Mark accordingly began to recite part of the first book of Caesar, beginning: "All Gaul is divided into three parts," which every schoolboy knows. But this was no better. "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. "What's the matter?" asked Jack. "I hope I haven't made them mad." "No; they appear to be delighted," said Mr. Roumann. And sure enough, the Martians showed evidences of pleasure. They pointed to the triangle on the head of their leader, and then to the one Jack had drawn. Then, from somewhere in the rear of the crowd, there came another man. He was slightly larger than his companions, but that was not saying much, for, aside from their great heads, the Martians were all little people, not much more than up to Andy's shoulder, and Andy was not much over five feet in height. But it was not the size of the newcomer that attracted the attention of the travelers so much as it was the device he had in the golden circle on his head. For this device was exactly the same as the one Jack had drawn in the sand to illustrate the problem. It was a triangle, with squares drawn out from the three sides. He looked at the drawing in the sand, and made a low bow to the newcomers. "Well, that appears to have taken their fancy," said Mark. "I can't understand it."