighton in her new motor to fetch me; at least, she will, if other papas have been as delightful as you have been."
He put his hand up and stroked her cheek with a gesture that was older than she was, and said with a smile which meant more than she could comprehend:
"Ah! so it _was_ a conspiracy, after all! Well, dear, I hope that, for all your sakes, it will turn out a successful one."
About the same time Brenda was saying to her parents:
"Poppa and Mammy, I"ve got some news to tell you, and I"ve slept on it, so as to make quite sure about the telling."
"And what might that be, Brenda?" asked her mother, looking up a trifle anxiously. "Nothing very serious, I hope."
"Anything connected with the Marmions?" asked her father, in a voice that sounded as though it had come from somewhere far away. He had the _Times_ propped up against the sugar basin on his left hand, and he had just read the announcement of Franklin Marmion"s lecture for the following evening, and this was quite a serious matter for him.
"It"s connected with them in this way," said Brenda, leaning her elbows on the table. "You and Uncle have wanted a coronet in the family, and you know that I"ve refused three, because the men who wore them weren"t fit to respect, to say nothing about loving. Well, I"ve just discovered that I do love a man who has one coronet now, and will have another some day, unless something unexpected happens to him; but mind, it"s the man I love and want to marry, and I"d want to do it just the same if he was still the same man he is, and hadn"t either a coronet or a dollar to his name."
"That"s like you, Brenda, and it sounds good," said her father, tearing his attention away from the alluring t.i.tle of Franklin Marmion"s lecture. "Now, who is it?"
"If it was only that nice young man, Lord Leighton!" said Mrs van Huysman, in a voice that sounded like an appeal against the final judgment of human fate, "but, of course, he"s----"
"No, Mammy, that"s just what he"s _not_ going to do," exclaimed Brenda, sitting up and clasping her hands behind her neck. "Nitocris Marmion is in love with some one else, and Lord Leighton is in love with me--at least he said so last night at "The Wilderness," and I don"t suppose he"d have said it if he hadn"t meant it--and I told him to go and ask his Papa: and now I"m going to ask my Poppa and Mammy if I may be Lady Leighton soon, and, perhaps, some day Countess of Kyneston. You see, Lord Leighton is just a viscount now----"
"What, just a viscount!" exclaimed Mrs van Huysman, getting up from her chair and putting a plump arm round her neck. "Just a viscount--and heir to one of the oldest peerages in England! Oh, Brenda, is it really true?"
"I guess Brenda wouldn"t say it if it wasn"t, and that"s about all there is to it," said her father, putting his long arm out over the table. "I congratulate you, my girl. Mammy and I may have been a bit troubled over some of those other refusals of yours, but you seem to have known best, after all: and I reckon your Uncle Ephraim"ll think the same. Lord Leighton"s a man right through. He wouldn"t have done what he has done if he hadn"t been. Shake, child, and----"
Brenda "shook," and then, without another word, she got up and hurried out of the room.
"The girl"s right!" said Professor van Huysman, as the door closed behind her; "and if I"m not a fool entirely, she"s found the right man."
"Hoskins, you can leave that to a well-brought-up girl like Brenda all the time. She _is_ right, and all we"ve got to hope for now is that the Earl will be right too," said his wife somewhat anxiously.
"He"s just got to see our girl and then he will be, unless he"s a natural born idiot, which, of course, he couldn"t be," replied Brenda"s father in a tone of absolute conviction. "Now, I wonder what that man Marmion"s going to let loose on us to-morrow night?"
"Good morning, sir," said Lord Leighton, as his father came into the breakfast-room at about the same time that Brenda left the other room in the Savoy.
"Good morning, Lester," replied the Earl of Kyneston, as father and son shook hands in the old courtly fashion which, within the last half century, has gone out of vogue save among those who have ancestors whose record is a credit to their descendants. "You are looking very well and fit--and there is something else. What is it? Had you a very pleasant evening yesterday at "The Wilderness"? Has Miss Marmion revoked her decision after all?"
"No, sir," said his son, looking at him with brightening eyes; "but she convinced me that I had thought myself in love with the wrong girl--and the other girl was on the lawn at the same time, talking with the man that Miss Marmion was, and is in love with, and will be always, I think."
"And the other young lady, Lester--because, of course, she is a lady, I mean in our sense of the word, much misunderstood as it is in these days?"
"She is Brenda van Huysman, sir."
"Oh, the Professor"s daughter.--I mean the other Professor"s daughter. A very good family. Her father is a distinguished man, and, if I remember rightly, a Van Huysman was one of the first colonisers of New England about four hundred years ago. It is the same family, I suppose?"
"Yes, sir; I can vouch for that."
Nitocris had given him the whole history of the family, and so he was sure of his facts.
"Lester, I congratulate you," replied his father, taking his arm, as they were accustomed to. "While you have been away digging among those Egyptian tombs and temples, this girl has refused at least three coronets, and one had strawberry leaves on it; so she loves you for yourself. That is good, other things being equal, as I think they will be in this case. Now, we will go to breakfast, and you shall tell me the whole story. I have not heard a real love story for a good many years."
CHAPTER XIV
"SUPPOSED IMPOSSIBILITIES"
It was only to be expected that the announcement of a lecture with such an alluring t.i.tle by such a distinguished scholar and scientist as Professor Franklin Marmion should fill the theatre of the Royal Society, as the reporters said tritely but truly, "to its utmost capacity."
The mere words, "An Examination of Some Supposed Mathematical Impossibilities," were just so many bomb-sh.e.l.ls tossed into the middle of the scientific arena. The circle-squarers, the triangle-trisectors, the cube-doublers, the flat-worlders, and all the other would-be workers of miracles plainly impossible in a world of three dimensions jumped--not incorrectly--to the conclusion that their favourite impossibility would be selected for examination, and, perhaps--blissful thought!--demonstration by one of the foremost thinkers of the day, to the lasting confusion of the scoffers. Learned pundits of the old school, who were firmly convinced that Mathematics had long ago said their last word, and that to talk about "supposed impossibilities" was blasphemy of the rankest sort, came with note-books and a grim determination to explode Franklin Marmion"s heresies for good and all.
Dreamers of Fourth Dimensional dreams came hoping against hope, for the Professor was known to be something of a dreamer himself; and added to all these there a.s.sembled a distinguished company of ladies and gentlemen who looked upon the lecture as a "function" which their social positions made it necessary for them to patronise. The reader"s personal friends and acquaintances, including Prince Oscarovitch and Phadrig, were naturally among the most anxiously interested of the Professor"s audience.
It is almost needless to say that Hoskins van Huysman had donned all his panoply of scientific war, and had armed himself with what he believed his keenest weapons; and that Professor Hartley looked with amused confidence to a veritable battle royal of wits when the lecture was over and the discussion began. The Prince and Phadrig were keenly antic.i.p.ative, and the latter not a little nervous.
A verbatim report of that famous lecture would, of course, be out of place in these pages. If Professor Marmion"s words of wonder are not already written in the archives of the Royal Society, no doubt they will be in the fullness of time when the minds of men shall have become prepared to receive them. Here we are mainly concerned with the results which they produced upon his audience. Certain portions may, however, be properly reproduced here.
When the decorous murmur of applause which greeted the President"s closing sentences had died away, and Franklin Marmion went to the reading-desk and unfolded his notes, there was a tense silence of antic.i.p.ation, and hundreds of pairs of eyes, which had some of the keenest brains in Europe behind them, were converged upon his spare, erect figure and his refined, clear-cut, somewhat sternly-moulded face.
"Mr President, my lords, ladies, and gentlemen," he began, in his quiet, but far-reaching tones. "The somewhat peculiar t.i.tle which I have chosen for my lecture was not, I hope I need scarcely say, selected with a view of arousing any but that intelligent curiosity which is always characteristic of such a distinguished audience as that which I have the honour of addressing to-night. I chose it after somewhat anxious consideration, because I am aware that the bulk of opinion in the world of science strongly insists upon the finality of the axioms of mathematics, and therefore it was with no little hesitancy that I approached such a subject as this. I am well aware that, in the estimation of most of my learned _confreres_ and fellow-seekers after scientific truth, to suggest those axioms may not embody final and universal truth is, if I may put it so, to lay sacrilegious hands on the Ark of the Scientific Covenant."
A low murmur, prelude of the coming storm, ran through the theatre, and Professor van Huysman permitted himself to snort distinctively, for which he was very promptly, though quietly, called to order by his daughter, who was sitting in front of the platform between him and Lord Leighton. Franklin Marmion paused for a moment and smiled ever so faintly. Nitocris looked round at the now eager audience a trifle anxiously, for she had a fairly clear idea of the trouble that might possibly be ahead. Her father went on as quietly as before:
"Of course, every one here is aware that the great Napoleon once said that the word "impossible" was not French. I need not remind such an audience as this that more than one distinguished student and investigator has suggested that it also may not be scientific."
The murmur broke out again, and Hoskins van Huysman blew his nose somewhat aggressively. His scientific bile was beginning to rise. He disapproved very strongly of the tone which his rival had begun. Its quiet confidence was somewhat ominous. The lecturer continued without this time noticing the interruption, and proceeded to give a lengthy and learned but singularly lucid _resume_ of the more recent progress in the higher mathematics and the deeply interesting speculations to which it had given rise. This, with certain demonstrations which he made on the great black-board beside him, occupied nearly an hour. When he had finished there was another murmur, which this time was wholly of applause, for this part of the lecture had not only been masterly but entirely orthodox. Then silence fell again, the silence of expectant waiting, for every one felt that the "Examination" was coming now. He began again in a slightly altered voice.
"What I have just been saying was necessary to my subject as far as it went, but for all that it was chiefly introductory to what I am now going to bring to your notice. But this is a matter rather for ill.u.s.tration and discussion than for mere disquisition. Therefore, to save your time as much as possible, I will proceed at once to the ill.u.s.tration, and then we will have the discussion."
Professor van Huysman snorted again, even as a war-horse that snuffs the fray. This time Franklin Marmion seemed to recognise the implied challenge, for he looked round the crowded theatre with a curious smile, which seemed to say: "Yes, gentlemen, I see that some of you are getting ready for a tussle. I am in hopes of being able to oblige you."
"Now," he continued, "it is generally conceded that an ounce of practice is worth a good many pounds of precept, so I will get to the practice. I need hardly remind you that ever since mathematics became an exact science, three problems have been recognised as impossible of solution--trisecting the triangle, squaring the circle, and doubling the cube. I have now the pleasure of announcing that I have had the great good fortune to discover certain formulae which, so far, at least, as I can see, make the solution of those problems not only possible, but comparatively easy--to those who know how to use them."
As he said this, Franklin Marmion looked directly at Hoskins van Huysman. He was the challenger now, and there was a glint in his eyes and a smile on his lips which showed that he meant business. The American writhed, and had it not been for Brenda"s gently but firmly restraining hand, he might have jumped to his feet and precipitated matters in a somewhat embarra.s.sing fashion. The chairman looked up at the lecturer with elevated eyelids which had a note of interrogation under each of them, and then there came that sound of shifting in seats and breathing in many low keys which denotes that an audience has been wound up to a very tense pitch of expectation. If a smaller man had said such words to such hearers some one would have laughed, and then would have burst forth a storm of derision. But the keenest critic had never found Franklin Marmion wrong yet, and he had far too great a reputation to permit himself to say in such a place that which he did not seriously mean. So the hum died down as he went to the black-board, and Nitocris looked at Merrill with something like fear in her eyes.