They were sitting on the azotea, two days after the Indians had retreated from Tlatonac. Rafael had just left them, full of glee at the proposed expedition to Janjalla, and it was then that Dolores had made the remark about the opal which lead to the conversation regarding Cocom, Totatzine, and the cañon road. In her lap Dolores had a pile of flowers, which she was arranging for the use of the house. Jack took a handful of these, and, kneeling down on the floor of the azotea, proceeded to illustrate his theory by constructing a map with the blossoms. "Behold, my own!" he said, deftly placing a bud here and there, "this rose is Totatzine, situate fifty miles from the coast in a straight line. Here is Tlatonac, indicated by this scarlet verbena. From the point where we embarked in the canoe to the capital is twenty miles." "I understand," said Dolores, much interested in this explanation. "From Totatzine to the point where we embarked, and from thence to Tlatonac, is what we call a right angle. Now, if I draw a straight line from the capital in a slanting direction, you can see that it passes through Totatzine." "I see that, querido! but the third line is longer than the other two." "It is longer than each of the other two lines if you take them separately. Shorter if you take them together. You do not know Euclid, Dolores, else you would discover that any two sides of a triangle are together greater than the third side." "Wait a moment, Juanito!" exclaimed Dolores, vivaciously. "From Totatzine to the point where we embarked is fifty miles, from thence to Tlatonac twenty miles--in all, seventy miles. But by your reasoning this third line is not seventy miles." "Of course not! Still I believe it is quite seventy miles from Tlatonac to Totatzine by this new way." "How so?" "Because we cannot go thither in a straight line. If we went by this one I have drawn, the distance would be much shorter than by the secret way of the sea. But as we have to follow the railway it is a longer journey--quite seventy miles. See! This is Cuavaca, at the foot of Xicotencatl--thirty miles from Tlatonac; from Cuavaca to the terminus of the railway it is twenty miles; from thence to Totatzine possibly another twenty--in all seventy miles. So you see that the distance each way, owing to the configuration of the country, is precisely the same." "Yes; but what of that?" "Can you not see? At the point where the railway stops it is only twenty miles to Totatzine. Now, if, as I suspect, there is a road leading up the cañon to the city, the distance from the termination of the railway works to that road cannot be very far. If, therefore, we discover the hidden road, we can take our troops up by rail, march the rest of the distance, and enter Totatzine through the mouth of the cañon." "Oh!" cried Dolores, astonished at this idea. "And you propose to attempt this entrance?"