Now, the School-Master was not only a man of profound learning, but a man of rapid mental processes. He had heard from his open window the discussion as his two friends slowly came down the street; and, in point of fact, his professional instinct had led him to note the mystic word when it dropped from the Envoy’s lips. This it was, rather than domestic expectations, that had kept him awake so late. And in the time that elapsed between the arrival of his friends and his appearance at the door, he had prepared himself to meet the situation. He listened solemnly to the question with the tolerant interest of a man of science, and he answered it without hesitation, in the imposing tone of perfect knowledge. [Illustration] “A cotillion,” he said, decisively, “is the one-billionth part of a minus million in quaternions, and is used by surveyors to determine the logarithm of the cube root. That is, its use has hitherto been forbidden to the government surveyors on account of the uncertainty of the formula. That, however, has been finally determined by Prof. Lipsius, of Munich, and hereafter it may be applied to delicate calculations in determining the altitude of mountains too lofty for ascent. Gentlemen, I should like to ask you in to take a night-cap with me, but, under the circumstances, you understand.... Doctor, I don’t think we shall need you to-night. Good-evening, friends.” The Doctor and the Head Burgess ruminated over this new acquisition to their stock of knowledge as they strolled on down the street. At last the latter broke the silence and said, in a tone in which conviction struggled with sleepiness: “Doctor, I have often thought what a hard life those poor devils on the mainland must have with their impassable mountains, and their railroads that kill and mangle you if they get a millionth part of a cube root out of the way, and the boundary-lines they are everlastingly quarreling about. Why, here in Ausserland, see how simple it all is! We never have any trouble about our boundary-lines. Where the land stops the water begins, and where the land begins the water stops; and that’s all there is to it!” [Illustration] And with these words, as the last puff of his pipe rose heavenward, the Burgess dismissed the matter from his mind, and the Emperor’s proclamation legitimizing the Third Figure of the Cotillion vanished from his memory--and from that of all Ausserland--passing into oblivion with those that had told of Ausserland’s change of nationality, of the conscription of her exempt citizens, and of the death of the great-grandmother of the hereditary Prince. “SAMANTHA BOOM-DE-AY.” It was a long, rough, sunlit stretch of stony turnpike that climbed across the flanks of a mountain range in Maine, and skirted a great forest for many miles, on its way to an upland farming-country near the Canada border.