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 embarrassing 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. "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 Gods 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.