It was a relief. Birbal sate down on the jeweller's stool and breathed again. Despite his incredulity he felt that his whole being, mind and body, had been impressed by the mountebank's manner. He had actually allowed it to overcome his reason.

William Leedes, still but half awake, in utter ignorance of why he had been brought thither, stood for a while stupidly, awaiting a remark. Finally he ventured to ask what was required of him.

"What?" echoed Birbal lightly, recognising with his usual craft, that the less said about his fear the better. "Only that the King is eager to know somewhat of the second facet."

The jeweller's face fell. "Therein lies the puzzle," he said "and I have not yet solved it. The thickness of the stone is great--almost too great, and to cleave it would be to remove, mayhap, too much. Yet without it to find true axis--the sun as we call it in the trade--is a problem that defies at present my geometry."

"Hast tried Aljebr?" asked Birbal, roused instantly to interest. "Show me thy work, sir jeweller, mayhap I can help."

Passed master as he was in the Eastern science of Algebra, they were soon at work with signs and figures.

"That comes more nigh it," said William Leedes, hopefully taking up a small style and going to the lathe.

"Were I to make this point the axis and----" the lathe spun round, then stopped suddenly as he bent to look closer.

"It--it scratches," he murmured, too astonished for bewilderment.

Birbal was by his side in a second, had wrenched the gem from its holding and had it at the light.