And the letters with which he built up his formulæ! The _a_’s and _b_’s and _c_’s he used for his quantities given or known; and the _x_’s, _y_’s, and _z_’s he used for the quantities sought or unknown, and especially his _z_’s, which twisted in zigzags like lightning flashes! And what turns and twiggles there were in his π’s, his λ’s, his ω’s! Even a Euclid or an Archimedes would have been proud of them! And as to his signs, in pure unblurred chalk, they were simply marvellous. His + showed the addition was unmistakable. His -, though humbler, was quite a work of art. His × was as clear as a St. Andrew’s cross. And as to his =, so rigorously equal were they, as to indicate without a chance of mistake, that J. T. Maston lived in a country where equality was no vain formula. His <, his >, and his ≷ were really grand! And as to his √, the root of a quantity or of a number, it was really a triumph, and when he completed the horizontal bar in this style √‾‾‾‾‾‾ it seemed as if the indicatory vinculum would shoot clean off the blackboard and menace the world with inclusion within the maniacal equation. But do not suppose that the mathematical intelligence of J. T. Maston was bounded by the horizon of elementary algebra. No! The differential calculus, the integral calculus, the calculus of variations were no strangers to him, and with unshaking hand he dashed down the famous sign of integration, the shape so terrible in its simplicity, the _f_ that speaks of an infinity of elements of the infinitely little. And like it was his Σ which represents the sum of a finite number of finite elements; like it was his ∝ with which mathematicians indicate the variant; like it were all the mysterious symbols employed in this language so unintelligible to ordinary mortals. In short, this astonishing man was capable of mounting the mathematical ladder to the very topmost rung. Such was J. T. Maston. No wonder his colleagues had every confidence in him when he undertook to solve the wildest abracadabrant calculations that occurred to their audacious brains! No wonder that the Gun Club had confided to him the problem regarding the hurling of the projectile from the Earth to the Moon! No wonder that Evangelina Scorbitt was intoxicated with his glory, and had conceived for him an admiration which perilously bordered on love! But in the case under consideration, the solution of the problem regarding the conquest of the North Pole, J. T. Maston had no flight to take in the sublime regions of analysis. To allow the concessionaries of the Arctic regions to make use of their new possessions, the secretary of the Gun Club had but a simple problem in mechanics to occupy his mind. It was a complicated problem, no doubt, requiring ingenious and possibly novel formulæ, but it could be done.