“I am not a mathematician, and you will therefore have to ask me something easier. But, even if I were an expert in mathematics, I would require a piece of paper and a pencil to figure it out.”

This remark of mine caused a great deal of merriment among all the gnomes present. They jumped and yelled, and punching each others’ ribs with the tips of their fingers, they cried—

“Ho! Ho! He does not know the cube-root of the diameter of a circle having a periphery of 3,1415,” and from every corner of the place, where groups of gnomes were standing, and from every projecting rock, where some of them were perching and listening, shouts of derisive laughter came back, repeating the suggestive and exasperating words: “Ho! Ho! He does not know the cube-root of the diameter of a circle having a periphery of 3,1415.”

“This is very idiotic!” I cried. “How could anybody know anything without figuring it out or being informed about it?”

A triumphant smile appeared upon Cravatu’s face, and Adalga looked downcast and perplexed, but my remarks only increased the hilarity of the gnomes, many of whom stood upon their heads, and swinging their legs, roared—

“He sees nothing! He knows nothing! He imagines to know what he is informed about! He knows nothing himself!”

In the midst of this uproar a blast of trumpets was heard. Order was immediately restored, and the gnomes whispered to each other—

“The king!”

A sound as of many tinkling silver bells announced the arrival of his majesty, and immediately afterwards I saw a globe of red light of unusual size, accompanied by many smaller ones approaching, and directly I stood in the presence of Bimbam I., king of the gnomes.

The king, whenever he condescended to assume a corporeal form, appeared as a gnome of noble bearing, medium-sized, and of middle age, having a yellow beard, while upon his head rested a crown with many stars; the greatest of them being a large carbuncle, emitting a living red light, which enveloped his person, and caused everything upon which it radiated to appear in a red colour.