y 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.