"Let me try a bit of Greek on him," said Mr. Roumann. "I used to be a pretty good Greek scholar."'

But Greek appeared to be an unknown tongue to Mars. The leader, however, seeing that the strangers had arrived at the end of their resources, called to some persons in the crowd, and these, coming forward, addressed the world–dwellers in different dialects. But they were no more understandable than had been the first speech of the man with the glittering triangle.

"Guess we'll have to resort to first principles, and draw pictures for them," said Mark.

Just then Jack uttered an exclamation, and pointed to the head of the leader.

"What's he doing? Making faces at you?" asked Mark.

"No; but look at that triangle!" exclaimed Jack. "It's a right–angled one."

"Well, what of it?"

"This: If they understand triangles, they must know something about mathematics and geometry. Suppose we draw for them that problem in geometry which states that the sums of the squares constructed on the base and altitude of a right–angled triangle is equal to the square constructed on the hypotenuse? If he knows that, maybe we can get to some understanding with him."

"Go ahead and try," assented Mr. Henderson.

Jack accordingly took up a stick, and drew in the sand the geometrical problem of which he had spoken. It is one of the simplest. No sooner had he done so than the Martians set up a cry.